AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Two Dimensional Shapes AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: M2 (B) Plot the position and movement of two-dimensional CP1.B. Examine information related to the problems. shapes. SP2.H. Accept major decisions CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS A rigid transformation is a Provide children with cut out shapes of 2-d figures and a Present flashcards with figures that show movement. movement that doesn’t mirror. Ex: change the size or shape of Children manipulate objects. a figure. Three kinds of transformation are sliding, flipping and turning. ------- Skills Trace Demonstrate Describe movements made. b) Identify draft Classify as flips, turns, and slides. Plot Differentiate Make mirror images. Examine Place cut-out shapes on onion skin or tracing _ _ _ _ _ _ _ _ _ _ _ _ _ _ Judge paper. Apply Outline shapes Verify Flip vertically or horizontally. Explore Outline shapes in its new position. Fold along the line of symmetry. Children identify images as a reflection. - 1 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Two Dimensional Shapes CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Attitudes Groupwork: c) Willingness to: Make a grid on shop paper Interact Put a little bit of water paint in the center of the first Participate quadrant. Respect opinion of others Cooperate Y Y A reflection is the flipping of a figure across a X X straight line. The new figure is a mirror image Children identify movements as slides, flips or turns. of the original. Create other images using shapes given. A graph can be used to show reflection. A reflection on the y- Fold the paper on the y-axis and press. axis will produce a Discussion: figure in which the “Reflected image.” Make more reflections using x and y axis. y axis becomes the line Construct grid on tracing paper. of symmetry. Copy ABC where A = (-4,2) B = (-1,1) C = (-3,4). Reflect images horizontally or vertically on a grid. A reflection on the x- Fold paper along the vertical axis so that ΩABC is on List co-ordinates of reflection axis will produce a the outside. figure in which the Trace the on the other side of the paper. x-axis will become the Observe and list co-ordinates of both triangles. 5 line of symmetry. Formulate rule for vertical reflection. 4 i.e. (x,y) (-x,y) 3 B C Repeat for horizontal reflection. 2 RULE: (x,y) (x,-y) 1 A D Practice reflections with other shapes. -5-4-3-2-1 1 2 3 4 5 -1 -2 horizontal - 2 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Two Dimensional Shapes CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS A rotation is the clockwise Place a triangle shape on a sheet of paper. or anti-clockwise Pin one corner with a tack. movement of a figure Turn and trace movements made. 5 around a point. Both 4 the position and 3 location of the figure 2 change. 1 A -5-4-3-2-1 1 2 3 4 5 -2 -3 -4 A –tack -5 vertical Note the movement as a rotation. Practice rotations using different shapes. Choose the rotated images from set provided. a) b) - 3 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Two Dimensional Shapes CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS c) I I I I I I I - 4 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Two Dimensional Shapes LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT ST2 achieve a deeper understanding of the revolution of the Exploring Mathematics bk. 7 & 8 – Scott, Foreman and Company. earth,moon and other celestal bodies in the universe. Math Advantage – Take Another Look – Harcourt Brace & Company, EA1 – e explore and experiment with styles and methods and techniques that have been used to create artistic representations. Mathematics – Silver Burdett Ginn SL4A – interpret simple forms, notes messages and follow instructions Math Advantage (Teacher’s Edition) Volume I and directions. EL2a Respond sentively and appropriately to auditory and visual stimuli. - 5 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Two Dimensional Shapes AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: CP1 (B) Examine information related to problem. M2B) Plot the position and movement of two-dimensional SP2 (A) Take part in group activities. shapes. SP2 (F) Help group to achieve its goals. CP1(C) Suggest ways of dealing with the problem. CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT Recommended Time: 2-3 wks Use shapes t review Indicate whether these transformations are reflection Subtopic: Translation reflection and rotation or rotations. Put children in groups to rotate shapes at different Use flashcards. The three types of transformation angles and to flip over to create images. are reflection rotation and Use grid on graph paper to show reflection and rotation translation. Reflection is the mirror image of a figure. 6 b) Rotation is the turning of shape 3 5 or figure in different position. 2 4 1 3 2 -4 -3 -2 -1 1 2 3 4 1 c) -1 -2 1 2 3 4 5 6 -3 -4 d) --------------------- e) - 6 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Two Dimensional Shapes CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Tanslation is the sliding of figures or Brainstorm situations where sliding is used to move Read the problem and solve shapes from one position to objects. I ) Rashawn and two classmates each moved one another. Only the location of e.g. Sliding a sofa set or a cupboard of these letters. Louis did not flip or slide his letter. the figure changes. Have students slide different objects horizontally or Meg did not use reflection to move her letter. We often slide objects or shapes verically across desk on floor, or chalkboard. Which letter did each move and what from one position to another. transformation did each use. A B A B G P C D C D G d A B C D Children will observe that only position changes when object slide from one portion to another. - 7 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Two – Dimensional Shapes CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Translation of shapes on a grid Children will note that when objects figures or shape Use worksheet using units and coordinates. slide from one position to another it is called Let children discriminate/differentiate which translation. represents a translation. Skills Children will be placed in groups to translate shapes Trace on shop pater and graph paper. 5 Demonstrate Trace shape in original position slide shape right/left 4 Identify or up/down trace translated position. 3 Plot 2 Differentiate 1 Examine -5 -4 -3 -2 -1 1 2 3 4 5 Explore B C B C Verify -1 -2 Draft -3 Translate A D A D -4 -5 Attitudes Share Interact Participate Interest 5 Cooperate B B C 4 Respect for opinion of others 3 A C A D 2 B 1 -5 -4 -3 -2 -1 1 2 3 4 5 A C -1 B C -2 -3 A D -4 -5 - 8 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Two – Dimensional Shapes CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Put children in groups. Have tem draw grid. Translate point A to the left 5 units. What are its new coordinates? (-2,4) Translate B down 3 units and to the right 2 units. 5 What are the new coordinates? A B 4 C D 3 C D 2 A B Y 1 D . 4 . A -5 -4 -3 -2 -1 1 2 3 4 5 3 -1 2 -2 -3 B . 1 X -4 -5 -4 -3 -2 -1 1 2 3 4 5 -5 -1 -2 Draw translations for given shapes. -3 .C Give coordinates for missing point. -4 Present group work to class. -5 Point C is translated to point D. How far andin which direction has point C moved? 3units to the left and 7 units up. Translate given shapes on grid. List the coordinates for the translation at different point. e.g. - 9 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Two – Dimensional Shapes CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT The vertices of ΩABC are A (-4,2) B(-3,4) C (-2,2) this triangle is translated. The new coordinates for point A are (2,2) B (3,4). What are the new coordinates for point C? (4,2) 5 .B 4 B 3 A C 2 A C 1 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 - 10 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Two – Dimensional Shapes LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT EL3.B Produce written work that demonstrates effective English usage Mathematics Today and grammar. Teacher’s Edition 19 Harcourt Brace Jovanovich EL3.D Produce written work for self-fulfullment and aesthetic satisfaction. Middle Grade Math Teacher’s Edition Chapin, Susan H SS2.A the relationship between the location of Belize and its climate Illingworth, Mark and weather conditions. Silver Burdett Ginn 1998 Mathematics – Daily Review 4 Math Advantage Take Another Look Teacher’s Edition Reteaching Author Brace Harcourt Graph paper Markers Cut – out shapes Pencils Flash cards, ruler Thumb tacks Tracing paper Onion skin - 11 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Patterns Using Shapes AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: CP1.6 Examine information related to the problem. M2C) Fit shapes together to form patterns SP2.a Take part in group activities. SP2.f Help group to achieve its goal. CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT Duration:2 weeks Put children in groups to observe concrete objects and Tell whether each shape forms a tesselation. Tesselation is a repeating patterns to identify properties. Write yes or no. arrangement of shapes that cover a plane with no gaps or overlaps. Figures must be joined edge to edge. Brainstorm for properties. - 12 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Patterns Using Shapes CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Triangles, squares and hexagons Give each group a shape. Trace each shape and try Question sheet: are used to make tessellations. to repeat tracing to form a tessellation. Do these shapes form tessellations? How do you know? Cut out and form patterns. Trace the polygon several times – cut out tracing, then fit pieces together. Use two equilateral triangles to form a diamond. Jdrwa tessellation using diamonds and half diamonds. Form patterns of tessellation using a combination of two shapes. - 13 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Patterns Using Shapes CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Skills Problem Solving example: For a tabletop design. Shawn uses octagons and Identify squares. Will his design tessellate a plane? Construct Sketch Draw Organize Arrange Explore Discover Create Analze Attitudes Erika is making a design from the shape below. Cooperation She wants the design to tessellate . Can she use Share this shape? Participate Respect for othe’s opinion Interest (Make model to solve) - 14 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Patterns Using Shapes LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT EL2.a Respond sensitively and appropriately to auditory and visual Math Advantage Teacher’s Edition – Harcourt & Brace. stimuli. Math Advantage – Take Another Look – Harcourt & Brace. WT1.c Construct a simple device to meet a need / solve a problem Math Advantage – On my own – Harcourt & Brace Ea1.e Explore and experiment with styles, methods and techniques that have been used to create artistic representations. Exploring Mathematics Teacher’s Edition bk. 7 & 8 Cutouts - 15 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Patterns Using Shapes AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: CP1.6 Examine information related to the problem. M2C Fit shapes together to form patterns SP2a. Take part in group activities. SP2f Help group to achieve its goal. SP2g Help to create consensus. CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT Duration: 1-2 weeks reteach basic patterns using shapes. Draw a design that makes a tessellation. Use one of the shapes or a different shape. Make at least Tessellation is a repeating three rows in your design. arrangement of shapes that cover a pane with no gaps or overlaps. - 16 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Patterns Using Shapes CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT All parallelograms can be ghe Chilren use the shape of a parallelogram to begin a Identify which tessellation has a circled vertex. centre of a tessellation as each tessellation . State yes or no. contains 3600. Colour these beginning shapes and identify a main Make tile patterns. This centre point of the tessellation vertex. is called the circles vertex. Find sum of the measure of angles that form the A tessellation can contain three or vertex. more shapes. Skills Identify Construct Sketch Draw Organize Arrange Create Discover Explore Analyze Attitudes Cooperation Draw tessellations using more than two shapes. Share Cut out shapes – Fit together to form tessellations Participate using three or more shapes. Interest Construct puzzles. Respect for other’s opinion Make paper quilt. - 17 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Patterns Using Shapes CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Use concrete objects to make tile work showing tessellation. Create portfolios. Collect and display concrete objects showing tessellations with three or more shapes. - 18 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Patterns Using Shapes LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT EL2a. Respond sensitively and appropriately to auditory and visual Math Advantage Teacher’s Edition – Harcourt & Brace. stimuli. Math Games & Activities – Claudia Zaslavsky. WT1.c Construct a simple device to meet a need/solve a problem. Exploring Mathematics Teacher’s Edition bk. 7 & 8. EA1.e Explore and experiment with styles, methods and techniques that have been used tocreate artistic representations. Cut outs - 19 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Money AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: M3b-Use and convert money based on its relative value and its use in financial transaction. CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Money used indifferent Teacher invites personel from Central Bank to update Ability to convert and use foreign currencies accurately. countries have different students on foreign currencies and their value. values. Use a checklist to monitor: participation Eg. U.S - $ Children construct posters showing currencies and rates accuracy Pound sterling – £ of exchange. BZE - $ Observation of children buying and selling and monitor Peso Children will use rates of xchange to convert froeign group participation Quetzal currencies to Belizean dollars value and use the Limperas Belizean dollar value to respective foreign currency up Check children’s accounts based on business Colon to a thousand dollars. transactions. Yen Set up practical situations where children are grouped to Profit or loss represents the practice using local and foreign currencies. Calculation of profit or loss. difference between the total cost and the selling price of Field trips to Mexico (Chetumal) Guatemala (Melchor). Participation and group interaction. goods. Problem solving using foreign currency. Calculation of discount. Set up a store in classroom and have children buy and sell in the class - 20 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Discounts in when an article Place children in groups and have each group buy is sold below the marked or goods and make goods to sell to each other eg. list price. oranges, cupcakes Have children record daily transactions Allow children to calculate gain or loss based on buying and selling prices. Problem solving involving cost price, selling price, profit and loss. Visit a clearance sale (eg. M & M’s boutique, Mikado, Publics) and record marked price and selling price then use them to calculate discount. Use class store and set up a clearance sale. Calculatiing discounts when buying at clearance sale in classroom. Problem solving involving discount. - 21 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: SETS AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: SP.1C 1) Take action based on principled choice M5b. Apply the concept of “Sets” to the practical situation. CP1B 2) Examine information related to the problem/ issue. CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT A set is a well defined collection Games usng objects like fruits, seeds, items in the Given word phrases of sets children list sets using of objects. classroom to depict sets. appropriate symbols. An empty set has no elements. Eg. The set of days of the week beginning with It is also called a null set. Ex. { , , , } the letter T. A set can be named using {Tuesday,Thursday} specific symbols. elecit from children the definition of sets. Members from a finite set comes Compare two sets; one with elements and one without. Given a set, children write phrases eg. to an end. (can be counted) State give name and symbols for empty set. {blue, green, red} a set of colours. Note that dots at the end of a set Ex. { } or ⊥ of elements means (never Use a capital letter of the alphabet to name a set. Collect two empty bottles, cups or cans, fill one with ending) Enclose sets in braces kool aid. Members from an infinite set Separate elements by use of commas. State observations does not come to an end. Ex. A = {dogs, cats, cows} Identify which shows the empty sets. (cannot be counted) Consider B = {a, e, I, o, u} and C = {1, 2, 3, …} Arrange various groups of elements on the The Cardinal number is the Explain which set is finite or infinite. blackboard. number of elements in a set. Elicit more examples from children. Children label which group is a correct set, Use classroom situations to ask questions eg. A = {x, y, 3} Ex. The set of children that wear glasses. B = (1, 2, 3} - 22 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: SETS CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Sets containing the same elements Use flash cards with different elements in them. Write finite or infinite for given statements. but not necessarily in the same “The race game” eg. 1) The set of all even numbers. order is called equal set. Flash cards quickly and let pupils give cardinal 2) The set of children in the classroom. Two sets that can be placed in one number to one correspondence are Oral interviews for finite and infinite sets. called equivalent sets. Ex. eg. 1) The number of stars in the universe Etc. The number of teachers in the school The number of grains of sand on the sea Give symbols for cardinal number. shore. Ex. A = {a, b, c, d} The number of buses that travel to N = {A} = 4 Chetumal. Each child group items from the class into different sets not necessarily in the same order. Given the sets Ex. B = { , , , } L = { 8, 10, 12, 14 } M = { 5, 7, 9, 11 } C = { , , , } N = { 8, 10, 12 } O = {10, 8, 14, 12 } Compare and contrast the elements of sets. Express which sets are equal, and which are Discuss that equal sets are sets that have the same equivalent. number of elements but not necessarily in the same order. Group children , distribute various items in envelopes. Arrange items into sets to show one to one