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.

Print your flik-flak onto A4 paper and laminate. Fold along the black lines and you’re ready to go.

In a large group:

Hold up the Digit Dog flik-flak and ask how many dogs can you see? You can show all the numbers from 0 to 10 by folding on the black lines. This allows children to practise counting sets of objects up to 10.

For example, you can fold the flik-flak like this:

Ask:

How many dogs can you see?

How many are there with red hats? How many with green hats?

What if there was one more dog? What if there was one less dog?

Show me with fingers how many dogs there are.

How many dogs? Do that number of jumps.

Once children can confidently count the dogs with 1:1 correspondence, encourage them to subitise i.e. to say how many dogs there are without counting in ones.

In a small group:

Give children individual flik-flaks and ask them show me questions. Use your questions to develop mathematical language and reasoning skills.

Use your flik-flak to show me:

Single digit numbers – 1, 2, 3, 4 ……etc.

The numbers 0 – 10 in order. How many ways can you show each number?

The same number as I am showing.

One less / one more than 3, than 4….. etc. How did you work it out? Can you do it without counting?

More/fewer than I am showing. Explain your answer. Has everyone got the same answer? Can you give me another answer?

copies of the baubles (download and print – make sure you set the print scale at 100% so that the shapes are the corect size)

a set of Numicon® shapes.

Match the shapes to the spaces on the bauble.

Give learners a limited number of shapes to choose from to match the spaces on the bauble. Can they find the shapes they need?

Have a complete set of shapes for children to choose from.

When the bauble is covered, one partner closes their eyes, the other takes away one shape. Which one is missing? Can you find it in the pile of shapes?

For an extra challenge, put the shapes in a feely bag and find the ones you need by touch alone.

Ask: Why does Calculating Cat think there might be more than one way of covering the shapes?

As learners are working, ask them to explain their thinking.

Why did you choose that shape?

How many shapes do you need?

Which shape do you think will fit here…..? Is it bigger than the orange shape?

Is the shape that goes here big or small? Bigger / smaller than a pink one?

Can you take away one shape and put two in its place?

You will need a Christmas tree (download and print) and Numicon® shapes.

Start with the blank Christmas tree and ask learners to use the Numicon shapes to cover it in any way they can.

Ask learners to explain how they covered the tree. Which shapes did they choose first and why? What did they notice? Are some shapes more useful than others?

How many different ways can you find to do it? Compare your tree with your friend’s. What’s the same and what’s different?

How many shapes have you used? Who has used most shapes? Who has used fewest?

Can you cover the tree using only odd shapes? Why or why not? What about even shapes?

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

Can you cover the tree using each shape at least once?

Look for learners who:

can reason about which shapes to use,

can explain their thinking,

can work systematically,

can see patterns and discuss why they are choosing particular shapes,

can substitute shapes so that they have more or fewer, rather than starting from scratch each time,