Grade 7 Math Unit 5

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    Grade 7 Mathematics Curriculum Outcomes 159Outcomes with Achievement Indicators

    Unit 5

    Grade 7 Mathematics

    Unit 5

    Operations with Fractions

    Estimated Time: 24 Hours

    [C] Communication [PS] Problem Solving[CN] Connections [R] Reasoning

    [ME] Mental Mathematics [T] Technology

    and Estimation [V] Visualization

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    Grade 7 Mathematics Curriculum Outcomes 160Outcomes with Achievement Indicators

    Unit 5

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    Unit 5: Operations with Fractions

    Grade 7 Math Curriculum Guide 161

    Unit 5 Overview

    Introduction

    Students will focus on developing skills and understanding the addition and subtraction of fractions. The

    big ideas in this unit are:

    Equivalent fractions represent the same quantities. The concept of equivalent fractions is very useful when comparing, ordering, simplifying, and

    operating with fractions.

    The use of manipulatives such as fraction strips and fraction circles, number lines, and patternblocks is an effective way to model the addition and subtraction of fractions. It creates aconcrete base for a traditionally difficult concept.

    Addition and subtraction of fractions requires common denominators. Estimation strategies for these two operations are based on using benchmarks like 0,

    4

    3,

    2

    1,

    4

    1etc.

    Context

    The students will model, using manipulatives, the addition and subtraction of fractions. They will be

    encouraged to informally generalize rules for these operations that are based on their investigations.

    Through the use of these investigations, and guidance from the teacher, the students will discover the need

    to use common denominators when adding, subtracting, comparing and ordering fractions.

    They will discover the algorithm for adding and subtracting fractions. Once again estimation will play animportant role in helping students to decide if their answers are sensible. The students will then apply

    these algorithms to adding and subtracting mixed numbers.

    Why are these concepts important?

    Developing a good understanding of adding and subtracting fractions will permit students to:

    Understand real-life situations that require fractions such as;The clock ("a quarter 'till").

    Electricians (gauge/length of wires).

    Plumbing (thickness of pipe, diameter of pipe, length of pipe).Carpenters (thickness/length/width of wood).

    Engineers (just math equations).Metal fabrication (length/width/gauge of metal).

    Taxes/budgeting (obvious math involved).

    Cooking (measurements like HALF a cup...).

    In your car (km PER hour, km PER liter).

    Paying for things in general (1 penny is 1/100 of a dollar, writing out checks.)

    Be ready to learn and understand future topics in math such as algebra and proportions.It isn't that they can't see the solution. It is that they cant see the problem.

    G. K. Chesterton (1874 1936)

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 162

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Specific Outcome

    It is expected that students will:7N5. Demonstrate an

    understanding of adding

    and subtracting positive

    fractions and mixed

    numbers, with like and

    unlike denominators,

    concretely, pictorially and

    symbolically (limited to

    positive sums and

    differences).

    [C, CN, ME, PS, R, V]

    Achievement Indicators

    Elaborations: Suggested Learning and Teaching Strategies

    Lesson 5.1 in the student text briefly models like fractionsusing pattern blocks, clocks and fraction circles. It primarilydemonstrates like denominators, but includes some examples

    in which one of the denominators is a simple multiple of theother. Teachers will need to model several more examples

    using these manipulatives in order to ensure studentunderstanding. Students should also have the opportunity to

    model using the manipulatives since they are hands-onexperiences.

    Lesson 5.2 uses fraction strips and number lines to support the

    same indicators. Students should be able to use the models tounderstand fractional equivalents and how they can be useful

    when adding fractions and changing them to their simplestform.

    Using the fractions strips and number line masters in the

    ProGuide pp. 6467, students will combine both the fractionstrips and number lines to model sums and to illustrate the

    concept of common denominators.

    7N5.2 Determine the sumof two given positive

    fractions with like

    denominators.

    7N5.1 Model addition of

    positive fractions, usingconcrete representations,

    and record symbolically.

    7N5.3 Determine acommon denominator for

    a given set of positivefractions.