correspondence. Children observe and note that they have the same cardinal number. Ex. A = { a, e, i, o, u } B = {1, 2, 3, 4, 5 } Therefore A~B. - 23 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: SETS CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT A subset is a part of a set. Children will brainstorm what is an equivalent Demonstrate the continuation of the pattern of If every member of one set is also a set from the above activity. subsets shown on chart. member of a second set then Consider Set A = { 1, 2, 3 } and B = {1, 2, 3, 4, 5 the first set is a subset of the } No. of Elements No. of subsets second set. Are the members of Set A in set B Observe that elements of one set are included in the other set. 4 ___ Formulate a definition for subsets. Introduce the symbol for Subsets, Ex. A=B. 5 ___ Identify as many subsets of other given sets. Note that for sets with many elements another 6 ___ method is done using the powers of 2. Ex No.of No. of elements Powers of 2 Subsets 2 22 2x2 = 4 3 23 2x2x2 = 8 CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR - 24 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: SETS MANAGEABLE SETS STRATEGIES ASSESSMENT The empty set is a subset of every List all the symbols we have dealt with Match Column A with B. set. Ex. subset =, empty set Each set is a subset of itself. { } , ⊥ , is equivalent to ~ etc. A B Symbols are used to indicate sets. ⊥ / ⊥ ~ = / ~ etc. LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT - 25 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: SETS SL1A – Interpret and respond appropriately to messages conveyed Active Mathematics Macmillanm, Prepared by E.A. through visual images. Guiterrez and other educators. EL1D – Apply functioned reading skills and interpretation. Today’s Mathematics 6th edition James W. Heddens EL2A – Respond sensitively and appropriately to auditory and visual William R. Speer stimuli. Refresher Mathematics – Stein M4.a. Make and apply reasonable approximations by observing and/ or using factual data. Materials :- Use waste material like cans, pints, cups etc. - cards - fruits - school utencils - 26 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: SETS AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: SP1C 1) Take actions based on principled choice M5b. Apply the concepts of “Sets” to the practical situation CP1B 2) Examine information related to the problem/ issue. CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT Recommended Time: 4 weeks Consider Set C = {1, 2, 3} and B = {1, 2, 3, 4, 5} List the subsets of Set A = {1, 2} Are the members of Set A in Set B? Demonstrate the continuation of the pattern of A subset is a part of a set. Observe that elements of one set are included in the subsets shown on chart. If every member of one set is other set. also a member of a second Recall the definition for subsets. set then the first set is a Review the symbol for subsets eg. A =B. Number of elements No. of subsets subset of the second set. Identify as many subsets of other given sets. The empty set is a subset of Write subsets using symbols. Ex. 2 4 every set. 3 8 Each set is a subset of itself. 4 __ 5 __ 6 __ 7 __ 8 __ etc. - 27 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: SETS CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT The set of all the elements we wish Recall that for sets with many elements the method Write true or false to consider in a particular we use is the powers of 2. Given Set A = {9, 3, 2, 0, 5} problem is called a Universal Set B = {1, 2, 3} set. Set C = {3} The universal set is commonly No. of elements Powers of 2 No. of subsets represented by the capital U B = A ------ Venn diagrams consists of loops eg. 2 22 2x2 = 4 C = A ------ representing certain sets. A = D ------ The union and intersection of sets 3 23 2x2x2 = 8 can be shown in a Venn Diagram Read statements orally and give answers. The union of sets consists of all Given U = {1, 2, 3, 4} Use set notation to show the union and intersection members in both A and B. Identify whether each of the following statements is of sets. true or false. Use a Venn Diagram to show the intersection of all {1, 2, 3} = U ------ the vowels in the word O,N,I,O,N and ⊥ = U ------ T,O,M,A,T,O. Observe A = {1, 2, 3, 4} A and B = {2, 3, 4, 5, 6} B - 28 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: SETS CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT The symbol for Union of set is U * Note that commas are not used within Venn Write each answer in set notation. the joining of two or more sets is Diagrams. Eg. {3,6,9,12} {1,2,3,4,5,6} called union. Overlap the two Venn diagrams. The intersection of sets is the set {4,2,6,8} U {1,3,5,7} whose numbeers are common A B Match Column A with Column B. to both sets. The symbol for intersection is . A B Symbols are used to indicate sets. \ Universal = The coomplement of a set stands Intersection U for what is not in a given set. Empty Subset U Note that members arenot repeated. Union ⊥ Observe that all members in A and B are {1,2,3,4,5,6} Given the Venn Diagram below Explain that the joining of sets is called union. Eg. A U B = {1,2,3,4,5,6} Identify the members in the intersection A U Introduce the symbol for intersection Write in set notation 4 A B = {2,3,4} List all the symbols we have dealt with A1 5 Eg. subset = empty set ⊥ union U etc. Study Venn diagram below A U - 29 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: SETS CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT The complement for Set A will be Explain that: Given the Venn digram below represented as A1. The horizontal shading stands for Set A. The vertical shading stand for U. This section is not Skills included in Set A and is known as the consider complement of set A. A U observe The complement for Set A is represented by A1. 4 recall Note that A1 stands for what is not in Set A. review A1 5 identify write explain A U List the following sets introduce U = ---------------- list A = ---------------- collect A1 = ---------------- arrange shade A1 Taking U = {1,2,3,4,5} A = {2,3} and B = {1,2,3] find Attitudes awareness A1 = -------------- sharing B1 = -------------- responsibility A B1 = -------------- imitating co-operating Define the following a union a subset universal set, etc. - 30 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: SETS LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT SL1.a – interpret and respond appropriately to messages conveyed References through visual images. New Progress in Mathematics – Rose Anita EL1.d – applly functional reading skills and interpretation Grade 7 Mc Donnell New Progress in Math – Rose Anita EL2.a – respond sensitively and appropriately to auditory and visual Grade 8 Mc Donnell stimuli Exploring Math 8 – Scott Foresman M4.a – make and apply reasonable approxiamtioons by observing Company and/or using factual data. Active Math – E.A. Gutierrez Wt1.a – identify a simple problem/need and other educators Materials Charts, student workbooks, crayons, markers - 31 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Prime and Composite Numbers AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: SP1a) Recognize the value associated with choices. M1d. Learn properties of Prime and Composite numbers. CP1b) Examine information related to the problem/ issue. CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT The set ofwhole numbers begin Approximate time required = 1 week Draw a number line showing the positive and with zero. negative integers. The set of natural or counting Note that zero is included as a whole number but is not Circle the even numbers bumbers begin with the a counting number 32 number 1. Observe whole numbers on a number line 19 The types of whole numbers are: 156 even, odd, prime and 375 composite. I I I I I I I I 50 Even numbers aere whole -3 -2 -1 0 1 2 3 4 106 numbers that are divisible by two. * All whole numbers are positive integers Identify the natural numbers Review that even numbers can be divided by two without a remainder - 32 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Prime and Composite Numbers CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT An odd number is any whole Observe some given even numbers Group beads, beans or seeds into even numbers number that cannot be divided eg. 4,8,352,96 etc. eg. evenly by 2. Divide to show that they have no remainders List other even numbers * Note Recall that odd numbers are numbers that cannot be An even number plus an even divided by 2 without a remainder number equals an even Divide 9,27,243 by 2 number List other odd numbers. An odd number plus an odd Notice that 7 is a prime number because it has only number equals an even two factors, itself and 1 eg. 7 = 1,7 number. Recall that the number 7 is also an odd number. Circle the whole numbers that are odd List more prime numbers 14, 27, 50, 89, 81, 102, 56, 21, 1603, 65 A prime number is any whole Explain that numbers can be factored until only prime number that is divisible by itself numbers remain. Double your Strategy Game: and one Form and label odd and even The prime numbers can be found by Ex: 36 using a factor tree The prime factorization of a number 0 0 0 0 0 0 0 0 is a way of showing a number 4 x 9 as product of prime numbers. The method of the Seive of Erotosthemes may be used to 2 x 2 x 3 x 3 find prime numbers less than a 7+7 = 14 even given number. Write repeated primes in exponential form. 8+7 = 15 odd One is not a prime number or a Ex. 36 = 2x2x3x3 composite number. = 22 x 32 - 33 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Prime and Composite Numbers CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT A composite number is any Present the method of Eratosthemes. Circle the prime numbers counting numer other than 1 84 f) 77 which can be expressed as a product of two smaller counting 1 2 3 4 5 6 7 8 9 10 11 g) 104 29 h) 67 number. 11 12 13 14 15 16 17 18 19 20 83 i) 31 21 22 23 24 25 26 27 28 29 30 49 j) 99 Skills Observe 31 32 33 34 35 36 37 38 39 40 Use a factor tree to find the prime factorization of Shade Apply 41 42 43 44 45 46 47 48 49 50 each number. Ex) 1) 45 2) 84 3) 70 Explain 51 52 53 54 55 56 57 58 59 60 Draw 61 65 63 64 65 66 67 68 69 70 Tell whether each number is prime or composite. Collect 1) 13 ----- 3) 21 ----- Demonstrate 71 72 73 74 75 76 77 78 79 80 2) 31 ----- 4) 19 ----- Arrange Compare Play the game “Pyramid Power”. Determine Shade the boxes that contains the prime numbers. Attitudes 1 Participation Awareness 56 Co-operation Sharing 117 42 29 75 57 13 87 143 24 119 15 39 98 67 103 63 45 37 - 34 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Prime and Composite Numbers CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Notice that two products multiplied forms a Give oral answers to problem solving application. composite number. Ex. Can a prime number have composite Ex 8 = 4x2 number as factor? Explain. Can you list the set of composite numbers greater Play the P or C game. Place the alphabet P beside than 21 and less than 40? the prime numbers and C besides Composite * Note that one cannot be used as a composite number. number. 1) 31 ----- 3) 14 ----- 5) 9 ----- 2) 16 ----- 4) 29 ----- 6) 30 ----- etc. Give oral answers to problem solving application. 1) Can a composite number have prime numbers as factors? Explain. - 35 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Prime and Composite Numbers LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT SL1a. interpret and respond appropriately to messages conveyed The Mathematic Test through visual images. Contemporary bk. Inc. EL1d. apply functional readign skills and interpretations. Math Advantage Vol. 1 by Harcourt Brace Active Math (McMillan Series by E.A. Guiterrez New Progress in Mathematics by Rose Anita McDonnell Materials Beans Cans Beads Seeds Number line - 36 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Whole Numbers AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: C.P.1b – Examine information related to the problem/issue. M1.a – Place Value in numbers up to ten digits. S.P.2a – Take part in group activities. M1.b – The consecutive sequence and position of numbers S.P.2e – Lead and follow where appropriate. 1 – 9,999,999,999 S.P.2f – Help the group to achieve its goals. M1.c – Quantity in numbers 0 – 9,999,999,999. CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT A number can be read, written or Place Value Game Use jig-saw puzzles to recognize numbers and expressed in different ways. Scramble Digits words. Figures - Pupils will arrange given work cards in correct order Words of value. forty three million, nine Standard form - Will write them in digits followed by writing them in 43,920,122 hundred twenty thousand, Expanded form expanded form. one hundred twenty two. Scientific form Eg: Work Card In pairs children will make numbers using given 4 tens number flashcards from zero to nine. Have 7 millions childeren challenge each other to read and write 8 ones numbers made. 5 ten thousands 2 hundred thousands 1 hundred 9 thousands - 37 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Whole Numbers CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT A sequence is a list of whole Answer Sheet Each child will get a blown up balloon having a numbers written in order. Each Correct order figures Expanded Notation number written in either expanded or standard whole number in the sequence form. cHildren will pair off to match their is called a term. 7 millions 7,000,000 7,000,000+200,000+ appropriate expanded form with standard form. 2 hundred thousand 200,000 5 ten thousands 50,000 50,000+ 9,000+100+ “Mathlete” Game. 9 thousands 9,000 40 + 8 Children will each get a worksheet 1 hundred 100 Standard form with numbers in standard form. 4 tens 40 They will then write each in 8 ones 8 7,259,148 scientific form. The person who finishes first with the most correct answer wins. Flashcards games using words and figures. Identify and write the value of the digits according to Ability to play a bingo gaqme having numbers its position. written in the five forms. Writing numbers from standard to scientific notation. Divide class into two groups. Distribute number Eg. Present children with a real life problem. chains to one group while the other group gets numbers to complete chains. Have children wearing number chains find the numbers to complete their chains. 33,500,000 Children will sail airplanes across the class. Whovever gets an airplane will write the speed inscientific notation. They will write their name on 2,5,11-- their airplane and give to teacher for assessment. (N.B. This activity can be reversed) - 38 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Whole Numbers CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Finding the pattern in a list of Place numbers in pattern on board. Answering riddles with rounded numbers. numbers can be used to Pupils identify patterns to complete Distribute copies of riddles to each group. complete the terms in a sequence. Students will take turns reading the riddles sequence. Group activity using sequencing cards. aloud. When students read the riddkles, they Whole numbers can be rounded to Make pattern puzzles. should fill in the blanks with numbers. The rest a certain place. Have pupils create their own sequence pattern and of the students in the group solve the riddle. A number line can be used to exchange with fellow students. eg: when rounded to the nearest million, I compare numbers. round to -------. What is the greatest number I Numbers can be compare by Explain rule for rounding numbers. could be? comparing digits place by place, Use number line to round numbers. from left to right, until a Have pupils circle the numbers that round to a given Pupils will read from table having various places difference between the digits in number then draw a rectangle around numbers and their respective distances. one particular place is found. that rounds to another given number. Children will compare the distances. Three possible relationships exist Eg: circle the numbers that round to 6,000,000. when comparing Draw a rectangle around the numbers that numbers: a>b round to 5,000,000. a,<,= 60 minutes = 1 hour 24 hours = 1 day Physical Education Link Oral drill. To convert customary units of Pupils work in groups to discuss, estimate and Collection of various objects to convert. length from larger to smaller measure distances for games. eg. tablespoon & medicine cup. multiply and vice versa. Social Studies Link Computing with customary measures using the four operations. How standard measurements were invented. eg. 5 tons 3 lbs (research) X8 Children definition/ explanation for the terms Distance, time, weight and capacity equations & inequality. can be estimated and measured Let d = 8 using non- standard measurement. Equation d + 7 = 15 8 + 7 = 15 Since 15 = 15 this is a true statement. <, >, = are mathematical symbols that express an inequality. Inequality:- d – 4 > 5 8 – 4 > 5 d – 6 < says, “A” number, But 4 > 5, so this is a false statement decreased by 6 is less than 16. and an inequality. Write >, <, = to make the statement true. 5 x 6 > 5 + 6 = 1200 10 100 - 50 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Measure, Estimate and Compute CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Metric Convert from smaller to larger units of measure, Collection of a variety of items to be measured. The standard unit of length in the divide. meter. List findings. Convert from larger to smaller units of measure, Metric units of length are related to multiply. Computation of metric measure using the four each other in the same way as operations. place value positions within the Group work – use customary and metric to measure decimal of numeration are related. volume of various objects. Cooperative learning through group work and discussion. Kilometer hectometer decameter Help children visualize equavalences in the metric system. 