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Mathematics: Number
Level indicator: Level 1i - Counting From One Level 1ii - Advanced Counting Level 2 - Early Additive Level 3 - Advanced Additive and Early Multiplicative Level 4 - Advanced Multiplicative Level 5 - Advanced Poportional

Number strategy

Advanced proportional

 Number strategy progression
About the Exemplars
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What the work shows

The task

The teacher set the problem: "If it takes 12 balls of wool to make 18 scarves, how many balls of wool will it take to make 15 scarves?" He asked the students to explain how they got their answer.

I said, 12 is two-thirds of 18, so I need two-thirds of 15, which is 10, so I need 10 balls of wool. Images of student problem solving process

Hine's work shows that she is able to:

  • use her knowledge of ratio to solve a problem involving multiplication.

I said, one and a half times 12 is 18, so one and a half times what makes 15? The answer is 10. Images of student problem solving process

Michael's work shows that he is able to

  • use his knowledge of ratio to solve a problem involving multiplication.

I took one-sixth of 18 and one-sixth of 12. So, 3 scarves need 2 balls. That's a ratio of 3 to 2. Therefore, 15 scarves need 10 balls of wool. Images of student problem solving process

Julie's work shows that she is able to:

  • use her knowledge of ratio to solve a problem involving multiplication.

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