Digit Dog and Calculating Cat have some red and blue baubles to put on their tree. They can only put 5 baubles on the tree and have to decide how many of each colour they use. How many different ways can they do it?

Look at the picture. What do you notice? Describe what you see.

What has Digit Dog done? What is Calculating Cat thinking?

How many different ways do you think they can put the baubles on the tree? Why do you think that?

Try it yourself. How are you going to record your different ways? How will you remember what you have done?

How do you know you have found all the different ways? Convince me.

Have you found any patterns?

Look for children who are starting to organise their work and systematically look for all the combinations. The activity is about exploring the combinations and reasoning about choices and patterns.

Ways to record

Provide enough baubles and trees so that each combination can be kept and checked. Children can then look at all the trees and say what is the same and what is different. Ask them to put the trees in order and look for a pattern.

Have number sentences on card and ask children to match the number sentence to the trees.

What does the 5 represent? It is the 5 blue baubles. The 0? There are no red baubles.

Write number sentences for each tree on separate post-it notes. These can then be sorted and put in order.

Use Numicon shapes to represent the number pairs.

What if…………

There was a different number of baubles on the tree? Explore other numbers.

Look for patterns within numbers and help children understand that whole numbers are composed of smaller numbers e.g. fold the Digit Dog flik-flak in half as shown:

Ask:

How many dogs can you see altogether?

What else can you see? I can see 3 dogs with red hats and 3 dogs with green hats. Three and three more equal six altogether. I can see two groups of 3. I can see 2 groups of 2 and 2 groups of 1.

Repeat by folding the flik-flak in other ways.

Now what can you see? What do you notice?

How many with red hats? How many with green? How many altogether?

How many on the top row? How many on the bottom? How many altogether?

I can see 8 with one missing.

Use the flik-flak as a quick way to practise number bonds to 10 (the pairs of numbers that add togther to make 10).

Show children the flik-flak and ask:

“How many dogs can you see?” “How did you count them?”

Explore the numbers of dogs in each row and column. Ask questions such as “Which row has most dogs?” “Which row has the fewest dogs?” “Which row has one more than the bottom row?”

Explore the groups of dogs you can see. I can see 5 dogs on the top half and 5 dogs on the bottom, 5 + 5 = 10. I can see 5 with red hats and 5 with green 5 plus 5 equals 10. I can see a group of 7 in the middle and 3 others, I can see 4 on one side and 6 on the other.

Before continuing, make sure children are confident that there are 10 dogs altogether.

Fold the flik-flak:

Ask:

How many dogs can you see now?

How many dogs are hidden? How many dogs can’t you see?

How do you know? Explain your thinking.

“How many dogs altogether?”

You want children to realise that they know there are 10 dogs altogether, that they can see 5 of them and need to work out how many of the dogs they can’t see. They might:

Count on from 5 to 10

Take away the 5 from 10

Use or visualise the Numicon shapes

Use their knowledge that 5 and 5 equals 10

Expect children to explain their thinking.

Fold the flik-flak in a different way:

Ask the same questions.

“How many dogs can you see now?”

“How many dogs are hidden?” “How do you know?” “Explain your thinking”.

“How many dogs altogether?”

Keep folding the flik-flak to explore all the combinations of numbers to make 10.

New from Digit Dog Challenges – the challenge cards are extended versions of Digit Dog’s popular posts and are now available in packs of 5 with links to Curriculum for Wales 2022.

Each pack has 5 challenge cards, linked to a theme, concept or resource. There is also an overview of how Digit Dog Challenges address the five proficiencies, and links to the relevant Descriptions of Learning in the Mathematics and Numeracy Area of Learning and Experience.

The latest pack contains activities that focus on solving problems that involve additive relationships. They are aimed at Progression Step 2 level descriptions:

Statement of What Matters 1

I have explored additive relationships, using a range of representations. I can add and subtract whole numbers, using a variety of written and mental methods.

Statement of What Matters 2

I can find missing numbers when number bonds are not complete.

Digit Dog and his bones are used as a context for exploring additive relationships and solving non-routine problems that focus on missing numbers.

This type of problem encourages learners to think and talk mathematically and use the link between addition and subtraction.

Ask children to:

Explain what the problem is about in their own words.

Explain what information they know and what they are trying to find out. How many spots are on the bug they can see? What number of spots cannot be under the leaf?

Find a way to work out how many spots are on the bug under the leaf.

Describe the strategy they have used. They might:

use counters to represent the spots and work out how many more they need to make 10

draw pictures of the spots

use number bonds – the numbers that add together to make 10.

I know that 7 + 3 = 10 so there must be a 3-spot bug under the leaf.

I know that 10 – 7 = 3 so there must be a 3-spot bug under the leaf.

Convince everyone that their answer is correct. Use sentence starters such as:

I know the answer is 3 because ….

First of all I…………then I………

I know that …….. so…………

Write a number sentence

Change the bugs – choose two different bugs, work out the total number of spots and then hide one under a leaf.

What if……….

……..you tried it with 3 bugs? Work out the total and then hide one bug under a leaf.

……..you tried multiplying the numbers? Hide one bug under a leaf but this time say “the product of my numbers is…..”

Set out the leaves with one bug on each leaf. Take turns to roll both dice and use either addition or subtraction to capture a bug. For example, if you throw a 5 and a 3 you can either add the numbers together, 5 + 3 = 8, and capture the 8 bug, or you can subtract the numbers, 5 – 3 = 2, and capture the 2 bug.

Explain your reasoning like Digit Dog.

When all the bugs have been captured, the player who has most bugs is the winner.

Which bugs are easiest to capture? Why do you think that?

Put your bottle top bugs in a feely bag or a box or under a cloth. Each player takes one bug out, puts it in front of them and says how many spots there are. The player with more spots captures both bugs.

Keep playing until all the bugs have been used. The winner is the player who has captured most bugs.

Ask:

Who has more spots? How many more?

Say:

I have ……. spots. I have ……. more spots than my friend.

Make sure that learners also practice using the word fewer.

Who has fewer spots? How many fewer?

I have …….. spots. I have …….. fewer spots than my friend.

Practise subitising (saying how many spots there are without counting in ones).

When you turn over a bug, say how many spots there are without counting in ones. How do you know how many spots there are?Calculating Cat knows she has 11 spots because she saw two groups of 5 plus 1.

Vary the game

Change the rules so that the player with fewer spots wins.

Players take two bugs and add the number of spots together. They then compare their totals. The player with the greater total captures all four bugs.

Players take two bugs and find the difference. They then compare their differences. The player with the greater / smaller difference captures the four bugs.

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?

Find a way 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?