1km=1000m 1km=100m 1dam=1m eg. 1km is KILO about the HECTO length of 11 DEKA football field METER/GRAM/LITER DECI CENTI meter deci conti MILLI 1m 1 deci 1cm =0.01m On most doors 0.1m The width Children interpret chart to help in problem solving. the distance of a piece of between the chalk is DATE a.m. 0C p.m. 0C floor and the about 1cm. knob is about Feb 27 10:05 -5 2:03 -3 1 meter Feb 28 10:06 -2 1:59 0 milli 1mi = 0.0001m - 51 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Measure, Estimate and Compute CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Converting from one unit to another Eg. Drew kept track of weather conditions. Above is is done by multiplying or dividing by a part of his chart recording the temperature. How powers of ten. manu minutes elapsed between the first and second Eg. 70 cm = ------- mm. readings or February 27? km = ------ m. Language Arts Link Converting form smaller units of Meaning of prefixes. (research) measure to larger, divide. Converting from larger units of measure to smaller, multiply. Computing with metric measures using the four operations. Eg. 5 cm 11 mm 15 cm 12 mm 33 cm 25 mm Review how to change one unit of measure to the other. Multiples of the unit are obtained by adding prefixes to the name of the unit. Eg. milli (thousandths) = 1 = 0.001 1000 centi (hundredths) = 1 = 0.01 100 deci (tenths) = 1 = 0.1 10 - 52 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Measure, Estimate and Compute CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT deca (tens) = 10 Combine the strategies of interpreting schedules and Questioning technique. hecto (hundreds) = 100 tables with the guess and test strategy in order to kilo (thousands) = 1000 solve word problems. Discuss and recall facts and apply their problem vary in difficulty. Some understanding of the metric system in solving Time require students simply to apply a problems. simply skill strategy to solve a Maps can be used for telling time. problem. Apply formula to solve relevant problems. Others lay special emphasis on the The twenty four hour clock can be interpretation of information Draw polygons and apply formula to solve the used to tell time in the p.m. presented in visual form eg. perimeter of each. eg.1:00 = 1300 hrs. schedules and tables. Others are multi – step or non-routine Work sheets provided. The whole earth is divided into 24 in nature. time zones. Practical work using rulers, tape measures, yard Within each zone, the time is the These exercises the imagination so needed to stick and paper to find perimeter. same. Eg. Chetumal is one hour develop the reasoning ability of the students. ahead of Belize. From time zone to time zone it is Discuss and recall what perimeter is and its one hour earlier as you travel west relevance to real life situation. and one hour later as you travel east. Draw picture of (fence, garden) to show these So, subtract one hour for each time situations. zone as you move from east to west & vice versa. Group activity – discuss various polygons and find the perimeter using both methods. Schedules and tables can be interpreted and calculated using Discuss real – world objects that have perimeters eg. different time zones. fence, picture frame, blackboard. Find the missing dimension when many other dimension are given. - 53 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Measure, Estimate and Compute CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Eg. Where the perimeter of a Solve word problems using formula and diagrams. square is known but the value of a 8 side is unkown the formula P = 4S Direct students to measure classroom items eg. solved for S, can be used (S = p/4) X 6 blackboard, desk etc. to the nearest inch, foot etc. thus if P = 24, S = p/4 = 24/4, S = 6 7 5 Practice finding area of irregular shape objects. Area y Draw a diagram/make a chart. Area of a region is the number of Find the missing lengths and the perimeter. square units it contains. X = 2 Write a formula. Y = 14 Use formulas to find the area of P = 42 As children complete the talk, observe and record polygons. results on the Performance Sheet. Area of a polygon is actually the Find the missing dimension when the perimeter and size of the region enclosed by one side is the known, use the formula. the boundaries of the polygon. P = 70 cm P = 2(l + w) It can be defined by the number L = 21 cm 70 = 2(21 + w) of square units that will fit into W = N W = P – L the region. 2 Area of the rectangle is the product W = 70 – 21 of its length and width (Basic 2 Formula). W = 14 cm To find the area of a rectangle, multiply the number of units of Estimate and measure area of blackboard, floor, wall, length times the number of units desk. of width. eg. Area = length x width or Use graph paper to show numbers of square units A = lw. inside a given figure. - 54 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Measure, Estimate and Compute CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT To find the volume of a cube Review . use the edge (e) to find the area of the base (edges are congruent) Identify cubes from among other figures measure different sizes of container then record and share information. 3ft Compute information. Count the amount of square units inside the figure. 3 ft (2 half square = 1 whole square) Exercises using formula to find volume of cube. Measure blackboard and other articles in classroom. multiply the area (e2) by the height (e). This is the same as cubing Record Measurements. e. Eg. e2 x e = (e x e) x = e3 Discuss the results. V = e3 Use the formula to find answers. To find the volume of a cylinder Eg. Brad’s toy box is 36 ins long and 18 ins wide. find the area (B) of How many square inches of tiles will be needed to the (circular) cover the top of the box? base. (Use the formula for area Art Link of a circle) A of Create geometric design or graph paper. B=;r2 multiply this area (B) Review exponential notation squares, square roots by the prism’s and irrational numbers. height (H) Display a box or similiar container. the product is the Discussion of volume. volume. Students count the number of cubic units in a figure. The volume of any prism is the measure of the region enclosed by its faces and bases. - 55 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Measure, Estimate and Compute CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Art Link Challenge students to solve. Design/Construct jewelry box, for jewelry crafts, A conical pile of sand contains 1084 cubic meters. d = 8 in collectables etc. If the height of the pile is 18 m, what is its diameter So r = 4 in V =Bh (d = 20m) 15,000 cubic meters of dirt were removed from a rectangular hole 50m by 30m. How deep was the 10in hole? (10m) B= ;r2 B=;(42) B=;16 B=50.24ins2 V = Bh V = 50.24 x 10in V = 502.4 in3 The formula for the volume of a cube = e3. Guess the volume of the classroom in cubic meters. Measure classroom and compute the exact volume. Collect various cylinder (milk cans, toilet paper rolls) Discuss the cylinder. Draw and cut out patterns an dmake models of cylinders working in small groups. When might you use a cylindrical container rather than a rectangular container? CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR - 56 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Measure, Estimate and Compute MANAGEABLE SETS STRATEGIES ASSESSMENT The volume of a container can be Discussion about the different items that are Think and discuss relatiionship between the pressured by theamount of material packaged in cylindrical containers. formula for finding the volume of a rectangular it can hold. Practical work using the cube to fill cylindrical prism and the formula for finding the volume of a containers. cylinder. The formula for the volume of a cylinder is V = ;r2h Group work – Use models to show that a cone must Problem solving. be filled with water three times in order to fill a V of cone = one third the volume of cylinder. Teacher made tests. a cylinder having the same base an height. Construct circles with different diameters. Problem solving Circumference Group activity – Estimate the distance around the Portfolio: to the nearest whole number, find the circumference of their circle. circumference of a circle with a radius of 5.75 in. Circumference of circle: the distance around it. Measure the ratio of the circumference of any circle Math Journal – compare the meaning of perimeter The symbol ; (pi) stands for the ratio to its diameter using objects in classroom. and the meaning of circumference. of any circular circumference to its diameter ; = c/d Use data to find the ratio of circumference or pi/;, Compare the formula they know for finding the which is c/d = ; perimeter of a polygon and the circumference of a The approximate value of ; is circle. expressed as the decimal 3.14 or as Elecit formula for finding the circumference. the fraction 22/7. C = ;d or C = ;r2 or C = 2;r If the diameter is 6 cm. The find circumference of a circle: C = ;d C = 3.14 x 6 if the diameter is C = ;6 C = 18.84 cm given multiply the diameter by ; C = ;d if the radius is given multiply the two radii by ; C = ;d CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT - 57 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Measure, Estimate and Compute A radius is any segment connecting If the radius is 21 m Record the center to a point on the circle. C = 2;r C =2;21 Reinforcement – Teacher’s tests. C = 2 x 22/7 x 21 C = 132 m Enrichment Social Studies Link Group work: construct circles and cut into pie shaped segments. Arrange them to form Circles on earth’s surface. Students work with a parallelogram and discuss. partner to investigate circles on the earth’s surface. Have them find: Observe that the base of the parallelogram is half what are great circles the circumference of a circle from which it is formed what is the arctic circle and the height of the parallelograms is equal to the A diameter is any segment that what is the measure of the equator radius of the radius of the circle. passes through the center and has what kind of circle is a meridian both endpoints on the circle. where do meridians intersect. Develop the formula for findings the area of a circle. The diameter is twice the length of A = b x h the radius. A = ½ c x r A = ½ (2;r) x r The formula for the circumference A = ;r2 of a circle is C = ;d or C = 2;r Problem solving . Area of Circle Practical Work:- find the area of objects in and Find the area of a circle by around the classroom. multiplying ; (pi) by the square of A B the radius. Use 22/7 for ; Use 3.14 for ; A = ;r2 A = ;r2 The formula for the area of a circle A = 22/7 x 14/1 x 14/1 = A = 3.14 x 6 x 6 is A = ; x r2 A = 616 mm2 A = 113 mm2 CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT - 58 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Measure, Estimate and Compute Scale Drawing – an accurate picture Estimate and measure to find the dimensions of the Group activity. of something but different in size. classroom. Observe; cooperate; participate and share. Scale – the ratio of th epictured Select a scale and make a scale drawing of the measure t the actual measure. room. Make a floor plan an draw to scale. A map is a scale drawing used for different purposes. Finding Actual measurement. eg. Road map, political map. Test participation through observation and ability to Scale ratio = Scale measure If the scale measure of the house floor plan was 1 recognize similarities and difference on the two Actual measure cm = 3 m, what would be the metric scale measure of scale. each of these? Temperature A picture window 2.4m wide Check list on thermomter constructed. 1 cm = w cm wide = 1/3 = w/2.4 = 2.4 Eg. neatness Celsius and Fahrenheit scales are 3 m 2.4m wide accuracy used to measure temperature. creativity w = 0.8 cm The symbol for Celsius is “C” . The symbol for Fahrenheit is “F” Use given scale to solve problems. The symbol for degrees is “ 0 ” Social Studies Link/Art On the Celsius scale, there are 100 unites/degree between the Identify distance and size between places in Belize temperature at which water freezes Draw map to scale and construct one map of Belize ( 0o ) and the temperature at which water boils ( 100o ) Display and discuss different kind of thermometers. On the Fahrenheit scale there are 180 unites/degrees between the temperature at which water freezes ( 32 o) at the temperature at which water boils ( 212 o) . - 59 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Measure, Estimate and Compute CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT The metre measurement of Compare their similarites and differences. Collect information on temperature. temperature is expressed in Alike Different degrees Celsius. (oC ) They are both based on The Celsius scale Compare Celsius temperature for different parts of the same reference divides the the country and the world. Convert from one scale The ratio of degrees Celsius to point. difference between to the other. degree Fahrenheit is 5:9, 5/9 The boiling point of references points water (1000C) (2120F) into 100 units Problem solving examples (teacher & students To change a Fahrenheit reading, The freezing point of called degrees made) subtract 320 from the Fahrenheit Water (00C) (320F) Celsius (00C) reading and then multiply by 5/9. The freezing point of The Fahrenheit scale Construct graphs and insert daily temperature Water (00C)(320F) divides the readings. This is expressed by this formula. difference into 180 Eg. If the temperature in Rita’s units called degrees Reading temperature on graphs as a daily routine. house reaches 250C, the air Fahrenheit (00F) conditioner comes on. The temperature is 770F. Is the air Group Work conditioner on? C = 5/9 x (F – 32) Construct Celsius and Fahrenheit thermometer. C = 5/9 x (77 – 32) Display children’s work. C = 5/9 x 45 = 250C Oral quiz. C = 250C Which is the most reasonable temperature eg. hot oven. a. 1000C b. 900C c. 2000C d. 10000C The temperature inside a closed car on a hot day. a. 700F b. 800F c. 1050F CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR - 60 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Measure, Estimate and Compute MANAGEABLE SETS STRATEGIES ASSESSMENT To change from degrees Celsius to Read and discuss the temperature at which water Collect information on temperature . degrees Fahrenheit. boils and freezes and body temperature in 0C and 0F. Compare Celsius temperature for different parts of F ( 9/5 x C ) + 32 Talk about how and why the reading differ from each the country and the world> Eg. Write the temperature in other. Belmopan in degrees Fahrenheit. Convert from one scale to the other. Conversion of temperatures from 0F to 0C and vice Temperature in Belmopan is 300C. versa. (Use formula) Problem solving examples (teacher & students made) F = (9/5 x 30) + 32 Social Studies Link F = 9/5 x 30 = 54 + 32 Construct graphs and insert daily temperature F = 860F Research on the origin of Celsius and Fahrenheit readings. themometers. Skills Reading temperature on graphs as a daily routine. Technology Link Recall Design and construct simple thermometers Memorize Compute Presentations Discuss Research Estimate Measure Convert Define Explain Write Interpret Invertigate Visualize Apply Solve - 61 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Measure, Estimate and Compute CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Count Record Observe Draw Make models Judge Attitudes Cooperation Participate Show understanding Interact Express interest Enjoyment Value Share LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT - 62 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Measure, Estimate and Compute ST4a – organization and characteristics of the earth’s spheres. Math Advantage Vol 1 and 2 – Harcourt Brace ST5a – how particle theory relate to change in different materials and New Progress in Mathematics 7 & 8 – Sadlier Oxford substances. Mathematics Series (New Edition) SS2a – the relationship between the location of Belize and its climate Active Math – McMillian Caribbean and weather conditions, EA1b – identify and produce rhythmic patterns syncopation. EA1e – explore and experiment with style, methods and techniques that have been used to create artistic representations. WT1b – design a device to meet a need/solve a problem. WT1c – construct a simple device to meet a need/solve a problem. WT1d – test a simple device to see if if meets a need/solve a problem. EL1d – apply functiona reading skills (including comprehension skills) in the selection, reading and interpretation of texts. EA1e – explore and experiment with styles, methods and techniques that have been used to create artistic representation. WT4d – activate the plan. ( This unit can be used for reinforcement in Std VI with more challenging teaching and assessment strategies) AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: - 63 - SP2.a Take part in group activities. CM:\2DDo cuTmhee ntrse laatniodn Ssehtipti ngbse\tNwOeRenA \Mayn gDleosc umine ndtsif\fUerpepnet r Ntweols-on\MATHC PU1p.bp.e rE Dxaivmisinioen i1n.fdoormc ation related to the problem/issue. dimensional shapes. SP1b. Choose between alternatives based on values. CP1b. Suggest ways of dealing with problem. AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Relationship Between Angles CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT Recommended Time – 4 weeks Place children in groups. Ask students to explain the following. Let each group construct various angles. how to use a protractor to measure an angle An angle is the union of two rays Find names for angles. Read angles names orally. each : right, obtuse, straight, acute that have a common end Measure different angles using a protractor. point called a vertex. One name for an angle is YXZ. Describe what Each angle is given a name. the three letters represent. Angles are measured in units A D called degrees. G Y A protractor is used to measure the degrees of an angle. B C E H X Z F I Match each angle with its name. Eg. ABC reads “Angle ABC.” A B Acute Right Review right angle, obtuse, acute, straight angles. Straight Obtuse CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR - 64 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Relationship Between Angles MANAGEABLE SETS STRATEGIES ASSESSMENT Two angles are complementary Place children for group activities. Construct angles with the following degrees and when the sum of their degree Let them construct various right angles. rave in portfolio. measure is 900 Show them flashcards having complementary a) 750 b) 1500 c) 900 d) 1800 e) 400 Two complementary angles make a angles. right angle. Ask them to identify any commom characteristics Each angle is called the they know or see eg. Pair Assessment: complement of the other. they see a right angle they see two angles within the right angle Let each pair question each other using flashcards the two angles will add up to 900. with complimentary angles; listing and naming complimentary angles measure and write the compliment of given angles. A C E G Allow children to give names for the two complimentary angles they see. B D F H A E C H I II B D F G I K M Eg. ABC EFH O J L CBD HFG N P Let children draw line within their right angles to form complimentary angles. Let them name What is the compliment of ABC? complimentary angles. Remember that each angle is called the compliment of the other.eg. M O If EFG measures 650 what is GFH. ↑MNO is a compliment of ↑ ONP N P - 65 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Relationship Between Angles CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Supplementary angles are two Use a protractor to measure both angles. Problem solving. angles whose sum is 1800. Using the diagram answer the following: Two suppementary angles form a A C straight line. ABC = 150 B F D CBD = 750 SUM = 900 B D A C E Since the sum of complimentary angles is 900 then what is EFG if GFH is 250? 