The idea of equal value is fundamental to mathematical understanding. Children need to understand that the “=” symbol means “equal value” and not “here is the answer”.

Ask:

How can you make the scales balance?

Which Numicon® shape could go in the pan balance?

What about this one?

How are you going to solve it? Explain your thinking.

What if ………..you changed the shapes?

Now using numerals.

Can you model this with the pan balance and Numicon® shapes?

What’s the missing number? Explain how you know. Record the sentence.

Make up some of your own.

Make sets of problems like this to put with a pan balance in your enhanced provision.

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?

Digit Dog and Calculating Cat are finding pairs of digit cards that make 10.

Digit Dog has found two cards that total 10. Calculating Cat is challenging him to find another two cards, 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 cards 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?

Look for learners who:

are systematic when looking for all the pairs that make 10.

can explain how they know they have found all the pairs.

are looking for patterns.

can organise their work.

What if……….

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

Download a set of Digit Dog’s 0 – 9 cards here Print double-sided to have DIgit Dog on the back!

Digit Dog has bought a chocolate egg for 50p. He paid for it using silver coins. Which coins do you think he used? Which coins did he definitely not use? Why?

How many different ways do you think he could pay?Convince me that you have found all the different ways. Explain your thinking.

What is the least number of coins he could use? What is the most?

What if…………..

……..Digit Dog bought something for 50p, 75p, £1……..any amount you like?

……..he could use any coins? How many ways to pay would there be then?

Make up some questions like this for your friends.

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).

This type of word problem requires more thinking than the problems where the end result is unknown e.g. “There are 4 chicks in my egg and 4 chicks on the floor. How many chicks are there altogether?”

Ask learners to:

Explain how to find out how many chicks are in the egg.

Describe the strategy they have used:

act it out – with children or toy chicks

use counters to represent the chicks

draw pictures

use an eight Numicon shape

use number bonds

Convince everyone that their answer is correct.

What number sentence can you write about the problem?

Make up some of your own problems like this one for your friend.

What if……….

………there were more than 8 chicks altogether?

………there were more or fewer chicks outside the egg?

Open the powerpoint, show the first slide and ask:

How many eggs do you think are in the pot?

Take some estimations and then reveal the answer.

Show the second slide. The first image is the pot from Slide 1.

Click to reveal a second image and ask:

How many are there in this pot?How are we going to estimate? Are there more or fewer than the first pot? How many more/fewer? Discuss some estimations before revealing the answer.

Click to reveal a third image. What about this pot? How many eggs? Ask for estimations and ask learners to explain why they chose the number they did. Why did you choose that number? Explain your reasoning.

Click to reveal the fourth image and see if learners are refining their strategies for estimating. Are they just guessing or are they using what they know about previous pots and reasoning about the number of eggs?

Digit Dog and Calculating Cat are estimating how many eggs are in the pot.

“I wonder how many eggs are in the pot?”

Can you estimate?

What do you think?

Will there be more than 10? How many more? A lot more? A few more?

Will there be more than a 100?

Digit Dog and Calculating Cat used the egg boxes to help find out how many eggs there are. They wanted to organise the eggs so that they could see how many there are without counting in ones.

What do you notice?

How do the egg boxes help to see how many eggs there are?

How can you count them?

What questions can you ask?

Next they used the Numicon shapes to help them count.