    7N5.4 Simplify a givenpositive fraction byidentifying the common

    factor between thenumerator and

    denominator.

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 163

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Suggested Assessment Strategies

    Pencil and Paper

    Write an addition sentence to represent the total fraction of each

    hexagon that is shaded. Use an addition sentence to find the totalvalue of the shaded hexagons in each case.

    A.

    B.

    C.

    Informal Observation

    An alternative, but similar activity would be to create cards with

    addition sentences and their equivalents in pattern blocks as used inthe Pencil and Paperexercise above. Each student would receive a

    card with either the addition sentence, or the pattern blockrepresentation. They mix-up and match-up within the class to findtheir partner. Each group must then explain to another group, or to

    their class, why they belong together.

    Resources/Notes

    The national library of

    virtual manipulativesprovides an interesting

    activity on adding usingcommon denominators

    with various models athttp://nlvm.usu.edu/en/na

    v/frames_asid_106_g_3_t_1.html?from=category_

    g_3_t_1.html

    Math Makes Sense 7

    Lesson 5.1

    Lesson 5.2

    Unit 5: Operations withFractions

    TR: ProGuide, pp. 46 &pp. 711

    Master 5.13, 5.18, 5.27Master 5.10, 5.11, 5.14,

    5.15, 5.16, 5.17, 5.19,5.28

    PM 28, PM 25CD-ROM Unit 5 Masters

    ST: pp. 178180

    ST: pp. 181185

    Practice and HW Bookpp. 106108

    pp. 109111

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 164

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Specific Outcome

    It is expected that students will:7N5. Demonstrate an

    understanding of adding

    and subtracting positive

    fractions and mixed

    numbers, with like and

    unlike denominators,

    concretely, pictorially and

    symbolically (limited to

    positive sums and

    differences).

    [C, CN, ME, PS, R, V]

    (Contd)

    Achievement Indicators

    Elaborations: Suggested Learning and Teaching Strategies

    In the previous lessons, students used models to add using likedenominators. They also modelled unlike denominators when

    one denominator was a multiple of the other.

    Lesson 5.3 develops the addition algorithm for fractions.The addition of fractions with unlike denominators that are not

    simple multiples of each other will require students to multiplythe numerator and denominator of each fraction by the same

    number. Example:

    Ideally, students should use the Least Common Multiple(LCM) of the unlike denominators.

    Through the use of benchmarks (close to1

    0, ,12 ) developed in

    Unit 3, students will estimate the solution and use their

    estimate to verify the reasonableness of the answer obtainedusing the algorithm.

    (This elaboration is continued on the next two page spread)

    7N5.5 Model addition of

    positive fractions withunlike denominators,

    using concreterepresentations, and

    record symbolically.

    7N5.6 Determine the sumof two given positive

    fractions with unlikedenominators.

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 165

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Suggested Assessment Strategies

    Pencil and Paper

    1. Create three addition sentences that give the same sum as6 3

    12 12+ . You cannot use like denominators in the sentences

    you create.

    2. Magic square. The sum of each row, column and diagonal inthis magic square must equal 1. Find the missing values.

    Magic Square Solution

    512

    7

    12

    1

    3

    1

    4

    16

    512

    512

    7

    12

    1

    3

    1

    12

    1

    4

    1

    4

    1

    2

    3. A tangram is a square puzzle that is divided into seven shapes.A. Suppose piece A is 1

    4

    . What are the values of pieces B, C,

    D, E, F and G?

    B. What is the sum of A and B?C. If you subtract D from the whole puzzle, what value

    remains?D. Which two tangram pieces add up to the value of C?E. Invent a problem on your own and solve it.

    Resources/Notes

    Math Makes Sense 7

    Lesson 5.3

    Unit 5: Operations withFractions

    TR: ProGuide, pp. 1215Master 5.14, 5.15, 5.16,

    5.17, 5.20, 5.29PM 27

    CD-ROM Unit 5 Masters

    ST: pp. 186189

    Practice and HW Book

    pp. 112114

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 166

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Specific Outcome

    It is expected that students will:7N5. Demonstrate an

    understanding of adding

    and subtracting positive

    fractions and mixed

    numbers, with like and

    unlike denominators,

    concretely, pictorially and

    symbolically (limited to

    positive sums and

    differences).

