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Demolition dollars

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.

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Tags

  • AudienceKaiako
  • Learning AreaMathematics and Statistics
  • Resource LanguageEnglish
  • Resource typeActivity
  • SeriesFigure It Out

About this resource

Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.

This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.

Specific learning outcomes:

  • Calculate rates to solve problems.
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    Demolition dollars

    Achievement objectives

    NA4-4: Apply simple linear proportions, including ordering fractions.

    Description of mathematics

    Number framework links

    Use this activity to help students:

    • consolidate their knowledge of basic facts (stage 6) and advanced multiplicative strategies (Stage 7)
    • develop strategies for solving problems involving rates and proportions (Stage 7).

    Required materials

    • Figure It Out, Level 3+, Proportional Reasoning, "Demolition dollars", page 16

    See Materials that come with this resource to download:

    • Demolition dollars activity (.pdf)

    Activity

     | 

    This activity requires students to work through a series of problems, each of which has one missing detail that can be deduced using proportional reasoning. The speech bubble and the answer to question 1 contain information that is needed for answering questions 2–7; questions 2–6 are not interdependent, but question 7 relies on correct answers for questions 2 and 6.

    The activity is rich with potential for proportional reasoning. Each part can be solved in a variety of different ways, and the numbers are such that there is no need for a calculator. Those who like the challenge of a puzzle may be able to work through each step independently, but you may prefer to discuss it first with your students before setting them to work in pairs or small groups. Make sure that you give them the opportunity to share their strategies.

    The following paragraphs suggest one way of reasoning out the answer to each question:
    For question 1, we know that the boys worked 24 hours in total and earned $120. Using a halving strategy, 120 ÷ 24 = 60 ÷ 12 = 5, so the pay rate is $5 per hour.

    The calculation for question 2 is 7 x 4 x 5 = $____. 28 x 5 = 14 x 10 = $140 (doubling and halving). Alternatively, students may realise that 1 boy working for 4 hours earns $20, so 7 boys working for 4 hours will earn 7 x 20 = $140.

    The weekly target mentioned in question 3 is $150. This represents 30 hours’ work. If 5 boys worked for a total of 30 hours, they each worked for 6 hours (6 x 5 = 30).

    In week 4 (question 4), the boys earned $225 in 5 hours, so in 1 hour they must have earned 225 ÷ 5 = $45. If the boys earned $45 in 1 hour, there must have been 9 boys working (5 x 9 = 45).

    In question 5, we know how many parents worked, so one approach is to begin by finding out what the parent contribution was. The 3 parents worked for 4 hours at a rate of $10 per hour, so they earned 3 x 4 x 10 = $120 of the total of $280. This means the boys earned 280 – 120 = $160.

    The boys also worked for 4 hours, so each hour they earned 160 ÷ 4 = $40. This means that 8 boys worked that day (5 x 8 = $40).

    In question 6, we have all the details we need to go straight to the answer: the boys earn $(10 x 4 x 5) and the parents earn $(2 x 4 x 10). 10 x 20 + 8 x 10 = 200 + 80 = $280.

    Question 7 requires students to add together the totals for the 6 weekends:

    • 120 + 140 + 150 + 225 + 280 + 280 = $1 195. So Braydn’s team is short of its target by $5.

    1.

    $5 (120 ÷ 24 = 5)

    2.

    $140 (7 x 4 x 5 = 140)

    3.

    6 hours (150 ÷ 5 = 30; 30 ÷ 5 = 6)

    4.

    9 boys (255 ÷ 5 = 45; 45 ÷ 5 = 9)

    5.

    8 boys (Parents earn 3 x 10 x 4 = $120; boys earn $160. Each boy earns 4 x 5 = $20. Number of boys is 160 ÷ 20 = 8)

    6.

    $280. (Parents earn 2 x 4 x 10 = $80; boys earn 10 x 4 x 5 = $200. 80 + 200 = $280)

    7.

    $5 short

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