Bear mixes

Bear mixes

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
This task is about calculating ratios, fractions, and percentages of numbers.
Questions/instructions
Write the number of blue bears and yellow bears in the boxes. The first one has been done for you.
 
   

Blue  

Yellow
1. There are 4 bears altogether. 2 are yellow. How many are blue?

2

2
2.

There are 10 bears altogether. 6 are yellow. How many are blue?

 

6
3.

There are 10 bears altogether. There are 2 more blue bears than yellow bears. How many of each colour are there?

 

 
4.

There are 12 bears altogether. There are twice as many yellow as blue bears. How many of each colour are there?

 

 
5.

There are 3 blue bears. For each blue bear there are 3 yellow bears. How many yellow bears are there?

3

 
6.

There are 15 yellow bears. For each blue bear there are 3 yellow bears. How many blue bears are there?

 

15
7.

There are 16 bears altogether. For each blue bear there are 3 yellow bears. How many of each colour are there?

 

 
8.

A quarter of the bears are blue. There are 3 blue bears. How many yellow bears are there?

3

 
9.

A quarter of the bears are blue. There are 12 yellow bears. How many blue bears are there?

 

12
10.

There are 20 bears altogether. A quarter of the bears are blue. How many of each colour are there?

 

 
11.

There are 15 bears altogether. 20% are blue. How many of each colour are there?

 

 

 

 

Task administration: 
Equipment:
Sheet of 20 yellow bears and 20 blue bears per student.
  • The sheet of bears needs to be printed in colour.
  • Question 11 was trialled by Year 8 students only.
Levels:
2, 4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
nemp, subtraction, fractions, percentages, ratios
Description of task: 
For this NEMP task students calculate ratios, fractions, and percentages of numbers to solve problems involving numbers of blue and yellow bears. A sheet of coloured bears is provided.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 3-4
Multiplicative thinking, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y4 (10/1997) Y8 (09/1997)
1. Given    
2. 4 79% 95%
3. 6 (blue)
4 (yellow)		 38%
36%		 65%
65%
4. 4 (blue)
8 (yellow)		 26%
27%		 60%
60%
5. 9 31% 78%
6. 5 28% 69%
7. 4 (blue)
12 (yellow)		 22%
20%		 63%
60%
8. 9 14% 42%
9. 4 13% 34%
10. 5 (blue)
15 (yellow)		 27%
25%		 71%
68%
11. 3 (blue)
12 (yellow)		 -
-		 33%
32%

Commentary:
Year 8 students struggled with three of the four items involving fractions and percentages. Year 4 students succeeded well with only one item, which involved a simple subtraction.