    [C, CN, ME, PS, R, V]

    (Contd)

    Achievement Indicators

    Elaborations: Suggested Learning and Teaching Strategies

    Here is another example of adding fractions with unlikedenominators.

    Find the sum of the fractions:

    6

    1

    4

    3+

    Students should think4

    3is a little bit more than a half and

    6

    1is

    less than a half so the answer should be close to 1. Then they

    can use the previous algorithm to calculate:

    12

    11

    12

    2

    12

    9

    2

    2

    6

    1

    3

    3

    4

    3

    6

    1

    4

    3

    =

    +=

    +=

    +

    Finally, they should look at their answer and ask themselves if

    12

    11is reasonable based on their estimate of 1.

    Note: When a common denominator must be found, thecommon denominator that is chosen should be the lowest

    common denominator. Simply multiplying the denominatorsof the fractions being adding or subtracted willnot guarantee a

    lowest common denominator. The lowest common

    denominator for6

    1

    4

    3+ is 12, not 24.

    7N5.5 Model addition of

    positive fractions withunlike denominators,

    using concreterepresentations, and

    record symbolically.

    (continued)

    7N5.6 Determine the sumof two given positive

    fractions with unlikedenominators.

    (continued)

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 167

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Suggested Assessment Strategies

    Performance

    Use pattern blocks to create a design on triangular grid paper

    (Program Master 27). Then use fraction addition to name thedesign. Consider the flower design illustrated in Appendix 5-A. It is

    possible to use several different addition sentences to name thesame design.

    Journal

    1. If a problem required you to add fourths and thirds, is itpossible for the sum to be sixths? Why or why not? You may

    use an example or a diagram to help you explain your answer.

    2. If a problem required you to add fourths and thirds, is itpossible for the sum to be sevenths? Why or why not? You may

    use an example or a diagram to help you explain your answer.

    Interview

    A classmate missed yesterdays class. When solving a problem

    today he suggested that5 5 10

    6 8 14+ = . How would you convince him

    that this is not a reasonable solution?

    Game/Activity

    Refer to Appendix 5-B for the Connect Three game.

    Resources/Notes

    Math Makes Sense 7

    Lesson 5.3

    (continued)

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 168

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Specific Outcome

    It is expected that students will:7N5. Demonstrate an

    understanding of adding

    and subtracting positive

    fractions and mixed

    numbers, with like and

    unlike denominators,

    concretely, pictorially and

    symbolically (limited to

    positive sums and

    differences).

    [C, CN, ME, PS, R, V]

    (Contd)

    Achievement Indicators

    Elaborations: Suggested Learning and Teaching Strategies

    Lesson 5.4 of the student text begins with subtractioninvolving unlike denominators using pattern blocks. Students

    will learn that addition and subtraction of fractions with unlikedenominators uses the same algorithm. Teachers may wish to

    model several examples using fraction circles or fractionstrips.

    For example:4 1

    5 5

    In this case, students must understand that they are simplyremoving one part of a set of equivalent quantities. This can be

    demonstrated by modelling 45

    using fraction strips or fraction

    circles and removing one portion representing1

    5. The answer

    is the remaining portion of3

    5.

    The subtraction of fractions with unlike denominators that arenot simple multiples of each other will require students to

    multiply the numerator and denominator of each fraction bythe same number. This is identical to the algorithm used for

    addition.

    Ideally, students should use the Least Common Multiple(LCM) of the unlike denominators.

    Through the use of benchmarks (close to 10, ,12

    ) developed in

    Unit 3, students will estimate the solution and use theirestimate to verify the reasonableness of the answer obtained

    using the algorithm.

    (This elaboration is continued on the next two page spread)

    7N5.7 Model subtraction

    of positive fractions, usingconcrete representations,

    and record symbolically.

