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.

How can you work out how many beans are under Digit Dog’s cup?

Explain how you know.

Convince me you’re right.

How do you think Calculating Cat used the 5-frame to help her work it out?

What if Digit Dog had 3 beans on top? How many would be underneath?

PlayUnder the Cup

Each player has a cup and 5 beans and takes turns to hide some of their beans under their cup.

Everyone closes their eyes and Player 1 puts some beans on top of their cup and some underneath. Everyone opens their eyes and Player 1 says “I have 5 beans altogether. I have ….beans on top of my cup. How many are hidden?” The other players work out how many beans are under the cup and explain how they know. Convince me that you’re right.

Encourage learners to visualise the beans under the cup. How many more do you need to make 5?

Use the 5-frames to help children begin to visualise. They need an action and an image before they can work out this problem mentally.

Step 1

Move the beans from the top of the cup and put them on the frame and say how many more are needed to make 5.

Step 2

Have the frame in front of learners but visualise the beans on it rather than actually move them. Imagine that the beans are moving. Describe what you can “see”.

Step 3

Remove the frame but visualise it. Visualise the frame and moving the beans onto it.

Use Numicon shapes in the same way as the frames to help visualise the problem.

Play this game with children so that they practise:

counting

subitising small numbers

using mathematical language – how many more?

seeing 5 and 10 as benchmark numbers

Fill the frame to 10

Work with a small group. You need two-sided beans and a 10-frame for each player. Each player takes a turn to:

Put 5 beans in their cup.

Shake and spill the beans.

Put the red beans thrown onto the 10-frame and say “I have ……..red beans. I need ……more to make 10”.

Keep playing until someone has 10 beans.

At the beginning of each turn children will need to put more beans in their cup and check they have 5 beans.

During the game, make sure that learners describe the number of beans using full sentences.

What do you notice about Digit Dog and Calculating Cat’s game? Who has most red beans? How many red beans will Digit Dog have when he puts his last throw on his frame?

How can he work it out? Encourage children to fill the top row first and talk about how they are partitioning the beans – I can split the 5 beans I have thrown into 2 and 3, use the 2 to make 5 on the top row and have 3 more on the bottom.5 and 3 equals 8. This shows the importance of 5 as a benchmark number – numbers greater than 5 can be described as 5 and some more.

How many more will he need to make 10? How do you know?

Talk about the number of spaces left to fill. I have 8 red beans altogether and need 2 more to make 10.The 10-frame provides a good visual image of numbers and their relationship to 5 and 10.

Download the Exploring 10 – Fill the Frame challenge card here.