1. The compliment of ↑ ACB. 2. The supplement of ↑ ACD. E 3. ------- Compliment ↑ FCD. G 4. ------- is the supplement of ↑ BCE. 5. If ↑ FCD is 600 then ↑ DCE is -------. F H 6. If ↑ BCE = 1400 then ↑ACB = -------. Place children in pairs to brainstorm all characteristics of the angles displayed on flashcards. Eg. a) identify straight line. b) name the two angle seen. C B A B c) a straight line measures 1800. ″ the sum of the two angles measure 1800. - 66 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Relationship Between Angles CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT A triangle contains three sides and Find the supplements of each of the following angles Group Activity three angles. using a protractor. Some triangles are classified a) 440 c) 390 e) c Sort out the cards ion the basis of their sides into 3 according to the length of their x groups. Label each group scalene, isosceles sides. a b d and equilateral. These are b) 1170 d)390 scalene f) d isosceles x 600 Scalene Isosceles equilateral a b c Allow children to explore triangular shape. In a scalene triangle each side is a Let them compare the three triangle shapes and tell different length. how they are same or different. Equilateral triangles have 3 equal sided and 3 equal angles. Equilateral A B C Isosceles triangles have two equal sides, and two equal angles. Children will comstruct several scalene triangle using given measurements. Eg. 5cm by 6 cm 7 cm. - 67 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Relationship Between Angles CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Some triangles are classified Allow children to pick out all equilateral triangle from Sort out by corners according to the measure of set given. Measure sides and angles. their angles. Right Obtuse Acute B These are: ↑ A = ↑B = ↑C Right Triangle Acute Triangle AB = BC = AC Obtuse Triangle A C Contruct several isosceles triangles. Find and name the equal sides. B Present to class. A C Game: TRIANGLE SORT OUT. Which sideds are equal? AB = AC Set children in 3 groups of 5. ↑C = ↑B Give each group a set of triangular shapes and packet with named either right, acute or Distribute triangular shapes to groups. obtuse. Children will identify these angles and give each a Each group must go around, find and collect all the name. Eg. a) right angle triangular shapes assigned on their packets. b) acute angle The group that finishes first wins. c) obtuse angle B Y R S A C X Z T - 68 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Relationship Between Angles CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT The sum of the angles of a triangle ↑ A is a right angle λλ Identify the types of triangles found in this is equal to 1800. ↑X, ↑Y, ↑Z is an acute angle diagram: ↑T is an obtuse angle. Allow children to consruct several triangle and use a A B If you know the measures of two protractor to measure the three angles. Let one angles of a triangle you can find child report what they found out about all the measure of the other angle. triangles. E C B X Z G F A C Y F H D A + B + C = 180 Y + X + Z F + G + H 60 + 60 + 60 = 180 100 + 30 +50 = 1800 90 + 45 + 45 = 1800 Pair activity sheet. Write each missing measure on the figure, use what you know of complimentary and Notice that the sum of the angles is 1800. supplementary angles and the sum of the angles of triangle. Children will add the two given measure of angles and subtract from sum to find the other angle, using an equation. - 69 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Relationship Between Angles CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT A quadrilateral is angy four – sided B firgure. 45 Some quadrilaterals are: parallelogram A C 1120 rectangle rhombus A=900 square B=450 trapezium X + 135 + 15 = 1800 X + 150 = 180 A quadrilateral can be split into two X + 150 –150 = 180 – 150 triangles. The sum of its angles is X = 300 3600. = X + 90 + = 1800 800 X + 135 = 180 200 X + 135 – 135 = 180 – 135 X = 450 Find the measure of the other angle for triangle on worksheet. Display several quadrilateral to students. Let them identify the common ones and guve their names. Give the names of the others. - 70 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Relationship Between Angles CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Characteristics of Quadrilaterals Work together You can use tangram pieces to form quadrilaterals. The parallelogram Two ways of forming a parallelogram are shown at the right. Rectangle Square Work with a partner. Record all possible ways you can use tangram pieces to form a parallelogram, rectangle, rhombus, square and trapezoid. Organize your results in a table. Compare your results with other groups. Parallelogram Rhombus Eg.λ Trapezium Eg. λλ Observe each quadrilateral. Write down main characteristics. Eg. λλλ Parallelogram – Opposite sides are parallel List the two pairs of parallel lines, A rectangle, a rhombus and a square is also a parallelogram, since they have the same characteristics. - 71 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Relationship Between Angles CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT The rectangle is a parallelogram Children will identify and label the following on the List the letters of all the polygons that have each with four right angles. rectangle. name. Two pairs of parallel ine. Four right angles. Eg. b II c Quadrilateral a b c The square is a parallelogram with four right angles and four congruent = = Parallelogram sides. a ll d Rhombus d e a, g,h f ab is parallel to cd Rectangle A rhombus is a parallelogram with ad is parallel to bc a, e, g four congruent sides. ↑ A, ↑ B, ↑ C, ↑ D are all right angles. Square g a, g Use a square to identify the following: Trapezoid h Two pairs of parallel sides M N Four right angles i Four congruent sides Q P Measure the sides of the given rhombus to prove that sides are congruent. Explain why it is called a parallelogram. - 72 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Relationship Between Angles CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT A trapezoid is a quadrilateral with Display a trapezoid and pupils will identify the Definition strip activity. exactly one pair of opposite characteristics. Will also compare it with other Group children by pairs. sides parallel. parallelograms. Will look around in environment to Match definition strips. identify this shape. Eg. a window A circle is a closed path or curve in Trapezoid a plane with each end the same exactly one pair of distance from a point inside opposite side parallel. called the centre. Reteach the parts of a circle using circular shapes You name a circle by its centre. and let children label the parts of a circle. The parts of a circle are: the radius diameter chord Centre radius Diameter chord - 73 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Relationship Between Angles CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT A circle contains 3600. Match terms with meaning. Problem solving. If a circle is divided into a number of A B angles, the sum of the angles Use the clock to find the answer: must add to 3600. Diameter ----- distance around a circle. 12 Radius ----- a line segment that has both 1 Skills chord end points on the centre. 2 Identify c) chord ----- a straight line from the Define centre to the circumference. 9 3 Analyze d) circumference ----- a straight line passing Compare through the centre touching 8 4 Contrast the circumference at both Solve ends. 7 5 Label 6 Record Identify the diameter as a straight line and elicit from What is the size of the angle between 1 and 2. Explain children how many degrees are in a straight line. The size of the angle between 2 and 5. Relate The size of the angle between 6 and 12 Sketch How many degrees does the hour hand of the clock Describe pass between 7o’clock and 11 o’clock? Attitudes Participate Interact A B Appreciate Enjoyment Identify how many right angles can be seen in the Respect other’s opinion circle. Share Each right angle = 900 4 right angles = 4 x 90 = 3600 - 74 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Relationship Between Angles CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Notice that there are 6 equal angles ″ 360 = 600 6 Each angle will measure 600 Notice that there are 8 equal angles ″ 360 = 450 8 Each angle will measure 450 - 75 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Relationship Between Angles LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT EA1e - explore andexperiment with styles methods and techniques that Teaching Elementary have been used to create artistic representations. School Math WT1c - construct a simple device to see if it meets a need/solves a Heath Mathematics Connections problem. Teacher’s Edition M3c - apply algebraic expressions to solve problems Middle Grades Math tools for Success EL1d - apply functional reading skills (including comprehension skills) in the selection, reading, and interpretation of texts. Mathematics A topical approach Refresher Mathematics Stein New Common Entrance Mathematics Walter Phillip Tangram puzzles Cut – out shapes Geometry set Protractor Geostrips Ruler - 76 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Whole Numbers AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: C.P.1b – Examine information related to the problem/issue M1.a – Place value in numbers up to ten digits S.P.2a – Take part in group activities. M1.b – The consecutive sequence and position of numbers S.P. 2e – Lead and follow where appropriate. 1 – 9,999,999,999 S.P. 2f – Help the group to achieve its goals. M1.c – Quantity in numbers 0 – 9,999,999,999 CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT A number can be read, written or Suggested activities can be used for Std VI using ten Suggested strategies/activities for assessment can expressed in different ways: digit numbers. be used for Std VI using ten digit numbers. standard form Eg: place value games Quiz (figures) Jig-saw puzzles Speed tests words Use of number line Interviews expanded form Work cards Portfolio assessment scientific form N.B. Suggested strategies/activities for assessment A sequence is a list of whole N.B. Suggested activities can be used for Std VI. using can be used for Std VI using ten digit numbers. numbers written in order. ten digit numbers Each whole number in the Creating sequence patterns. sequence is called a term. Use of number line. Identify and explain patterns. Exercises on Fibonacci sequence: Eg. a) 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 etc. - 77 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Whole Numbers CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT Whole numbers can be rounded to a certain place. b) 3 , 7 , 10 , 17 , 27 , 44 , 71 , 115 , 186 etc. Exercises on Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 - 78 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Whole Numbers CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Numbers can be compared by N.B. Suggest activities from Std V can be used in Math Log: comparing digits place by place, Std VI. Students write short paragraphs outlining the from left to right until a estimation skills learned. difference between the digits in Math Talk!! one particular place is found. Children state real life situations in which numbers Game: have been estimated and yet remain meaningful. Round We Go! Eg. population of towns Students in teams form circles. The first player in A family’s grocery list etc. each team tosses a bean bag to the player right and name a number. The catcher round Children compare estimations and actual answers. the number to the nearest ten and then tosses Children estimate sums and differences using Front the bag to the right naming another number. End Method. Play continue in this way until the bag completes the circle and all players sit down. 1100 The first team seated win. +214 +100 1200 Other suggested estimation methods include: Clustering and using compatible numbers. Bean Bag Suggested activities from Std V can be used in Std VI using ten digit numbers. Table readings: Children will read table having distances, Have children explain concepts learned. populations, salaries and make comparisons in Pupils create games in groups to show complete sentences. understanding of concept learnt. - 79 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Whole Numbers CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT In maths we use the operation of Pupils do math journals on whole numbers by addition, subtraction, writing their understanding and giving multiplication and division. Place Population examples on the different topics. Operations have certain Orally define what is the commutative property of characteristics or properties. Belmopan addition. The commutative property of Using flash cards, orally for pupils to continue the addition states that when we Hattieville variables. add one number to a second Ex. A + B = --------------. number we get the same sum Cotton Tree as when we add the second Show the commutative property of these numbers. number to the first. San Ignacio 0 x 5 = --------------- The commutative property of 2 x 5 = --------------- multiplication states that when La Democracia 6 x 5 = --------------- we multiply one number by a second number we get the same product as when we Which property is being used in the following. multiply the second number by N.B. Population subject to change. Match Col. A with B. the first number. The associative property of addition Explain that 5 + 6 = 6 + 5 A B permits us to group or associate Explain that 5 x 6 = 6 x 5 Property Number the first and second number Explain (5+6) + 4 or 5 + ( 6+4) and add their sum to the first Explain the multiplication 5 x (6 x 4) = (5 x 6) x 4 A) Commutative P of Ad. a) 8 x 6 x 5 number. Note that grouping is done in the associative B) Commutative P of X b) 7 + 5 = 5 + 7 property. C) Associative P of + c) 8 + 6 = 6 + 8 D) Associative P of X d) 5 x 6 = 6 x 5 - 80 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Whole Numbers CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT The distributive property of Use the distributive property in computation such as Complete to show how to use the Distributive multiplication over addition and 2 x 23 Property to find each product. subtraction states that when we Eg. 2 x 23 = 2 x (20 + 3) multiply one number by the sum = 2 x 20 + 2 x 3 or difference of the second and = 40 + 6 a) 8 x 14 = 8 x ( + 4) a third number we get the same = 46 result as when we add or = ( 8 x ) + 8 x ) subtract the product of the first eg. 4 x ( 7-3) = (4 x 7) – ( 4 x 3) and second numbers to the 4 x (4) = 28 – 12 = + product of the first and third. 16 = 16 When we subtract, multiply, divide = etc. or add a set of numbers (eg. Divide a number by itself the quotient is 1. whole numbers) and get as our Ex. 8 ∋ 8 = 1 b) Use the distributive property to make an answers a number of the same easier problem. ( one is done) set we say that the set is closed Raise 1 to any power the answer is 1. under that operation. This Eg 15 = 1 x1 x1 x1 x1 = 1 4 x 33 property is called “CLOSURE”. ( 4 x 30 ) + ( 4 x 3 ) A number which when added to a Subtract zero from any number is the number. given number, does not change Ex. 6 – 0 = 6 but the subtract a number from 6 x 25 the given number is called the itself we get zero. 7 x 24 additive identity. Therefore O is Eg. 6 – 6 = 0 the additive identity. A number which when multiplied by In each case identify the law illustrated. Closure, a given number, does not Commutative, Additive Identity, Associative, change the given the number is Multiplicative Identity, Distributive Property. called the multiplicative identity. Therefore, is the multiplicative identity. - 81 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Whole Numbers CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Skills 5 + 3 = 3 + 5 --------- Read (6 x7) x 4 = 6 x ( 7 x 4) ---------- Arrange 9 x ( 3 + 5) = ( 9 x 3 ) + ( 9 x 5) ---------- Speak 8 x 7 = 7 x 8 ---------- Write 9 + 5 = 5 + 9 ---------- Create ( 2 x 8 ) x 5 = 2 x ( 8 x 5 ) ---------- Explain 7 x ( 5 + 4 ) = ( 7 x 5 ) + ( 7 x 4) --------- Identify 7 x 5 = 35 6 – 6 = 0 Attitudes 16 = 1 Co-operate Share Respect Tolerate Enjoy Understand - 82 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Whole Numbers LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT SL4.a Interpret messages and follow instructions and directions Heath Mathematics Connections Volume 1 Level 4 SL3.c Demonstrate the ability to write for specific purpose Math Advantage Teacher’s Edition EL3.b Produce written work that demonstrates effective English usage Volume One and grammar. New Progress in Mathematic EL4.b Use speech for self fulfillment. Rose Anita McDonnell M1.e The base of other number systems. Materials Bristol boards Work cards Work sheets Booklets Bean bag Props - 83 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: CP1c Suggest ways of dealing with the problem/issue. M4b. - Predict the likely occurrence of an event through logical SP2a Take part in group activities. reasoning, based on trends. SP3b Assess progresses in relation to achievement of M5a – Collect, analyze and interpret data and predict probable goals and adjusts goals or strategies as necessary. outcomes. CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT Recommended Time 3 – 4 Identify the letter using the following order pair. weeks 4 Eg. (2, 2) = C 3 (-2, 2) ------ Statistics is a systematic F 2 C (2, -3) ------ collection, organization, and 1 (-2, -3) ----- interpretation of sets of data. A graph is a method used to note that you start reading your co-ordinates from picture in a clear, interesting -4 -3 -2 -1 0 1 2 3 4 the x axis. and meaningful way. -1 -2 I H -3 J -4 - 84 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Use graph when plotting co- Observe the graph presented. Plot using the co-ordinates (2,2), (2, -3) (-2, -3) and ordinates Identify the x-axis and the y-axis form a figure. Explain that (0,0) is called the origin A horizontal and a vertical number Explain that the x-value is the distance right or left of line can be placed together to the origin and the y-value is the distance above form a pair of cordinate axes. or below the origin. 