    7N5.8 Determine thedifference of two given

    positive fractions with like

    denominators.

    7N5.9 Determine the

    difference of two given

    positive fractions withunlike denominators.

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 169

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Suggested Assessment Strategies

    Observation

    Ask students to use concrete materials or diagrams to show why the

    following is an incorrect procedure.

    3 1 3 1 2 1

    8 4 8 4 4 2

    = = =

    Informal Observation

    Students can play the game Tic-Tac-Toe Fractions. A really useful

    game for adding and subtracting fractions. See ProGuide (Page V)and Master 5.8a, 5.8b and 5.8c.

    Resources/Notes

    Math Makes Sense 7

    Lesson 5.4

    Lesson 5.5

    Unit 5: Operations withFractions

    TR: ProGuide, pp. 1720& pp. 2124

    Master 5.12, 5.14, 5.15,5.16, 5.17, 5.21, 5.30

    Master 5.14, 5.15, 5.16,5.17, 5.22, 5.31

    CD-ROM Unit 5 Masters

    ST: pp. 191194

    ST: pp. 195198

    Practice and HW Book

    pp. 115117pp. 118120

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 170

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Specific Outcome

    It is expected that students will:7N5. Demonstrate an

    understanding of adding

    and subtracting positive

    fractions and mixed

    numbers, with like and

    unlike denominators,

    concretely, pictorially and

    symbolically (limited to

    positive sums and

    differences).

    [C, CN, ME, PS, R, V]

    (Contd)

    Achievement Indicators

    Elaborations: Suggested Learning and Teaching Strategies

    Find the difference of the fractions:

    3

    1

    9

    4

    Students should think9

    4is a little bit less than a half and

    3

    1is

    a little less than a half. The difference between them shouldtherefore be almost 0 or just a little bit more than 0.

    9

    1

    9

    34

    9

    3

    9

    4

    3

    3

    3

    1

    9

    4

    3

    1

    9

    4

    =

    =

    =

    =

    Finally, they should look at their answer and ask themselves if

    9

    1is reasonable based on their estimate of something a little

    bit more than 0.

    7N5.7 Model subtraction

    of positive fractions, usingconcrete representations,

    and record symbolically.

    (continued)

    7N5.8 Determine thedifference of two given

    positive fractions with likedenominators.

    (continued)

    7N5.9 Determine the

    difference of two given

    positive fractions withunlike denominators.

    (continued)

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 171

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Suggested Assessment Strategies Resources/Notes

    Math Makes Sense 7

    Lesson 5.4

    Lesson 5.5

    (continued)

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 172

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Specific Outcome

    It is expected that students will:7N5. Demonstrate an

    understanding of adding

    and subtracting positive

    fractions and mixed

    numbers, with like and

    unlike denominators,

    concretely, pictorially and

    symbolically (limited to

    positive sums and

    differences).

    [C, CN, ME, PS, R, V](Contd)

    Achievement Indicators

    Elaborations: Suggested Learning and Teaching Strategies

    Now that the models for addition and subtraction have beenstudied separately by the students, the same models and skills

    can now be used in the study of mixed fractions.

    Lessons 5.6 and 5.7 explore the subtraction of mixed numbersusing fraction circles, number lines and fraction strips. Lesson

    5.7 also introduces Cuisenaire rods as a model for subtractingmixed fractions. Teachers may consult the link for use of this

    model in the resource section of this guide.

    When adding and subtracting mixed fractions students mayapproach the problem in different ways. They may choose to

    keep the mixed fraction form or, they may change the mixedfractions to improper fractions.

    For addition:

    Mixed Fraction Form Improper Fraction Form

    18

    13

    18112

    18

    192

    18

    151

    18

    41

    3

    3

    6

    51

    2

    2

    9

    21

    6

    51

    9

    21

    =

    =

    =

    +=

    +=

    +

    and

    18

    13

    ...54,36,181855

    18

    33

    18

    22

    3

    3

    6

    11

    2

    2

    9

    11

    6

    11

    9

    11

    6

    51

    9

    21

    =

    =

    +=

    +=

    +=

    +

    (This elaboration is continued on the next two page spread)

    7N5.11 Determine the

    sum or difference of twomixed numbers with like

    denominators.

