Number Shapes Years 1 - 8

Calculating Changes has permission to reproduce any sections of the CAN Report which will help achieve its objective of enhancing children's number sense. The following example is from pages 12 and 13 and is an example of the richness available to member schools.

Materials

• One MathMaster or MathMate per child
• One Poly Plug 5x5 per child
• Large pieces of paper (at least A4) per child and markers (pencils/pens are OK, but they are not so much fun to use)

Procedure

When young children start to work on CAN, the following activity, invented by a teacher, is a popular one:

Put a number inside a square.

Then put a number at each corner of the square so that the four 'corner' numbers add up to the number in the square.

Gary's way of doing this (Figure 3.1) was a surprise to his teacher, who had not yet 'done' any work with these six-year-old children on place value in hundreds. However, Gary seemed to have found out how to decompose a three-digit number into hundreds, tens and units, although he was not yet sure which way round to write 7.

At the same time, in the same class, Sara was experimenting with seven and eight-digit numbers. She was also varying the activity, using triangles with three numbers (Figure 3.2)

Variations

These variations on the Number Shapes activity have been developed by Calculating Changes teachers.

1. Make any number of gaps in the red Poly Plug board. Store the plugs in the plastic bag so you don't lose them. Remove the same number of plugs from the yellow/blue board. Arrange the yellow/blue plugs at each corner of the red board. Draw a picture. Record a sum showing how the plugs combine to make the number of gaps. Can you check your sum? Can you check your sum another way?
2. Repeat Variation 1 as a team of four (each contributing a board to make 2 x 2 square) and using numbers up to 100.
3. Continue Sara's idea and use other shapes.
4. Whatever shape is used, require that each of the corner numbers is the same.
5. Whatever shape is used require that the product of the 'corner' numbers is the number inside the shape.

Extensions

Figure 3.12, Page 22

Figure 3.13, Page 22

Figure 4.15, Page 31