4 The horizontal line is called the Discuss the term ordered pair 3 x axis. The vertical number line Find the ordered pair for point B 2 is called the y-axis. Remind children that the first number in the ordered 1 The coordinate plane is divided into pair always gives the x-value 4 quadrants. Discuss how the ordered pair (+4, +2), (+2, +4) are -4 -3 -2 -1 0 1 2 3 4 different -1 The x and y-values are called co- Graph points C, J , H as illustrated on the chart and -2 ordinates of the point. discuss each ordered pair. -3 Demonstrate the four quadrants. -4 Explain that the x-axis and y-axis divide the plane in four spaces. X O Y, Y O X1, X1 O Y, Y1 O X. Eg. Y for home assignment II I (Quadrants) Give the ordered pair for each point on the graph. Y 0 B D III IV C A X Show point (0,0) which is called the origin. E G F H - 85 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Pictographs are graphs that are Explain then in II x is negative Y is positive. In I both 1) A ( - ) 2) B ( - ) 3) C -----. very effective visual tools for x and y are positive, III x and y are negative showing data. IV positive and negative. which points are in Quadrant I? Which points are in Quadrant IV? A stem and leaf graph is such to Collect data from children about the types of fruits interpret simple data. they like. Collect data about their class ( such as the monrths Stem and leaf plot is used to Kind Number in which students have birthdays) and make a organize data when you want to pictograph from the data. see each item on the data. Orange 2 Using the chart answer these questions Banana 5 What score is shown by the second stem and its Apples 3 fourth leaf -------- Grapes 4 How many children scored 84? ---------- What was the highest score? ------------ etc. Illustrate how the data is placed on a pictograph 0 Kind Numbers (2 people for 1) Oranges 0 Bananas 0 0 0 Apples 0 0 Grapes 0 0 - 86 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT A bar graph is used to compare Scores of an English Test Interview and record data on a bar chart. amounts. Eg on the types of books used in a class. Remember the scale should always Stem Leaves start at 0. Explain the following bar graph by answering 6 2 4 5 questions. FAVORITE SPORTS 7 0 1 1 3 8 8 1 4 4 6 9 9 25 9 2 5 6 7 7 8 20 15 Observe the graph above Explain that it shows the English test scores of 10 children Note that data is grouped by tens digits. 5 The data is organized from least to greatest We use tens digits as stems and ones digits as 0 basket volley soft foot leaves ball ball ball ball Discuss the chart ( of 25 pupils) 3 children scored in 60’s eg. 1 child scored 62 1 child scored 64 1 child scored 65 etc - 87 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Collect heights of children in your class. How many pupils play football? Make data chart. How many enjoyed playing football? Eg 5children – 3 ft Which sport do the pupils like the most? 2 children – 4 ft How many pupils are in the class? 1 child – 5 ft demonstrate how this data could be placed on a bar chart. Eg. 8 7 6 No of 5 children 4 3 2 1 0 1ft 2 ft 3 ft 4 ft 5 ft Height of chiilren - 88 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT A line graph shows how an amount Observe, study and discuss the following line graph. Use the line graph to answer the following changes over time. questions. Pupils who buy Panades in class V 40 200 30 150 20 100 10 . 50 0 0 M T W Th F 1 2 3 4 5 Day Time in hours. on which day did the pupils buy the most panades. How far did the bus travel in 2 hours? How many panades did they buy on Thursday,etc. How long did it take to go 200 km? How far did the bus travel in 3 hours? John’s mother made a cake for the family. She shared half of it among the children. She gave a quarter to her husband and what was left to Demonstrate on the board the steps for making a her neighbors. Show this on a graph and label A circle graph is a common way of circle graph. it. showing how to represent a Have a volunteer divide the circle into 4 parts. Bring a cake, pie, orange to the class to show the whole or 100% of something. Discuss equivalents for different parts that makes a whole. a whole pie – 100% ½ of the pie – 50% ¼ of pie – 25% - 89 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT A frequency table shows the Collect data to take a survey of the classmates number of times each piece of about favorite pets. data occur. Ask each student A tally table is a table that has “ Of the following pets, which is your favorite?” categories that allow you to Make a table like the one below to record each record each piece of data as it student’s choice with one tally mark. occurs. Favorite Pet Pet Tally Total Have a volunteer label and shade the part that represents 25% etc. Dog III 3 Make a tally of the children in the class with their Cat IIII I 6 primary colour that they prefer: Children choose a preference between blue, red and Rabbit yellow. Children stand as each color is called. Teacher Parrot tallies on chart. Turtle Favorite Primary Color Tally Frequency Blue IIII IIII 9 Red IIII IIII 10 Yellow I 1 - 90 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Skills What does tally mark, or 1, represent? Work with a partner to take a class survey. Choose How is the frequency in the third column determined? one of the following topics. After you pick your Draw How many students are in the class? Describe two topic use the question and answer choices to Observe ways you can find this number: Discuss: survey as many classmates as you can. Use a Discuss tally mark to record everyone’s choice. Graapph Plot Illustrate which place wouldyou most like to visit? Divide The zoo Tally Altun Ha Choose Caye Caulker Collect Gale Point Survey Analyze Interpret Which class colors would you choose? Predict Red and Black Compare Silver and Black Label Green and Gold Specify Red and blue Record Demonstrate Arrange Which instrument would you like to be able to play? Identify Piano Conclude Drums Violin Guitar - 91 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Attitudes Which animal would you most like to own? Dog Understand Horse Participate Cat Reponsibility Bird Leadership Independence Use the data from your survey to complete the Co-operation table. Write a title for your table. Then write a heading for the first column. Title: Tally Total Write a question about your data. Have a classmate use the table to answer the question. Place in your portfolio. - 92 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT EL1.a Use context clues and cues effectively to communicate when References reading orally New Progress Math – Rose Anita McDonnell EL2.a Respond sensitively and appropriately to auditory and visual stimuli. Certificate Math – A.Greer & C.E. Layne EL3.c Demonstrate the ability to write for a full range of purposes. Refresher Math – Stein EA1.e Explore and experiment with styles, methods and techniques Active Math – E.A. Gutierrez & other educators that have been used to create artistic representations. Math Advantage – Harcourt Brace SL4.a Interpret simple forms, notes, messages, and follow instructions and directions. Middle Grade Math – Prentice Hall Course I WT1.a Identify a simple problem and need Heath Mathematics Connections – Teacher’s Edition Level 4 Materials Graph paper Flash cards Charts Crayons and markers - 93 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: SP2. F – Help the group to achieve its goals. M1a – Place value of decimal numbers up to nine digits. CP1.b – Examine information related to the problem or M1b - The consecutive sequence and position of decimal issue. numbers up to nine digits. M1c – Quantity in decimal numbers up to nine digits. CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT A decimal number can be read, Give children digits on cut-outs with a blank place value Have children complete table: written or expressed in chart. different ways: Have children fill in the places eg. Tens/ Ones/ Tenths/ words Hundredths/ Thousandths Standard figures Form Words Expanded Scientific scientific Children will place digits on place value chart to expanded indicate or show number read. Have children read the values of digits. Volunteers will give decimal numbers while class write in words. Give children words on rabbits and figures on tail. Children will pin number tail on the rabbit that corresponds with. Matching decimal numbers Expanded Scientific This can be reversed. - 94 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT 2) A sequence is a list of decimal Pupils will do practical exercises of writing decimal 3) Journal entries on their understanding of numbers written in order. Each numbers in expanded and scientific forms. expanded and scientific notation on decimal decimal number in the sequence is b)Decimal Map: numbers. called a term. Pupils will each get a card divided into quarters. Standard Words Expanded Scientific 2) Creating sequencing games. They will write a decimal number in standard form Teacher assess presentation of games. and complete the card. Children will challenge each other. 3) Decimal numbers can be 3) Interview students on the comparison of compared by comparing digits place decimal numbers. by place. 2. Have children write numbers vertically aligning on - Adding zeros to the right of the the decimal points. Write any necessary zones. Teacher records and analyze as pupils explain. decimal does not change its value Compare value of digits. but does help to make comparison easier. - Arrange the numbers in the specified order ie ascending descending and vice versa: 2.12302 Since .12302 is less 2.12305 than .12303 which 2.12303 is less than .12305 then: 2.12302 < 2.12303 < 2.12305 (least to greatest) - 95 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT 4. Decimals are rounded just as - Play a game: Observation checklist whole numbers. Leader calls out a decimal number such as Teacher formulates his/her own problem solving - To round decimal numbers, look 0.9362417 activity using decimals: at the value of the number in the Each player must give either a smaller or bigger one Eg. Menu place value one place lower than depending on what the leader calls out. Maps(distances) etc. the place value to be rounded. - Use of number line to round to nearest whole If that number is greater or equal to number. Teacher also construct criterion statements for five add one to the place value to be - Identify place value to be rounded: problem. rounded. If that number is less than eg: Round 2.406314 to the nearest thousandths - will use statements to assess pupils. five that number is changed to zero 2.406314 Understanding of decimals. and then dropped. 3 is less than 5 so round down. Etc Skills - Round money to the nearest dollar. Read - Using cents as decimal numbers: Match 2 shillings & 2 dimes = 35 cents = .35 Identify 2 nickles 4 pennies = 14 cents = .14 Arrange Explain Attitudes Cooperate Share Respect Tolerate Understand Enjoy Approximate time: (2 weeks) - 96 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT SL4.a Interpret messages and follow instructions and directions. New Progress in Mathematics Rose Anita Mc Donnell EL3.c Demonstrate the ability to write for a specific purpose. EL3.b Produce written work that demonstrate effective English usage Heath Mathematics Connections and grammar. Volume 2 Level 4 EL4.b Use speech for self fulfillment. Exploring Math Grade 7 & 8 Materials: flashcards place value chart bristol boards decimal work cards sequencing games coins - 97 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: 3D Figures AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: CP1B – Examine information related to problem M2D The relationship between angles in different two- CP1C – Suggest ways of dealing with the problem. dimensional shape. SP2A – Take part in group activity. SP2F – Help the group to achieve its goal. CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT Recommended time – 2 weeks Examine two sets of vertically opposite angles. Understanding concepts. Name the 4 angles When two lines intersect, they Which pair is equal I will form four angles. The two angles opposite each other are A D said to be vertically opposite. O Vertically opposite angles are G H J equal. C B Do the angles above represent Adjacent angles Construct two straight lines cut at point O. adjacent angles a) Measure A O C and D O B supplementary angles When a straight line stands on What do you notice? both. another straight line, two adjacent angles are formed. b) Measure B O C and A O D. What do you If I H J is 700 then G H I is . notice? The sum of two adjacent angles on a straight line is 1800. Present several flashcard to groups, with adjacent angles. Let them identify and name the straight lines they see. - 98 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: 3D Figures CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT 2. Congruent angles have the Let them measure A C D and B C D and find the Discriminating between angles. same measure and same length or sum. Find 3 pairs of congruent angles. same shape and same size. Compare results with other groups. The symbol for congruent is ↵. D A B C B C A D A C D + B C D = 1800 E F Each group of children will measure angles to find which are congruent. G H ↑A ↵ ↑G ↑B ↵ ↑D 650 650 ↑C ↵ ↑E E F ↑E is congruent to ↑F ↑E ↵ ↑F Draw 3 pairs of congruent angles. Teacher will measure to check for congruency. Review sides and angles of polygons. - 99 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: 3D Figures CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT 3. To find the sum of angles in a 1. Let children divide polygons of different sides into Make a book entitles “Polygons and Their Angles.” polygon use the formula. triangles. Draw and label polygons of 3, 4, 5, 6, 7, 8, 9 and S = n x 1800 10 sides. A B Divide each polygon into triangles, using broken Where s = sum of angles and lines. n = number of triangles Calculate the sum of the angles in each polygon. OR Display work. s = t x 1800 View and critique accurateness. Where t = number of triangles. Listen to explanations and justifications of answers. 4. To find the missing angle: Name each polygon. x = s – n 2. Count the number of triangles present in Use a formula to find the sum of the angles. where x = missing angle diagrams. s = sum of angles in A = 2 B = 4 1. polygon n = sum of given angles. 3. Children use their P.K. of number of degrees in a triangle to work in groups and formulate the formula for number of degrees in a polygon. ex. a) quadrilateral b) sum of angles: 4. Children use their P.K. of sides in a figure to 2 x 1800 = 3600 calculate sum of angles, using teacher’s guidance. OR (4-2) x 1800 2 x 1800 = 3600 - 100 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: 3D Figures CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Skills - Give children the following problem to use their Find the degree measure of x in each polygon. P.K. to solve. Identify Define Analyse 1200 X Compare 1200 Contrast 1200 1100 Solve 600 700 Label Record 900 X Explain - Assess children’s procedures. Sketch - Compare results and make conclusions of method Relate used. Describe Attitudes Participate Interact 760 760 Appreciate Enjoyment Respect other’s opinion share 750 900 900 - 101 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: 3D Figures LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT SL4.a: interpret simple forms, notes, messages, and follow instructions New Common Entrance Mathematics, Second Edition and directions. Walter Phillips M4.a make and apply reasonable approximations by observing and/or Mathematics for Caribbean Schools using factual data based on meaningful references. Book I Longman Caribbean EA1.h explore and experiment with styles, methods and techniques Althea A Foster that have been used to create artistic representations. Addison – Wesley Mathematics - 102 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Decimals AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: SP2F Help the group to achieve its goals M2a Draw and construct three dimensional objects SP2G Help to create consensus. CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT Duration – 2 weeks Children should: Free reponse journal entry based on three Draw rectangle on paper dimensional objects. A 3D figure is also called a solid Identify and name number of dimensions Share journal with peers, figure. It takes up space and Fold paper into cylinder matching edges of the has three dimensions rectangle. Guided questions: namely; length, width and Identify and name number of dimensions. Identify solids in the class. height. Research definitions of terms – face, edge, vertex How many faces do they have? All solids have faces. A face Group discussion of definition How many edges do they have. may be flat (plane) or Record curved. Most solids also have edges. An Models or objects representing prisms and edge is a line where two Complete the following table: pyramids. faces meet. Edges may be (Make observations of manipulatives). Examine models curved or straight. Discuss similarities and differences A vertex is a point or corner Shapes # of Vertices # of Edges # of Faces Suggest that children begin collecting 3D objects to where edges meet. build a class sculpture. A prism is a solid figure that has Ex:Cube Hold intermediate discussion as sculpture a pair of parallel faces. Cuboid progresses. Rectangular Make reflective journal entries. Prism Label figures. Hexagonal Pyramid - 103 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Decimals CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT A pyramid is a 3D figure that has a Children observe and make skectches of three Observe - displayed work. polygon for the base and dimensional figures. participation level triangular sides that meet at a co-operation point called the vertex. The number of faces, edges and vertices of the solids differ. Sketches can be made of 3D objects. Prisms and pyramids can be constructed using nets. Skills Identify Label Classify Compare Contrast Sketch Define Demonstrate Construct Examine Explain Visualize Experiment - 104 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Decimals CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Attitudes Use objects to make nets. Eg. matchbox trays, Problem Solving: chalkbox. Name figures that could be formed from each net. Willingness to Cut edges and flatten shapes to make open nets. Participate Compare nets Experiment Sketch nets ofr solids eg. triangular prism, square Share base pyramid Cooperate Respect opinion of others Be industrious Question and analyse how well children can explain. Experiment with nets to construct solids. - 105 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Decimals LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT WT1a. Design a device to meet a need/solve a problem The World book of Math Power bk1- World Book Inc. WT1c. Construct a simple device to meet a need/solve a problem. Middle Grade Math Tools for Success – EA1e. Explore and experiment with styles, methods and techniques Prentice Hall that have been used to create artistic representations. Exploring Mathematics bk 7& 8 Mathematics for Caribbean Schools bk1 Common Entrance Mathematics – Stanley Thornes Ltd. Objects from environment Models of 3D objects. - 106 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Decimals AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: SP2F Help the group to achieve its goal. M2a Draw and construct three dimensional objects. SP2G Help to create consensus. CP1.c Suggest ways of dealing with problem/issue. CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT Recommended Time: 2 weeks Display models of cones, cylinders and spheres. Vocabulary: Match each three dimensional figure with its A 3D figure takes up space and Observe description. has 3 dimensions. Identify and name models. sphere Discuss properties – faces, edges, vertices. cone Three three dimensional figures cylinder are cones, cylinders and Complete the table: The set of all points in space that are an equal spheres. distance from a given point. A cone is a 3D figure that has a Figure Base Name of Figure A figure formed by two congruent circular regions closed curve for a base and joined by a curved face. a surface that comes to a point or vertex. Manipulatives/Group Work A sphere is the space version of Have children work in group of 2-3 to create a model a circle. It considt of a set of in the shape of a cylinder, sphere or cone. points all at a fixed distance Name each solid from a given point. Any 1. 