    7N5.10 Model additionand subtraction of mixed

    numbers with likedenominators, using

    concrete representations,and record symbolically.

    7N5.12 Model additionand subtraction of mixed

    numbers with unlikedenominators, using

    concrete representations,

    and record symbolically.

    7N5.13 Determine the

    sum and difference of twomixed numbers with

    unlike denominators.

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 173

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Suggested Assessment Strategies

    Interview

    Consider the following two problems:3

    14

    and3

    110

    Without calculating, explain how you could determine which

    answer would be greater.

    Journal

    Describe at least two ways you can calculate1 5

    22 6 .

    Resources/Notes

    An introduction to

    Cuisenaire rods and theiruse in the study of

    fractions can be found athttp://teachertech.rice.ed

    u/Participants/silha/Lessons/cuisen2.html

    Math Makes Sense 7

    Lesson 5.6

    Lesson 5.7

    Unit 5: Operations withFractions

    TR: ProGuide, pp. 2529& pp. 3034

    Master 5.13, 5.14, 5.15,5.16, 5.17, 5.23, 5.32

    Master 5.13, 5.14, 5.15,5.16, 5.17, 5.24, 5.33

    PM 28CD-ROM Unit 5 Masters

    ST: pp. 199203

    ST: pp. 204208

    Practice and HW Bookpp. 121122

    pp. 123124

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 174

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Specific Outcome

    It is expected that students will:7N5. Demonstrate an

    understanding of adding

    and subtracting positive

    fractions and mixed

    numbers, with like and

    unlike denominators,

    concretely, pictorially and

    symbolically (limited to

    positive sums and

    differences).

    [C, CN, ME, PS, R, V](Contd)

    Achievement Indicators

    (All Contd)

    Elaborations: Suggested Learning and Teaching Strategies

    For subtraction:

    Mixed Fraction Form Improper Fraction Form

    21

    141

    21

    122

    7

    7

    3

    21

    3

    3

    7

    42

    3

    21

    7

    42

    =

    =

    Students will be challengedby 1214 and therefore mustthink about regrouping.

    Students should think:

    21

    141

    21

    12

    21

    211 andand

    which will allow them to

    calculate:

    21

    19

    21

    141

    21

    331

    =

    21

    19

    2135

    2154

    7

    7

    3

    5

    3

    3

    7

    18

    3

    5

    7

    18

    3

    21

    7

    42

    =

    =

    =

    =

    7N5.11 Determine thesum or difference of twomixed numbers with like

    denominators.

    7N5.10 Model addition

    and subtraction of mixednumbers with like

    denominators, usingconcrete representations,

    and record symbolically.

    7N5.12 Model additionand subtraction of mixed

    numbers with unlikedenominators, using

    concrete representations,and record symbolically.

    7N5.13 Determine thesum and difference of two

    mixed numbers withunlike denominators.

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 175

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Suggested Assessment Strategies Resources/Notes

    An introduction to

    Cuisenaire rods and theiruse in the study of

    fractions can be found athttp://teachertech.rice.ed

    u/Participants/silha/Lessons/cuisen2.html

    Math Makes Sense 7

    Lesson 5.6

    Lesson 5.7

    (continued)

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 176

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Specific Outcome

    It is expected that students will:7N5. Demonstrate an

    understanding of adding

    and subtracting positive

    fractions and mixed

    numbers, with like and

    unlike denominators,

    concretely, pictorially and

    symbolically (limited to

    positive sums and

    differences).

    [C, CN, ME, PS, R, V]

    (Contd)

    Achievement Indicators

    Elaborations: Suggested Learning and Teaching Strategies

    Throughout the sections on adding and subtracting fractions, itis necessary for students to simplify their answers. Simplified

    answers may be proper fractions, improper fractions or mixednumbers in simplest form depending on the context of the

    problem.

