Category: Making totals

Numicon® shapes are weighted and so are the perfect resource for exploring equivalences. Make sure that learners have had the opportunity to play with the scales and the shapes before doing the challenge.

Ask:

How are you going to record what you have found?

Learners might:

1. Use the shapes and an equals sign (download here) as a record. Ask children to explain what they have done. Ask:

Are all the pairs different?

How do you know that your pair of shapes are equal to 10?

2. Use a pan balance working board (download here) to record the shapes on.

3. Select a written number sentence (download here) that matches their shapes.

4. Record in their own way.

5. Record number sentences.

An extension of Investigating totals

Put the shapes on the grid but this time each row, column and diagonal has to have the same total.

You might want to make the task simpler:

1. Make each row total 6
2. Make each column total 6
3. Make the rows and columns total 6
4. Include the diagonals.

Which shapes are you using in each row / column? Why?

Is there more than one way of completing the grid?

Look at your partner’s grid. What is the same and what is different?

Make the task more challenging:

1. Use digit cards instead of the shapes.
2. Don’t give the total – Can you put the Numicon shapes on the grid so that each row, column and diagonal add to the same total?

What do you think the total might be? Why?

How are you going to start? What are you going to try first?

What if.……..you used three different consecutive shapes?

3 twos, 3 threes and 3 fours                                 3 threes, 3 fours and 3 fives

or  

What will the totals of each row be now?

Digit Dog has got a 3 x 3 grid and 9 Numicon shapes – 3 one shapes, 3 two shapes and 3 three shapes. He is going to put the shapes on the grid and investigate the totals he can make.

This is what he does first:

Copy what Digit Dog has done.

Digit Dog says that the sum of the shapes in the first row is 6. Do you agree with Digit Dog? Why or why not? Are you sure?

Expecting learners to explain their thinking helps develop their reasoning skills.

If you agree, convince me that Digit Dog is correct. If you don’t agree, explain why you think he is wrong.

Encourage learners to explain why the total of the first row is 6. Use the Numicon shapes to show that the 3 shapes in the first row are equivalent to a six-shape. Explanations are much easier when you use concrete apparatus.

Use the pan balance to explain.

Calculating Cat says that the total of the shapes in the third column is 6 too. Is she right? How do you know?

What is the same and what is different about Digit Dog’s row and Calculating Cat’s column?

Can you find any other rows or columns that total 6? Are there any that total more than 6? What about less than 6?

Can you find a row or column that totals 1 more than 6? What about 1 less than 6?

What else do you notice?

How are you going to record the totals you have found?

Now arrange the shapes on the grid in any way you want and investigate the totals that you make. What do you notice? What is the largest total you can make? The smallest total?

Look at a grid your friend has done. What is the same? What is different?

What if you used other shapes?