2. 3. plane cut through the center of a sphere will give two identical parts and the cut forms a circle. Half a sphere is called a hemisphere. - 107 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Decimals CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT 4. A cylinder has two plane faces Write as many names of everyday objects that Observe displayed work and one curved face. resemble cones, spheres and cylinders. Participation level Cooperation. Draw and cut bases and faces, taping them together to make 3D objects. Sketches can be made of 3D Name figures that can be formed from each net. objects. Children observe and make sketches of 3D objects. Design a unique 3D figure, using either a cone or a cylinder. Name it and think of a use for the Cones and cylinders can be design. constructed using nets. Collect 3D objects. Connect objects. Connect A net of a solid is the plane shape Use models to make nets. objects with wine or glue to create a geometric obtained when a solid is cut along Cut edges and flatten shapes. sculpture. its edges then flattened out. Compare nets. Sketch nets for solids Experiment with nets to construct solids. Discuss the use of these geometrical solids Ex. net of a manufacturing cone: - 108 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Decimals CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Skills Net of a cylinder Design a unique 3D figure, using either a cone or a cylinder. Name it and think of a use for the Identify design. Compare Collect 3D objects. Connect objects with wine or Draw glue to create a geometric sculpture. Construct Define List Sketch Explain Examine Visualize Attitudes Willingness to Participate Experiment Share Cooperate Respect opinion of others Be industrious - 109 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Decimals LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT WT1a – design a device to meet a need/solve a problem. Exploring Mathematics – Scott Foresman & Co. WT1c – construct a simple device to meet a need/solve a probem. Common Entrance Mathematics – Stanley Thornes Ltd EA1e – explore and experiment with styles, methods and techniques Mathematics for Caribbean Schools bk1 that have been used to create artistic representations. Longman Caribbean EL1d – apply functional reading skills in the selection, reading and Certificate Mathematics A Revision Course for the Caribbean interpretation of data. A Green & CE Layne (3 Edition) EL1b – demonstrate fluency through appropriately applying word Bristol board, drawing paper, models identification strategies. - 110 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Decimals AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: SP2.F – Help the group to achieve its goals. M1.a – Place value in numbers up to ten digits. CP1.b – Examine information related to the problem/issue. M1.b – The consecutive sequence and position of numbers SP1.c - Take action based on principled choice 1 – 9,999,999,999. SP2.a – Take part in group activities M1.c – Quantity in numbers 0 – 9,999,999,999. SP1.a – Recognize the values associated with choices. M1.e Learn base of other number systems SP1.b – Choose between alternatives based on values CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS ASSESSMENT 1. A decimal number can be Suggested strategies from Std V can be used in Std VI Suggested strategies from Std V can be used in Std read, written or expressed in using ten digit numbers. VI using ten digit numbers. different ways, Words Others: Others: Figures Use graph sheets to show decimal numbers. Reading and recording measuring devices. Scientific Expanded Rearranging decimal digits. Eg: 1 2 3 4 The number 2. The number nearest to 1 nearest to 50 2. Writing decimal numbers in expamded scientific and standard forms. 1.234 43.21 - 111 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Decimals CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT A sequence is a list of decimal Suggested strategies from Std V. can be used in Std 2. Complete chart numbers written in order. VI. Each decimal number in the Substance Density Expanded Scientific sequence is called a term. Group activity: Form Form Each member writes down any decimal number Water 1.00 Decimal numbers can be compared (between 0 and 1) and draws a model for the Zinc 7.14 by comparing digitd place by number. They’ll sequence their numbers. Calcium 1.54 place. Hydrogen 0.07099 Use number line to compare decimals. Use inequality signs to compare decimals. Decimals are rounded just as whole Maze sequencing decimal numbers in numbers. 4. Suggested strategies from Std V can be used in ascending or descending order. Std. VI using ten digit numbers. Eg: 1.46 1.54 1.6 Rounding decimals using the front end method: 1.52 1.55 Use of number line 1.62 Rounding decimal number distances. 1.64 Round money to the nearest cents and dollars. 1.7 Journal: Pupils will compare decimals using the populations of two towns. - 112 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Decimals CONTENT ORGANIZED INTO SUGGESTED TEACHING/LEARNING SUGGESTED STRATEGIES/ACTIVITIES FOR MANAGEABLE SETS STRATEGIES ASSESSMENT Skills Writing journal: Explain giving illustrations the rule for rounding Read decimals. Arrange Construct Portfolio assessment on decimals. Write Explain Rounding numbers using balance beam: Draw Eg Compare Attitudes Cooperate Share Respect Tolerate 160 165 170 Understand Enjoy 167 = 170 - 113 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: MATHEMATICS STANDARD V UNIT: Decimals LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT SL4.a: Interpret messages and follow instructions and directions. Mathematics Volume 1 Silver Burdett Ginn. ELc: Demonstrate the ability to write for a specific purpose. New Progress in Mathematics EL3b: Produce written work that demonstrates effective English usage Rose Anita McDonnell and grammar. Heath Mathematics Connections EL4b: Use speech for self fulfillment. Volume 2 Level 4 Materials: Graph sheets Measuring devices Work cards Number cards Maze Balance beams - 114 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: SP1.c – Take action based on principled choice M1.e Learn base of other number systems SP2.a – Take part in group activities. SP1.a – Recognize the values associated with choice. SP1.b – Choose between alternatives based on values. CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Place Value to Billions Group Activities Math Journal Bring and share newspaper on magazine articles Place value – the value of a containing large numbers & decimals used in science digit depending on its and other areas. position or place in a standard numeral. Design and construct place value chart from numbers in Eg. 843, the 4 is in the tens the articles. Write a rule explaining if interchanging the digits within place and means 4 tens or PLACE VALUE each number changes the value of each 40 Our system ofnaming 0 0 5 3 1 0.0531 numbers is based on ten. 1 6 2 3 0 5 1 . 1,623,051 Place value is used to express whole numbers and decimals. Eg.324 and 3124 Other exercises for independent work. Each place has a value ten times the value of the place at its right. To read a standard numeral Start at the left. 1- 1 5- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Read the digits within a Apply procedure for reading standard numerals and period; then say the decimals. name of that period. Continue in the same way Problems dealing with money in regard to buying and reading each group of selling. digits; then name the period. Two distinct concepts involved Naming the place and telling the value of the digit in that place. The place and value of the place do not change from numeral to numeral. Thus, the tens place is the second place to the left of the decimal point and its value is ten in every numeral. Name the period: Eg: 8, 961 238 thousands 649 736 145 ones Practical work involving real life situations The word “and” is not used in reading whole numbers. 1- 1 6- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Place value chart is Group activities: Checklist assessment on group acitivity e.g. extended to include Game cards – one set write numbers in factored form Participation numerals for numbers less Other set write the exponential form for Accuracy than 1. these numbers. Cooperation Such numbers are called decimals. Match cards. To read standard numerals for a decimal: Elicit and discuss with class, pairs of numbers whose Journal entry acitivity: Read the whole number product is 100, 1000 etc. Imagine you are going to present a monetary gift to your part first school which has 20 figures. (if there is one) Practice and discussion on assigned exercises. Show what this figure looks like in expanded form. Read the decimal point as and Read the decimal point as you would a whole number ending with the name of place of the last digit. Expanding notation using Exponents Expanded notation can be written in several ways. Eg. the multiplicative property is used Eg. 785 = (7 x100) + ( 8 x 10) + 5 1- 1 7- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Exponential notation can be Encourage students to look for patterns to help them Checklist on rules and game created. E.g. used find rules that will aid them in computation. Creativity Eg. 4692 = ( 4 x 10 x 10 Accuracy x10) + ( 6 x 10 x 10) + Art Link Listening skills (9 x 10) + 2 Make sets of cards for Matching Game. Sharing 4 x 103 + 6 x 102 + 9 x 101 + 2 Exponent – a number that tells how many times a number, called the base, is used as a factor. Exponents are used to express numbers that are products of the same factor. 103 – exponent base 10 used 3 times 10 x 10 x 10 = 1000 Any number, to the first power is that number; 101 = 10 Any number, except zero, to the zero power is 1 : 100 = 1 1- 1 8- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Base – is the number used Recall procedures for expanding base ten numerals Construction of place value chart for each base 2,3,5,8. as a factor Eg. 2,567 = ( 2 x 1000) + (5 x 100) + (6 x 10) + ( 7 x 1) Factor – one or two or more ( 2 x 103) + (5 x 102) + (6 x 101) + (7 x 100) Involvement in practical activities. numbers that are multiplied to form a product. Teacher made test. involve children in a trial and error activity expanding Exponential notation is a numerals in base 2,3,5 or 8 shortcut for writing a eg. 2334 = ( 2 x125) + ( 3 x 25) + (3 x 5) + ( 4 x1 ) number in which a = (2 x 53) + ( 3 x 52) + (4 x 51) + ( 4 x 50) single expression is used as a factor several times. Group objects to represent numbers in base 5 Eg. Bases: In our number system we use ten digits ( or numerals) 0,1,2,3,4,5,6,7,8,9 to write 11 = 215 all our numbers. Our system is therefore called a Repeat the process for other bases. base ten number system. Use the idea of expansion to convert any numerals of Besides base ten there are any base to base 10. other number bases. Each Eg. Convert 135 to base 10 number base uses a 135 (1 x 5) + ( 3 x1) different number of 5 + 3 = 810 numerals. Eg. base five used 0,1,2,3,4 1- 1 9- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Use repeated dvision to convert base 10 numeral to other based. Eg. Convert 8 to base 5 8 1 + 3 The number is read off as 135 1- 2 0- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: CP1.c Suggest ways of dealing with the problem/issue. M4b – Predict the likely occurrence of an event through logical SP2.a – Take part in group activities. reasoning, based on trends. SP3.b – Assess progress in relation to achievement of M5a – Collect, analyze and interpret data and predict probable goals and adjust goals or strategies as necessary. outcomes. CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Statistics is a systematic Brainstorm in groups what children recall about Data. Label the quadrants on the graph below collection, organizaton Eg. Plot the following co-ordinates and interpretation of a recording information (0,2), (2,3) etc. set of data. using graphs Name the point located by the ordered pair. Data can be collected by tallying (+2),-1) etc. many means including different graphs looking in books or encyclopedias or by Distribute typing sheets making a survey. Demonstrate what they recall about a graph assigned to Data is facts and them.(drawing) information. Present and share what each group drew. Data can be displayed on Discuss concepts of graphs to show co-ordinates. graphs and frequency Review x and y axis and also quadrants. tables. Identify co-ordinate points A graph is a method used to Plot some examples of co-ordinates. picture data in a clear, interesting and meaningful way. 1- 2 1- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS 4 4 A H 3 3 2 2 1 1 X1 0 X B 0 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 -1 -1 -2 R -2 -3 -3 -4 -4 Use your graph paper to plot coordinates. Plot the points (+3,=4), (-3,+4) (-3,-2), (+3,-2) 1- 2 2- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Bar graphs are used to Name and discuss these graphs below. Make a bar graph showing the types of books the show comparison. students favored. Circle graph are usd to KAREN’S TEST SCORE The chart shows the types of books preferred by show the parts related students in Mr. Smiths’ class. to a whole 100 Line graphs are used to Books No of Students show change over time. 90 Pictograph are very Mystery 10 effective visual tools for 80 showing data. Science Fiction 7 Stem and leaf graph are 70 used to organize data. Comedy 3 60 History 4 50 40 Be sure to : title of graph 0 1 2 3 4 5 6 7 label the horizontal and vertical axes. WEEK accurately graph the data. LINE GRAPH CIRCLE GRAPH 1- 2 3- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Blue fish Caught in Dangriga Look at the circle graph below. III SATURDAY SUNDAY MONDAY TUESDAY (1 fish represent 10) PICTOGRAPH IV Income from Fund Raising What fruit is least likely to be brought in the cafeteria? What fruit is most likely to be bought in the cafeteria? $600 $500 $400 $300 $200 $100 0 Bake Car Craft Yard sale wash fair sale BAR GRAPH 1- 2 4- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS A circle graph shwo parts of V Use the information in the table to complete the line a whole. You can use Stem Leaf graph. decimal or fraction to Then use the graph to answer the questions. divide the circle. To 188 make a circle graph you 0237 Visitors to the Belize Zoo need to find the number 138 of degrees represented 03568 March April May June July by each part. Since 12 there are 3600 in a 90 110 125 100 130 circle, multiply the fraction or decimal for STEM AND LEAF GRAPH 140 each part by 3600. Develop an equivalent chart with pupils. 130 Fraction decimal percent 120 ¼ .25 25% 110 ½ .50 50% 100 ¾ .75 75% etc 90 80 Provide practise in finding percent of 3600. Eg. 75% of 360 0 March April May June July 3 90 eg. 1) The table gives data for 6 months. How many 75 X 360 = 2700 months are shown on your completed line 100 1 graph --------. 4 1- 2 5- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS A frequency distribution Complete the following table below; then draw a circle Make up a table and a circle graph for each of the table shows the number graph for each. following . of times each piece of In a recent election for class president 35% of the data occurs. Fruit Percent Degrees students voted for Arturo, 25% for Pedro, 30% for Anita and 10% for Carlos. A cumulative frequency is Apples 35% 1260 On a form there are 20 horses, 40 cows, 30 hogs and the total frequency of all 30 sheep. scores up to and Peaches 30% 1080 including the score given. Oranges 20% 720 Answer the following questions using the table previously discussed. Pears 15% 540 100% 3600 How many pupils scored 80%? What is the frequency of the score 90? How many pupils scored 80 or less? Use a protractor to determine or divide the pie chart into What is cumulative frequency of 100? etc. degrees. Display results on wall along with chart. 1- 2 6- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Brainstorm in groups what they can recall about the frequency distribution table. Discuss the parts of a distribution table. Pupils test scores. Score Tally Frequency 60 II 2 70 II 2 80 III 3 90 IIII 4 100 I 1 Total 12 Explain cumulative frequency. Discuss the definition of the term average. Explain how to calculate the means of a set of data using the frequency table.ex 1- 2 7- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS The mean or average is the Scores in a Science Test Find the mean of each of the following using the formula sum of a group of discussed. number divided by the Scores Tally Frequency Score Frequency Eg. a) 18, 23, 19, 19, 21 number of addends. Sum of Scores 100 I 1 100 No. of elements Averages can be calculated 90 II 2 180 from a frequency 80 IIII 4 320 18 + 23 + 19 + 19 + 21 = 100 =20 distribution table. 70 IIII I 6 420 5 5 60 IIII 4 240 50 I 1 50 {11, 5, 16, 20, 3} {127, 135, 118, 120, 125, 124, 126} Total 12 960 The Median Game The median is the middle Place cards arranged at random on the chalk board. number in a group of Thus . Means = sum of scores numbers arranged in Number of elements in set 13 10 12 11 10 numerical order. = 960 = 80 When there are two middle 12 numbers the median in the mean of the two Note that when dealing with a lot iof scores, a frequency A volunteer student arranges cards in order from middle numbers. table is used. smallest to largest. Distribute a set of cards with numbers to children. Arrange cards in order from least to greatest 10 10 11 12 13 Find the Central number. Discuss that, that is the median. Student now remove cards simultaneously from each end until only the middle one or two are left. If one remains that is the median. If two remains calculate to find the median. 