    Example: Kyra is making cookies. She has1

    24

    bags of

    chocolate chips. She adds2

    13

    of these bags to her cookie

    dough.

    a) What fraction of the total amount of chocolate chips is left?

    b) Kyra then decides to add11

    12bags of butterscotch chips to

    the dough as well. How many bags of chips does Kyra use intotal to bake her cookies?

    For part a), students should think 1

    24

    bags is a little more

    than two bags. Kyra then uses2

    13

    bags which is a little less

    than two bags. Therefore she has two little bits or about half a

    bag left over.Then they calculate:

    127

    12

    20

    12

    27

    4

    4

    3

    5

    3

    3

    4

    9

    3

    5

    4

    9

    3

    21

    4

    12

    =

    =

    =

    =

    Kyra has7

    12of a bag of

    chocolate chips left.

    Students must reflectupon their answer to

    determine if it isreasonable.

    In this case, seven

    twelfths is very close to ahalf.

    (This elaboration is continued on the next two page spread)

    7N5.14 Simplify the

    solution to a givenproblem involving the

    sum or difference of twopositive fractions or

    mixed numbers.

    7N5.15 Solve a given

    problem involving theaddition or subtraction of

    positive fractions ormixed numbers, and

    determine if the solution isreasonable.

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 177

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Suggested Assessment Strategies

    Journal

    Is it possible to find two mixed numbers which add together to form

    a whole number?Explain your answer and, if possible, give an example to support

    your explanation.

    Pencil and Paper

    1. Andrew plays guitar in a rock band. For a song that is 36measures long he plays for

    14

    2measures, rests for

    38

    8

    measures, plays for another 16 measures, rests for 124

    measures

    and plays for the last section. How many measures are in thelast section?

    2. This week, Mark practised piano for 132

    h, played soccer for

    16

    4h, and talked on the phone for

    14

    3h.

    A. How many hours did Mark spend practising piano andplaying soccer?

    B. Hour many more hours did Mark spend playing soccerthan talking on the phone?

    Resources/Notes

    Math Makes Sense 7

    Lesson 5.6

    Lesson 5.7

    (continued)

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 178

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Specific Outcome

    It is expected that students will:7N5. Demonstrate an

    understanding of adding

    and subtracting positive

    fractions and mixed

    numbers, with like and

    unlike denominators,

    concretely, pictorially and

    symbolically (limited to

    positive sums and

    differences).

    [C, CN, ME, PS, R, V]

    (Contd)

    Achievement Indicators

    Elaborations: Suggested Learning and Teaching Strategies

    For part b) students should think1

    24

    bags is a little more than

    two bags and11

    12is almost one full bag, but not quite.

    Therefore Kyra uses a little more than 3 bags of chips in total.

    Then they calculate:

    6

    13

    6112

    6

    72

    2

    2

    12

    142

    12

    142

    12

    11

    12

    32

    12

    11

    3

    3

    4

    12

    12

    11

    4

    12

    =

    =

    =

    =

    =

    +=

    +=

    +

    and

    Kyra used1

    36

    bags of chips

    in total.

    Note that the final answermust be simplified.

    Students must reflect upon

    their answer to determine ifit is reasonable.

    In this case, the answer is

    very close to the estimate.

    7N5.14 Simplify the

    solution to a givenproblem involving the

    sum or difference of twopositive fractions or

    mixed numbers.

    (continued)

    7N5.15 Solve a givenproblem involving the

    addition or subtraction ofpositive fractions or

    mixed numbers, anddetermine if the solution is

    reasonable.

    (continued)

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 179

    Outcomes with Achievement IndicatorsUnit 5

    General Outcome: Develop Number Sense

    Suggested Assessment Strategies Resources/Notes

    Math Makes Sense 7

    Lesson 5.6

    Lesson 5.7

    (continued)

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    Strand: Number

    Grade 7 Mathematics Curriculum Outcomes 180

    Outcomes with Achievement Indicators