Super value shapes
Problem
Each of the following shapes has a value
Image
|
4 |
Image
|
8 |
Image
|
15 |
What is the total value of the following two shapes when you put them together?
| How about these? | Image
Image
Image
|
| Tell us about this | Image
Image
Image
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Use a combination of shapes to show the following values. Can you find more than one way to show the values?
20, 27, 35, 36, 50, 66 and 100
Can you find some numbers between 5 and 50 that cannot be made using these shapes?
Student Solutions
Thank you to The Math Club of the Seacrest Country Day School in Naples, Florida for providing a 'shapes' solution for each of the following values.
| Value | Shapes solutions |
|---|---|
| 20 | 5 triangles |
| 27 | rectangle circle triangle |
| 35 | 2 circles triangle rectangle |
| 36 | 4 circles triangle |
| 50 | 2 rectangles 5 triangles |
| 66 | 2 rectangles 8 triangles |
| 100 | 4 rectangles 4 circles 2 triangles |
Was there only one shapes solution each of the values that you were given? Did you find any other possibilities?
Let us know if you were able to find other solutions to the problems.
Teachers' Resources
Super Value Shapes
Each of the following shapes has a value
Image
|
4 |
Image
|
8 |
Image
|
15 |
What is the total value of the following two shapes when you put them together?
| How about these? | Image
Image
Image
|
| Tell us about this | Image
Image
Image
|
Use a combination of shapes to show the following values. Can you find more than one way to show the values?
20, 27, 35, 36, 50, 66 and 100
Can you find some numbers between 5 and 50 that cannot be made using these shapes?
Why do this problem?
Possible approach
To make the work more concrete, have pattern block shapes available. Values can be written on sticky labels and put on the shapes until children feel confident enough to work more abstractly by transfering the assigned value to the shape.It is important to put a number like 29 into the set, because there is no solution for this total. The children could be asked for suggestions about changing the given values so that a solution could be found.
Once the original solutions are found, ask the children to find alternative solutions and to discuss the possibilities offered.
Key questions
How would you like to record your answers?
Possible extension
Using the four shapes, can the children find new ways to show the given values? Have the children make up problems for friends or neighbours to solve.