1- 2 8- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS The mode of a group of Note that if there are two Central numbers, add it and The following is a set of mathematics test scores made numbers is the number find the means. by 20 pupils. that occurs most often. Eg. a) Consider this series of scores: 75, 70, 80, 85, 85, 85, 55 There may be one mode, 13, 14, 17, 19, 25 60, 60, 75, 95, 50, 65, 55 more than one mode, or The median is 17 75, 80, 65, 75, 55, 90 no mode at all. b) 20, 30, 35, 40 30+35 = 65 or 32½ Find the median of the set of scores. Probability can help you 2 Find the mode of the set of scores. predict what the result The median is 32½ Find the mean of the set of scores. of an experiment might be. Have children look up the meaning of mode in their II Conduct a survey to find the weight of pupils in class dictionaries. VI. Skills Write and discuss the definition on the chalkboard. Present a set of data for Steve’s math score on a chart. Arrange the data Draw Eg. { 60,60,70,80,80,90} Analyse data to find means, mode and median of Collect There are two modes 60 and 80. survey. Analyze Enter in Journals. Interpret Brainstorm in groups what probability is. Predict Show what you recall about probability. Use materials to make a spin wheel in groups. Explain Label the sides of a number cube with numbers Eg. Compare 1, 2, 3, 4, 5 and 6. Label Eg. Use cube. How many outcomes are possible? Specify Name each outcome. Conclude Ans. 6 outcomes; 1, 2, 3, 4, 5, 6. Record b) Are al of the outcomes on a number cube equally Demonstrate likely? Tell why or why not. Arrange Identify Survey 1- 2 9- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Observe Ans. Yes each appears on only one equal side of the How many favorable outcomes are there for Calculate cube. How many possible outcomes are there? Discuss Name them. Graph Plot Illustrate Divide Tally Choose Attitudes Understand Participate Responsibility Leadership Independence Co-operation 1- 3 0- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT EL2.a – Respond sensitively and appropriately to auditory and visual New Progress Maths – Rose Anita Mc Donnell stimuli. Certificate Maths – A Greer & C.E. Layne Refresher Maths – Stein EL1.a – Use content clues and cues effectively to communicate when Active Maths – E.A. Guiterrez and other educators. reading orally. Math Advantage – Harcourt Brace Middle Grade Maths – Prentice Hall SL4.a – Interpret simple forms, notes messages, and follow instructions Course I and direction. Heath Mathematics Connections Teacher’s Edition Level 4 EL 3.c – Demonstrate the ability to punctuate and capitalize written Exploring Maths – Scott, Foresman & Company work. Materials WT1.a – Identify a simple problem/need. Graph paper Flash cards EA1.e – Explore and experiment with style, methods and techniques Charts that have been used to create artistic representations. Crayons Markers 1- 3 1- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Data Handling AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: CP1.b Examine information related to the problem/issue. M3b Use and convert money based on its relative value and SP1.b Choose between alternatives based on value. its use in financial transaction. SP2.a Take part in group activities. SP2.e Lead and follow where appropriate. SP2.f Help the group to achieve its goals CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS The value of currencies Make a collection of kinds of foreign currencies (notes, Use checklist to evaluate pupils’ collection of money, fluctuate depending on coins) appearance, organization effort etc. economic situations. Profit or loss is determined Research on and make a chart showing the various Complete a table of foreign exchanges in group. by the selling price. In currencies and their present value. Presentation anfd explanation of table. a profit situation, the selling price equals the Use the rate of exchange to convert foreign currencies Oral group reports on field trip. sum of the cost and the to Belize currency of any amount and vice versa. gain. In a loss Interpretation and analysis of data collected. situation, the selling Field trip to Mexico (Chetumal) or Guatemala (Melchor) price equals the cost Presentation and critique of problems. minus the gain. When Problem solving dealing with the conversion of money. the selling price is Eg. Mom has $150 Bz to buy curtain material in Ability to calculate accurately: profit, loss, selling price, reduced there is a Chetumal. the material cost 60,000 pesos. How much cost price or discount. discount. Bz. dollars does she have after she buys her material? Interview business people. Make a record of types of goods sold cost price and selling price profit or loss discount 1- 3 2- C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS The gain or loss percent is Let children formulate their own problems. Application of formulas to calculate profit, loss and the percentage of the discount percent. cost that the merchant Complex problem solving involving profit and loss. gains or loses when he Eg. Mr. Young sold his boat which cost $3500 at a loss Explanation using appropriate language. sells the article. of $150. How much was it sold for? Accuracy of the rule. The rate of discount is the Revision of formulas Eg. How do you find simple interest. percent taken off the selling price. Using data collected from previous interviews calculate Accuracy of the collection, recording and organization of the profit, loss and discount percent. data. Interest is the money paid Complex problem solving involving profit, loss and Application of formula to calculate simple interest, rate, for the use of money discount percent. time, principal and amount. borrowed or the money Eg. A refrigerator was marked down in price from earned for money that $2490.50 to $1990.60 during a sale. What was the rate Participation, clarity, accuracy of terms. is saved. of discount? Journal entry: Principal is the amount Name and explain the terms which relate to simple formulas borrowed or saved. interest. transaction Rate is a percent charged explanations or offered by the bank. Write a rule to find simple interest, rate, time, principal problem encountered Time is the length of time and amount. the money is borrowed or is in the bank. Allow children to conduct a survey on the interest rates offered or charged at the local banks and credit unions. Compare and contrast the different rates. Problem solving finding simple interest, rate, time, principal and amount using the formulae. Eg. Mr. Flores bought a car for $2790. He paid 1/3 of the cost and borrowed the rest. He paid 10% simple interest on his loan. How much interest did he pay on the loan in one year? - 133 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Commission (C) is the Through brainstorming activity elicit from children the Complete a table by inserting the missing term. amount of money paid meaning of commission and relative terms. Eg. ta an agent for selling (rate/total sales) goods or services. Total Sales Rate of Commission Commission Rate of commission (R) is Role Play the percent of the total Set up a business firm and let children act out roles of $610 30% ? amount of goods or manager and agents. This can be done in groups. ? 6% $396 services sold that is earned Let them formulate rules to find commission rate and $50 ? $6.25 by the agent. total sales. ? 4% $36.80 Total sales (TS) is the total Calculate the total sales made. $7000 ? $525 amount of goods or Decide on the rate of commission. services sold. Calculate to find the commission. C = TS x R Checklist to evaluate presentation, neatness, R = C Problem solving involving commission, rate of organization, relevance, oral expression, appropriate TS commission and total sales language, etc. TS = C Eg. Mr Collins received $1560 to buy merchandise. He R deducted $65 for his commission. What was the rate of commission. Develop questions and conduct interviews. Taxation Record field experiences A tax is a compulsory Group projects and presentation . payment made by citizens Organize groups and have each research on a type of Accuracy of computational skills. to their government . Some tax. types of tax collected in i,e a) definition Belize are: b) reason tax is collected income tax c) who pays taxes land tax d) departments responsible for collecting sales tax e) derivation of tax/ valuation/ rates business tax property tax custom duties social security - 134 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Budgeting is a plan to Have students investigate the sales tax in their Ability to follow instructions. spend money wisely. community. Try to obtain a sales tax table used by Institutions such as the merchants to compute tax and discuss its use. Accuracy of computational skills. family and school develop budgets. The Have students cut out pictures of items from newspaper Construction of budget and thrift in allocation of funds. government also of catalogues. Have them compute the sales tax on develops a yearly these items using their local rates. budget to show how it operates financially. Fill out income tax forms with assistance from income tax personnel. Development of questions constructing interviews . Recording data. Problem solving to calculate taxes. Eg. Construction and accuracy of graph. A home is assessed at $15,800 and the tax is $711. What is the tax rate? Reporting their field experiences. Oral expression. Have students construct personal budget showing how Budget terms often used their allowance is allocated. are income, expenditure, allocation, deficit, surplus Discuss fixed expenses as opposed to varied expenses. assets. Discuss how their budgets might be adjusted to use their money wisely. Brainstorming activity to familiarize students with budgeting terms. Have students research through interviews how government (local/central) operates financially. Construct a circle graph to show income allocations. - 135 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Billing is a note of charges Plan a trip to National Assembly to observe and listen to Oral interpretation and explanation of features. for services rendered. the reading of the budget speech or have them listen to Use of appropriate language. Some bills are: it on national radio and make presentations of particular Name and describe. - Electricity areas. - water - telephone Revision - cable Listing of public services rendered in their community. - grocery Examine old bills. Ratio Discuss the different features on the bill eg. account Collect and analyse. Ratio is the comparison number, service address, billing date, due date,meter Recording, observing, reading and writing skills of two numbers or reading, consumption etc. accuracy of computation of bills group reports. quantities by division. Have groups of students read different metres in their 9. Proportion own homes. Then use the local rates (obtain them from A proportion is a local utility company) to create a fictitious bill for a mathematical sentence week/month of service. which states that two rates are equal. Problem solving involving calculation of utility bills and Ability to calculate means and extremes. A proportion can be grocery bills. Participation direct, indirect or positive. Write problems which require the use of ratio to solve. Eg. On a test with 50 questions, there were 15 fraction problems to the total number of problems on the test? In an indirect or inverse Present proportions. proportion one quantity is Have students identify the means and extremes in decreased as the other is each. increased. Cross multiply to prove that the proportion is true. Team competition to prove whether given ordered pairs are proportions. - 136 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Present scenarios to bring out the concept of indirect proportion. Eg. Form 2 groups; one with 5 pupils and one with 2 pupils. Give eac group 10 biscuits. Have each group eat the biscuit and record the time. Discuss why one group finished before the other. Form a proportion from the scenario and solve. Pupils = time Pupils time 5 pupils = 2 mins 2 pupils x large = large small small Teacher made test to evaluate pupils’ application of 5 pupils = x method to solve indirect proportion problems. 2 pupils 2 mins 5 x 2 = 10 x = 5 mins 2x 2x Problem solving with indirect proportion. - 137 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Partitive Proportion or Present scenario t bring out the concept of partitive Teacher made test to evaluate pupils’ application of proportion by parts is used proportion. method to solve partitive proportion problems. to solve problems Eg. Do the actual sharing of 60 marbles among 3 describing a total amoount boys in the ratio 1:2:3 being distributed into unequal parts. Through questioning develop a method for solving a problem using partitive proportion. 1 part + 2 parts + 3 parts = 6 parts 1/6 + 2/6 + 3/6 = 60 1/6 of 60 = 10 2/6 of 60 = 20 3/6 of 60 = 30/60 problem solving involving partitive proportion. - 138 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT M5a Collect, analyse and interpret data and predict probable Exploring Mathematics outcomes. Teacher edition Bk 7 & 8 SL4.a Interpret simple forms notes, messages and follow instructions New Progress in Arithmetic and directions. Math Power EL1.a Use context clues and cues effectively to communicate when reading orally. Carlong Revision Guide for Junior Math. SL4.b Demonstrate the ability to read using correct punctuation, Active Mathematics intonation and stress. Barons EL4.b Use speed (English) effectively and appropriately in a variety of situations ( for a variety of functional tasks) Progress in Arithmetic H1.b The effects of diet on health. New Common Entrance Mathematics M4.a Make and apply reasonable approximation by observing and/or using factual data base on meaningful references. - 139 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: M1F Apply the concept of rational and irrational numbers to real life situations. CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS A rational number is any Activity: Portfolio – begin a portfolio number which can be Have the students study each number named below and written in the form a/b then match it with the same number in the box at the Ability to identify/recognize rational numbers. where b is not equal to right. zero. Integers, Group Activites Worksheets fractions and decimals ½ 0.01 Eg. ½ = _____ decimal are all rational 1/10 -2.25 numbers. 1/100 0.5 0.5 = _____ fraction Every terminating or -2¼ 0.1 repeating decimal is a 2 4/5 -8/3 checklist for grouping: rational number. -2 2/3 2.8 e.g participation e.g. 0.5 = ½ and 0.3 = -2 1/3 6 2/3 task is completed. 1/3 5 5/3 -7/3 Rational numbers can be Children construct and label numberline using Rational shown on a number numbers. line. Rational numbers can be Cooperate in construction/building of number lines compared by using Remember to insert portfolion entry. a = b a > b a < b - 140 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR ORGANIZED INTO ASSESSMENT MANAGEABLE SETS Fill in the empty boxes with the appropriate rational number to Two to four students can play a guessing game with complete the number line. fractions. The first player should think of a fraction less than 1 with a denominator no greater than 12, I I I I I I I I and write this fraction on a piece of paper. The other -1½ -1 -½ 0 ½ 1 2 player then take turns guessing what the fraction is. If any guess is incorrect, the first player should only 1.5 state that the guess is ‘too’ much or ‘not enough’. All players may use pencil and paper for calculations. Game: Let’s Be Rational The player who guesses correctly takes the place of the first player, and the game continues. -5 -2 -½ -1 -1 1 1 ½ 2 5 6 3 3 6 6 3 3 6 Observation checklist: -1 0 1 Eg. cooperation Participation Listening skills Leadership (show) -1.0-0.9 -0.7-0.5 -0.3 -0.1 0 0.1 0.3 0.5 0.7 0.9 -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0.8 1.0 -7 -¾ -5 -½ -3 - ¼ -1 1 ¼ 3 ½ 5 ¾ 7 8 8 8 8 8 8 8 8 From Start to End, shade a path that always leads to a greaterm number. Materials: Poster 3-2 (on previous page), 23 plain cards for each pair of students. Directions: Give each pair of students 23 plain cards - 141 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS 5. Like real numbers and have them copy the rational numbers shown on the rational numbers can be poster onto the cards. Have them shuffle the card and sequenced or written in deal half the cards to each partner, discarding the extra ascending or descending card. order. Rules: Make sure the students understand the rules: Simultaneously, each player reveals the top card of his or her stack. The player with the card of the larger value takes both cards (refer to poster number line if necesssary). The player who takes the greater number of the cards wins. Children can create problems and share them with a partner. Peer Teaching Activity: Game Materials: 20 index cards marked with different numbers (integerss, fractions or decimals). *only one set of numbers can be used at a time e.g. all integers, all decimals etc. Stack the cads, face down, between two students. Each student selects a card and compares the two numbers. The student with the greater number keeps both cards. After all the cards have been selected, the student with the most cards attempts to sequence all 20 cards. If he/she is unsuccessful, the other player attempts the same. The player who sequences all cards in ascending or descending order first wins the game. - 142 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS 6. To order fractions with Activity Sheets: In small groups, each child will write a fraction on a unlike denominators, find e.g. Write the fractions in order from least to greatest. sheet of paper. Children will order fractions in any the L.C.M. method of their choice ascending or descending. ½ , 3/8, 2/5 order: 3/8, 2/5, ½ 15 16 Use dominoes. Each dominoe represents a fraction 40 e.g. Give one problem on the board and walk around classroom to observe how children are solving the problem. When adding and subtracting fractions Teacher may need to use other methods for slower with unlike children. Activity denominators it is very e.g 3/5 + ½ (Equivalent Fractions) Use these dominoes to make true sentences. convenient to find the change to similiar denominators L.C.M. of denominators. 3/5 (x) ½ x (5) 6/10 + 5/10 = 11/1/ = 1 1/10 Add across and down: 1 ½ 3 ¾ 5 ¼ 1 5/8 2 3/8 When necessary re-arrange numbers to subtract. - 143 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Portfolio entry e.g + + I + II + - 144 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS When multiplying fractions, Multiply across and down. Tip: cancel where Have students write the answer. necessary then X Eg. multiplying the 5/12 4/5 When Pam soled a problem, she wrote the equation numerators and 1/12 – ¾ = ? Ask students to explain why the denominators. 