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:

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.

Digit Dog is looking for two Numicon® shapes that are equal to the 10 shape. Calculating Cat is challenging him to find another two shapes, and then another two, and then another two.

Find one example, then another, then another, then one your friend hasn’t foundis a good strategy to encourage learners to use their reasoning skills. Once they have found one pair of shapes challenge them to find another pair, ask:

Is this pair different?

How will you know when you have found all the pairs?

How are you going to record your work?

Look at the pairs that your friend has found. Are they the same? Different?

Are there any shapes you haven’t used? Why?

Encourage learners to check their pairs by putting them on the 10 shape.

Can you put your pairs of shapes in order?

Why can’t you use the 5 shape?

What if……….

You choose three shapes to total 10? How many ways can you do it?

There are 8 rooms and the number tells you how many eggs are in each room. Digit Dog has to go into the rooms and collect the eggs BUT he can only go into each room ONCE.

How many presents can Digit Dog collect?

How many different ways can he go though the store?

Can you record his routes? How might you do this?

Can you do it a different way, Digit Dog, and collect more eggs?

What’s the most eggs you can collect?

What’s the smallest number of eggs?

Look for children who are planning the routes and can explain their thinking.

Simplify the task

Put Numicon® shapes in each room so that Digit Dog can collect a shape when he has gone through the room. These can then be added together to find the total number of eggs.

I went to rooms 1, 2, 3, 7 and 8. How many eggs did I collect altogether?

I have put the shapes on the number line so that I can see the total without counting in ones.

2. Use the blank store and put just numbers 1, 2 and 3 in the rooms.

3. Put just Numicon® shapes in the rooms – no numerals.

4. Put mini-eggs in the rooms. Instead of counting in ones, put the eggs in the Numicon® ten-shapes to find the total.

Extend the challenge

Use the blank store and put higher numbers in each room.

Challenge children to find all possible routes and to explain how they know they have found them all.

Digit Dog and Calculating Cat are using the Numicon® shapes to cover the picture of the Easter Chick .

You will need the Chick picture (download and print on yellow paper) and a set of Numicon® shapes. Ask learners to use the Numicon® shapes to cover the chick in any way they can.

How many different ways can you do it? Describe what you’ve done.

Compare your chick with your friend’s. What’s the same and what’s different? How did you check that your way was different from your friend’s?

Play What’s missing?

When the chick is covered with shapes, one child closes their eyes, another takes away one shape. Which one is missing? How do you know?

Put some shapes in a feely bag, take them out one at a time and place on the chick. Can you find the shapes you want by touch alone? This helps with visualising the shapes.

Ask:

How did you cover the chick? How many shapes did you use? Talk about how you chose the shapes. Which shapes were most useful?

Can you cover the chick using different shapes?

How many different ways can you do it?

What is the fewest number of shapes you can use? The most?

Can you just use odd shapes? Even shapes?

What if you weren’t allowed to use the same shape more than once? How many ways can you do it? Is this more difficult? What are you thinking?

Can you use one shape repeatedly to cover the chick? Which shapes will work? Which won’t? Why?

Encourage learners to describe and explain what they are doing.

Look for those learners who have a strategy for choosing shapes and those who use trial and improvement.

Look for learners who swap shapes for other equivalent shapes each time they look for a new arrangement rather than starting from the beginning.

Encourage learners to put all their completed chicks together and ask “what is the same?” “what is different?”

Try the same activities with the Easter Bunny (download here).

It’s the Chinese year of the pig and Digit Dog and Calculating Cat are using the Numicon® shapes to cover the picture of the pig.

You will need the pig picture (download and print on pink paper) and a set of Numicon® shapes. Ask learners to use the Numicon® shapes to cover the pig in any way they can.

How many different ways can you do it? Describe what you’ve done.

Compare your pig with your friend’s. What’s the same and what’s different? How did you check that your way was different from your friend’s?

When the pig is covered, one child closes their eyes, another takes away one shape. Which one is missing? How do you know?

Put some shapes in a feely bag, take them out one at a time and place on the pig. Can you find the ones you want by touch alone? This helps with visualising the shapes.

Ask:

How did you cover the pig? How many shapes did you use? Talk about how you chose the shapes. Which shapes were most useful?

Can you cover the pig using different shapes?

How many different ways can you do it?

What is the fewest number of shapes you can use? The most?

Can you just use odd shapes? Even shapes?

What if you weren’t allowed to use the same shape more than once? How many ways can you do it? Is this more difficult? What are you thinking?

Can you use one shape repeatedly to cover the pig? Which shapes will work? Which won’t? Why?

Encourage learners to describe and explain what they are doing.

Look for those learners who had a strategy for choosing shapes and those who did it randomly.

Look for learners who swap shapes for other equivalent shapes each time they look for a new arrangement rather than starting from the beginning.

Encourage learners to put all their completed pigs together and ask “what is the same?” “what is different?”

Try the same activities with the other animals (download here).

There are 8 rooms and the number tells you how many presents are in each room. Digit Dog has to go into the rooms and collect the presents BUT he can only go into each room ONCE.

How many presents can Digit Dog collect?

How many different ways can he go though the store?

Can you record his routes? How might you do this?

Can you do it a different way, Digit Dog, and collect more presents?

What’s the most presents you can collect?

What’s the smallest number of presents?

Look for children who are planning the routes and can explain their thinking.

Simplify the task

Put Numicon® shapes in each room so that Digit Dog can collect a shape when he has gone through the room. These can then be added together to find the total number of presents.

I went to rooms 1, 2, 3, 7 and 8. How many presents did I collect altogether?

I have put the shapes on the number line so that I can see the total without counting in ones.

2. Use the blank store and put just numbers 1, 2 and 3 in the rooms.

3. Put just Numicon® shapes in the rooms – no numerals.

Extend the challenge

Use the blank store and put higher numbers in each room.

Challenge children to find all possible routes and to explain how they know they have found them.

Two Numicon® shapes – which shapes are in the Christmas sack?

Show me 2 shapes that could be in the sack. Why do you think that? Are you sure? Convince me.

Are they the only 2 shapes it could be?

How many pairs could it be?

If I show you one of the shapes will you know for sure what the other one is?

Encourage children to explain their reasoning. At first, why don’t they know for sure which two shapes are in the sack? How many possible pairs can it be? Show one pair, and another, and another………..

When you know one shape, how can you be sure what the other shape is?

Variations

Put one shape in the sack and give children clues so that they can work out which shape it is. An opportunity to model mathematical language. My shape is:

one more / one less than………

two more/ two less than………

in between……

an odd/even number

If I add …and …..I get this number

If I take my number away from 10, I am left with……

The difference between my number and 6 is………

……more than……

a multiple of ……….

a factor of………Get the children to ask questions about your shape to work out which one it is.

Put 3 shapes in the sack. The total is 15 which shapes could they be? What if I show you 1 shape, how does that change your thinking?

Digit Dog and Calculating Cat are trying to find the Numicon shape that fits on their presents.

Present Challenge 1

Spread out one set of presents (download here) and one set of Numicon shapes.

Ask: Which shape fits each present?

Which shapes are easy to find? Why?

Which are more difficult? Why?

For more of a challenge: Put the Numicon shapes in a feely bag. Choose one present, then feel in the bag to see if you can find the shape that fits it.

Ask children to reason about which shape could fit on each present:

What are you thinking?

Which shape do you think it will be?

Which shape can’t it be?

Is it bigger than the red shape? Is it smaller than the purple?