2/5 5/8 equation is wrong. When dividing fractions, we Ans. ¾ is greater than 1/12 keep the fist fraction and multiply it by the Sharing fruits: realia reciprocal of hte 1 ½ apples for 3 people second. Remember Activity can be more challenging by using mixed = 3/2 x 3/1 = 9/2 = 4 ½ apples. cancvelling should be numbers. done before Portfolio Entry multiplication if Workcards with problems necessary. e.g. (a) 2 7/9 ∋ 1 5/6 5 1 5 5/6 ∋ 2 1/3 = 35 x 3 = 5 = 2 /2 Observation checklist: 6 7 2 Eg. steps are followed: 1 mixed numbers are converted to improper fraction cancellations are done Children write steps for solving problem. second number is inverted Children can create acronym or use visual clues (signs) Explain method of solfing problems. Divide across and down. 7/16 7/10 1/6 2/7 - 145 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS In working with complex Rules for solving complex fractions: Journals, Booklets fractions, the rules Solve section with bracket first shoudl be adhered to in Secondly solve section that contain the word ‘of’ Describe and explain method of solving problem. order to solve them Solve multiplication and division section next correctly. Lastly solve addition and subtraction section. Observation checklist e.g. 1. Steps are being completed/rules are followed. B rackets first Children can use the acronym BOMDAS or BODMAS 2. Children are confident in solving problem O f – solved secondly M ultiplication and D ivision next e.g (3 ¾ - ½ ) + ( 1/3 + 3/8) A ddition followed by 3 ¾ x 12/15 ∋ 1 4/5 S ubtraction Step 1 3 ¾ - ½ 3 3 – 2 = 3 ¼ 4 Step 2 Step 3 2. 1/3 + 3/8 3. 3 ¼ + 17/24 8 + 9 = 17 3 6 + 17 = 3 23 24 24 24 24 Step 4 1 3 4. 3 ¾ x 12/15 = 15 x 12 = 3 4 15 1 Step 5 1 3 ∋ 1 4/5 = 3/1 ∋9/5 = 3 x 5 = 5/3 1 9 3 - 146 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS When adding integers with Step 6 Colored Counters or cuisenaire rods can also be used to like signs, the same 3 23/24 ∋ 5/3 = 95 x 3 = 19/8 = 2 3/8 assess. sign is kept in the 24 5 answer. 8 1 Ans: 2 3/8 Bean Bag Toss When adding integers with Teacher throws bean bag, student who catches it will unlike signs the sum solve to give a problem. will take the sign of the integer with the greater observation using the number line +3 + +2 = +5 Use thermometer as example for integers with positive value or (magnitude) and negative values. hence: +2,-5 therefore the answer would be a negative number as 5 I I I I I I I I I I I has the greater value. -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 When subtracting integers, Worksheets the additive inverse Use colored counters or cuisenaire rods. Different Observation checklist: method can be used. colors represent positive & negative : Use to add Eg. children are following This method is effective integers. for subtracting like and Portfolio entry unlike signs. Use number Iine Mnemonic or jingle competition based on rules In multiplication when the (children’s creativity) signs are the same, the Learning number ladder. result is always positive. +4 When multiplying integers Integer +3 with unlike signs, the Ladder +2 result is always +1 negative. 0 -1 -2 -3 -4 - 147 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS When dividing integers with Eg. -2 - -3 reverse problem Mnemonics like signs, the result is -3 + __ = -2 Worksheets always positive. Begin with the second term. Observation checklist When dividing integers with Eg. Rule: unlike signs, the result (+) x (+) = (+) Family Budget reports shoplist is always negative +3 x +3 = +9 Journal of children’s expenses per day. In the addition of decimals, (-) x (-) = (+) the decimal points are -3 x –3 = +9 Portfolio Entry always aligned. Pair and solve : children create problems and ask partners to solve. Eg. Rule (-) x (+) = (-) -3x +3 = -3 eg. Rule: (+) ∋ (+) =(+) (-) ∋ (-) = (-) (-)∋ (+) = (-) Children create jingle or rhyme to remember rules.(mnemonics) Eg. .23 .458 69.51 - 148 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS In the subtraction of Income and Expenditure Reports The decimal pyramid decimals, the decimals Write decimal from the box in the circles. The sum of are always aligned. School Profits Per Week each side showed equal 20.5. Expenses Mon Tues Wednes Thurs Fri Total 1.73 Meatpies $33.25 $50 $23.75 $20 $62.25 ? 3 5.45 Ideals $6.25 $5.23 $0.75 $10 $1.75 ? 1.6 4.75 When decimals are Chips $7.00 $5.80 $10.50 $9.85 $11.00 ? multiplied, the decimal in the product is placed Total for Week ? according to the number of factors that Subtraction Machine follow the decimal point. This is placed in the In Out answer counting from Subtract the right to the left. 0.3 e.g. 2.05 2 decimal places x 0.31 2 decimal places 205 worked as whole numbers 000___ 0.6355 decimal placed now included - 149 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS 21. When dividing Game: Multi – Spin Worksheets/Journal Entries decimals, make the divisor Portfolio entries a whole number. The same 0.07 0.45 0.009 0.16 number of places moved in A Product Trick the divisor should be the same number of places moved in the dividend. Add 3.75 12 1.5 18 0.375 zero when necessary. 0.125 0.4 0.05 0.6 0.0125 0.25 0.8 0.1 1.2 0.025 0.46 2.74 0.062 1.4 1.25 4 0.5 6 0.125 0.01 0.032 0.004 0.048 0.001 Have a volunteer spin the arrow and call out the product of the two numbers indicated. The first student to give Follow these steps the correct answer earns one point and becomes the Ring any number in figure1 next caller. Cross out all other numbers in the same row and column as the ringed numbers. Repeat step 2 and 3 until you have ringed five numbers and crossed out all other numbers. Find the product of the five ringed numbers. - 150 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS 22. A decimal is another Divi –Snake Portfolio Entry way to name a fraction Materials : a piece of tagboard, marked as shown, or a mixed number. stopwatch Observation checklist Whole number places are to the left of the Report decimal point. Decimal places are to the right. Technology – use calculator to show different place Decimals can be shown 0.06) 31.8 0.23) 581.9 value and map on number line. Teacher gives on a place value chart. number line with some numbers missing and children will insert missing digits using a calculator. When changing a fraction to a decimal, Portfolio Entry divide the numerator by the denominator. When changing a 0.34) 1.7 3.8) 0.19 Fraction Decimal Percent decimal to a percent move the decimal place ¼ two places to the right. 0.5 57.5% 0.036) 0.09 0.375 Have students time themselves individually to see who 7/20 can go from START to FINISH most quickly. - 151 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS To change from a percent Activity : Portfolio Entry to a decimal move two The Pizza Hut is having a contest. Brandon can get a Observation Checklist places from the right to bargain pizza if he finds the row where all three left. Make the numbers are equivalent. Which row should Brandon Fractions and Repeating Decimal Pictures decimals to a fraction pick? In the diagram below, the decimal for each fraction has and cancel when A ¼ 0.25 2/5 exactly one digit that repeats. necessary. B 1/5 0.20 2/10 Repeating decimals are C 2/4 0.50 6/10 If the repeating digit is even, shade the square for that decimals that repeat D 8/10 0.40 4/5 fraction. endlessly in a quotient. If the repeating digit is odd, do not shade the square for A bar over the last digit 0.2 5 that fraction. When you have finished, the shaded is used to indicate Eg. ¼ 4) 1.020 ans: 0.25 squares should form another name for 1. repitition. Rational numbers can be Eg. 0.2 . 5 = 25% used in problems featuring real life Eg. 80% = .8 . 0 . = 0.8 situations. Eg.0.8 = 8 4 = 4 10 5 5 Worksheets: 50% of MAKE is = MA 37½% of MATERIALS = MAT 5.66 Eg. 17/3 = 5.6 3 )17. 0 0 15 2 0 1 8 2 0 1 8 2 - 152 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Worksheets Brownies for all Children create examples and share with a partner. Vanilla Brownies Carrie used 1 1/8 yd of a 2 5/16 yd. length of material to cups sugar make a backpack. How much materials left? tbsp baking powder ¼ cup melted butter Children can bring in recipes of their own. 4 eggs, beaten 2 cups milk Eg. The temperature at dawn was 160C. By noon it had 4 cups flour risen 60C. It fell 80 from noon until sunset. What was 1 tbsp vanilla the temperature at sunset? _300 Combine the sugar and eggs in one bowl and beat. Combine the flour and baking powder in another bowl. Alternate adding some of the dry mixture and some of noon _200 ___ ___ the milk to the sugar mixture. Stir after each addition. dawn _160 + 60 -80 Add the butter and the vanilla. Spoon the mixture into sunset muffin papers. Bake at 4000F for about 20 mins. _100 Suppose you need muffins for 30 people. How would you change the recipe to feed everyone? _00 To find out how to change the recipe to make exactly 30 muffins, divide 30 by 24. Convert the answer to a fraction (30 ∋ 24 = 1 ¼ ) Multiply each of the ingredients by the number from Step 2, and rewrite the recipe. Be sure to write that it now makes 30 muffins. - 153 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS To find perfect squares, the Eg. Jamaal, Rosa and Stacey collected a total of 95.73 Portfolio Entry root is multiplied by pounds of garbage from the beach side. What was the Cooperative group work itself. average amount collected by each person? Reports The square root of a number is one of its Children can create a table of Perfect Squares for easy two equal factors. To Root Perfect Squares referece. find the square root of 1 x 1 = 1 smaller numbers, the 2 x 2 = 4 Portfolio Entry factor method is very 3 x 3 = 9 effective. However, to 4 x 4 = 16 Journal/Portfolio entry find the square root of 5 x 5 = 25 larger number 6 x 6 = 36 Visual organizers to show steps. (5digits+), the pair and 7 x 7 = 49 divide method can be 8 x 8 = 64 Observation checklist to ensure that children are used. 9 x 9 = 81 completing and applying steps. 10 x 10 = 100 Factor method 484 Step 1 484 = 2 x2 x 2 = 2 x 2 x 121 Portfolio Entries = 2 x 2 x 11 x 11 Observation Step 2 = (2 x 11) x (2 x 11) Checklist = 22 x 22 Step 3 = 222 Therefore, 484 = 22 Worksheets Cooperative Learning - 154 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Factor Method 484 2 484 2 2 242 2 x 11 = 22 11 121 11 11 11 1 Large Numbers 4 Step Method Step 1 Mark off the number in periods of 2 beginning from units place and going toward the left. The left hand period may contain either one or two digits; the other periods must contain 2. 29’ 16 Step2 Find the number which when squared is nearest to, but not more than, the first period to the left. In this case it is 5 because 5 x5 = 25 5 29’16 25 416 - 155 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Step 3 Double the root already found (2 x 5) and use it as a trial divisor, leaving room for another figure to be inserted to the right of 10. The whole divisor will be one hundred something. Divide 41 by 10 = 4 5 29’16 25 IC 416 Step 4 There are three things to do with this 4 Place it above 6 as the second figure of the root. Place it to the right of 10 making 104 the real divisor. Multiply 104 by 4 104 x 4 = 416 Write 416 under 416 and subtract To check multiply 54 by 54 4 29’ 16 25 416 x4 416 - - - Problem Solving: A contains 256 square . What is the legnthof its side? What is the perimeter. - 156 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money LINKAGES/CONNECTIONS RECOMMENDED RESOURCES: TEACHER/STUDENT Exploring Mathematics BK 7 & 8 Math Advantage Heath Mathematics Vol 1 & 2 Active Mathematics Progress Grade 7 & 8 New & Old Editions Mathematics Today Math Advantage Home/School Connection Today’s Mathematics - 157 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money AREA OF STUDY OUTCOMES CROSS-CURRICULAR OUTCOMES Pupils should: M1F Apply the concept of rational and irrational numbers to real life situation CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Rational numbers can be Children recall rational numbers: eg. Integers Describe and explain features of Rational Numbers compared by using Decimals (Report). a = b Fractions Math Logs a > b Refer to games in Std 5. a < b Game: Let’s Be Rational Worksheets Math Logs Like real numbers rational e.g. ¼ < 1/8 Games numbers can be sequenced or written in Games: Log Entry ascending or Children can create games using sequencing of Children can create worksheets on their own. descending order. numbers. Dominoe Game To order fractions with Worksheets: unlike denominators, 3/5, 5/8, 2/3 find the L.C.M. 72, 75, 80 120 Greatest to least: When adding and 80, 75, 72 subtracting fractions 2/3, 5/8, 3/5 with unlike denominators it is very convenient to find the L.C.M. of denominators - 158 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS When multiplying fractions, Two Methods: Math Log. cancel where L.C.M. necessary then Equivalent Fractions Observation checklist: multiplying the Magic boxes. Steps are being followed. numerators and Cancellations are done. denominators. Magic Squares When dividing fractions, we Relia – sharing fruits keep the fist fraction Refer to Std 5. and multiply it by the reciprocal of hte Workcards with problems: second. Remember Acronyms Math Log. cancelling should be Rhymes done before multiplication if Observation checklist necessary. Have children follow the rules for solving complex Children are confident in solving problems. fractions. Steps are being followed. In working with complex fractions, the rules Refers to rules Std 6. Bean Bag Toss. should be adhered to in order to solve them Use of the number lines. Thermometer. correctly. Use colored counters or cuisenaire rods BOMDAS, BODMAS – Number ladder. Acronyms When adding integers with like signs, the same sign is kept in the answer - 159 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS When adding integers with Number line Colored Counters. unlike signs the sum Number ladder will take the sign of the integer with the greater value or (magnitude) hence: +2,-5 therefore the answer would be a negative number as 5 has the greater value. When subtracting integers, the additive inverse E.g. -2 - - 3 reverse problems Observation method can be used. -3 + ___ = -2 Checklist This method is effective for subtracting like and unlike signs. In multiplication when the signs are the same, the Rule: Observation checklist result is always (+) x (+) = (+) positive. (-) x (-) = (+) Math Log When multiplying integers Pairing /Cooperative Learning with unlike signs, the Rule: result is always (-) x (+) – (-) Mnemonics negative. Refer to Std 5 When dividing integers with Unit of Work unlike signs, the result (-) ∋ (+) = (-) is always negative. - 160 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS When dividing integers with (+) ∋ (+) = (+) Family Budgets like signs, the result is (-) ∋ (-) = (-) Reports always positive. Shoplists In the addition of decimals, E.g. .23 Journals the decimal points are .458 always aligned. 69.51 In the subtraction of Refer to Std 5 decimals, the decimals Have children create reports and expenditure The decimal pyramid. are always aligned. statements. When decimals are multiplied, the decimal Refer to Std 5 in the product is placed Subtraction machine according to the number of factors that Refer to Std 5 unit of work: follow the decimal point. Games: Multi Span This is placed in the answer counting from the right to the left. When dividing decimals, make the divisor a whole number. The same number of places Game: Divi Snake Math Log moved in the divisor Refer to Std 5 Unit of Work Observation checklist should be the same number of places moved in the dividend. Add zero when necessary. - 161 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS 19. A decimal is another Activity: Technology way to name a fraction Refer to Std V Unit of Work Refer to Std. 5 unit of work or a mixed number. Whole number places Portfolio Entry are to the left of the decimal point. Decimal places are to the right. Decimals can be shown on a place value chart. 0.25 20. When changing a E.g. ¼ 4 1.00 Ans. 0.25 fraction to a decimal, divide the numerator by E.g. 0.2 . 5 . = 25% the denominator. When changing a decimal to a percent move the decimal place two places to the right. 21. To change from a E.g. 80% = . 8 . 0 . = 0.8 Portfolio Entry percent to a decimal Observation Checklist move two places from E.g. 0.8 = 8 4 = 4 the right to left. Make 10 5 5 the decimals to a fraction and cancel Worksheets: when necessary. 1) 50% of MAKE = MA - 162 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Repeating decimals Fractions and Repeating are decimals that repeat E.g. 17 = 5.6 Decimals Pictures endlessly in a quotient. 3 5 . . 6 6 Refer to Std V unit of work. A bar over the last digit 3) 17. 0 0 is used to indicate 15 repitition. Rational numbers can 2 0 Brownies for all be used in problems 1 8 Refer to Std V unit of work. featuring real life 2 0 situations. 1 8 Portfolio entry To find perfect squares, 2 Reports the root is multiplied by Worksheets Co-operative group work itself. Children can create examples and share with partner. The square root of a Children can bring in recipes of their own. Children can create a table of Perfect Squares for easy number is one of its two Eg. The temperature at dawn was 160C. By noon it had reference. equal factors. To find risen 60C. It fell 80 from noon until sunset. What was Portfolio Entry the square root of the temperature at sunset? smaller numbers, the Journal/Portfolio entry factor method is very Root Perfect Square Visual organizers to show steps effective. However, to Observation checklist to ensure that children are find the square root of 1 x 1 = 1 completing and applying steps. larger number 2 x 2 = 4 (5digits+), the pair and 3 x 3 = 9 divide method can be 4 x 4 = 16 used. 5 x 5 = 25 6 x 6 = 36 factor Method refer to Std V unit of work Worksheets Co-operative Learning Large Number Method Refer to Std V unit of work - 163 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Skills Interpret Manipulate Observing Discussing Comparing Identifying Estimating Explain Distinguish Ordering Computing Solving Organizing Reading Writing Analyze Apply Recognize Examine Matching - 164 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc AREA OF STUDY: Mathematics STANDARD VI UNIT/THEME: Money CONTENT ORGANIZED SUGGESTED TEACHING/LEARNING STRATEGIES SUGGESTED STRATEGIES/ACTIVITIES FOR INTO MANAGEABLE ASSESSMENT SETS Attitudes Co-operation Sense of Achievement Tolerance Understand the importance of using the mathematical rules Appreciation and respect for one another’s ideas Awareness - 165 - C:\Documents and Settings\NORA\My Documents\Upper Nelson\MATH Upper Division1.doc