## Exploring inverse relationships with the Bottle Top Bugs

### How many spots are under the leaf? Digit Dog is using the bottle top bugs and leaves to create some number problems.

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

• 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 there altogether? How many spots are on the bug you 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 concrete representations to work out how many more they need to make 10, for example, Put counters on a ten frame to represent the total amount and the number of spots you can see. Use Numicon shapes to represent the total and spots. Either use the pegs or shapes. Make sure that learners can explain what the resources represent. The pink shape represents the number of spots Calculating Cat can see. Using concrete resources helps learners to explain their thinking.
• draw pictures of the bugs and spots.
• find the numbers on a number line and count on or find the difference.
• 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 a more difficult problem?

• Use 3 bugs. Work out the total and then hide one bug under a leaf. What strategies will you use now?
• Use two bugs but try multiplying the numbers. Hide one bug under a leaf but this time say “the product of my numbers is…..”
Posted in Christmas, Numicon, Problem solving

## Baubles again

These baubles have a larger space to cover with Numicon shapes.

Ask learners to use the Numicon shapes to cover the space in any way they can.

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

What is the total of the shapes you have used? Can you wite a number sentence to record what you have done?

Digit Dog didn’t use any shape more than once? Can you try this? How many ways can you do it? Is this more difficult? What are you thinking?

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

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

What if you use only odd shapes? Only even shapes?

Look for learners who:

• can reason about which shapes to use,
• can discuss what they are doing and 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,
• can talk about similarities and differences.

Posted in Christmas, Numicon, Problem solving

## Christmas Baubles

If you enjoyed Cover Santa’s Sleigh and Cover the Christmas Tree, here’s another version of the activities.

You need:

• 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. 1. Give learners a limited number of shapes to choose from to match the spaces on the bauble.  Can they find the shapes they need?
2. Have a complete set of shapes for children to choose from.
3. 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?
4. For an extra challenge, put the shapes in a feely bag and find the ones you need by touch alone.
5. 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?

Posted in Christmas, Numicon, Problem solving

## Can you use the Numicon shapes to cover the Christmas tree?

This is a variation on the popular Cover Santa’s Sleigh activity.

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,
• can talk about similarities and differences.

## NEW! Challenge card pack – Exploring Additive Relationships

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:

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.

Packs are available for purchase at https://www.collectivelearning.co.uk/product/digit-dog-challenges-exploring-additive-relationships-lynwen-barnsley/

Posted in Logical reasoning, Problem solving

## 100 square jigsaw again

Here’s another 100 square jigsaw.

Blank grid Look at the jigsaw grid. What is different from the jigsaw in the last post?

To make it easier

Print out a complete 100 square (square 1 or square 2) and match the jigsaw pieces to the board. Say the numbers on the pieces.

Use a smaller board to do the same activities – 1 – 30 or 1 – 50

Posted in Logical reasoning, Problem solving

## 100 square jigsaw

Digit Dog and Calculating Cat are doing a 100 square jigsaw. They are looking at each piece and deciding where it goes on the grid. Have a go at completing the puzzle.

Think about which piece you are going to put in first. Why have you chosen that one? Which piece has the lowest number on it? Where does that go? How do you know?

Where does the highest number go?

Whenever you place a piece on the board, explain why you are placing it there.

Challenge yourself

• Turn all the pieces face down. Turn over one piece at a time and work out where it goes on the grid. Explain your thinking.
• If you want to try an interactive version of this puzzle, go to https://nrich.maths.org/5572
• Print this 100 square and cut out your own puzzle pieces for a friend to solve.

Posted in Calculating, Logical reasoning, Money, Problem solving

## How much is in the purse? Calculating Cat has 5 coins in her purse.

Think about which coins they could be. Get some coins and work out the possibilities.

What is the largest amount that could be in the purse? Which coins would that be?

What is the smallest amount that could be in the purse? Which coins would that be?

Digit Dog thinks that Calculating Cat might have 6p in her purse. Which coins is he thinking of? What about 10p?

Explore which coins could be in the purse. How many different amounts could there be?

Record the different amounts you have found.

Organise your answers so that you can be systematic and work out all the possible amounts.

What if there were fewer coins in the purse? Try it with just 2 or 3 coins.

What if the coins in the purse were silver coins?

What if there were only 1p, 2p, 5p and 10p coins in the purse?

What if no coin was worth more than 20p?

## Counting and calculating with target boards – numbers to 100

Develop fluency with the target boards. Use the target boards to:

• recall and remember useful number facts;
• use number facts to calculate mentally;
• explain thinking and methods of calculating.
• use mathematical language correctly Print Target Board 4

• Say each number out loud.
• Say the numbers in order – from smallest to largest and back again.
• Point at a number – how many tens and how many ones make that number?
• Point at a number – what is 10 more than that number?
• Point at a number and count in 10s from that number. How far can you count?

Look at the target board and:

Find two numbers that total / add up to 30 / 40 / 50.

Find more than two numbers that make those totals.

Choose your own totals to make.

• How do you know you are correct?
• How did you work it out? Explain your thinking.

Find two numbers with a difference of 10, a difference of 12………… What other differences can you find?

Find the column with the highest total. Which column is easiest to add up? Why?

Find the number that is double 14, double 7, double 20………..

Find the number that is half of 80, half of 36………

Find the answer to 5 x 2, 9 x 5, 3 x 4…………..make up some questions of your own.

Find numbers that are multiples of 5 (are in the 5 times table), multiples of 2, multiples of 10……..

## Calculating with target boards (4)

Develop fluency with the target boards. Use the target boards to:

• recall and remember useful number facts;
• use number facts to calculate mentally;
• explain thinking and methods of calculating.
• use mathematical language correctly. Print Target Board 3

• Say each number out loud.
• Say the numbers in order.
• Point at a number and then find that number of objects.
• Point at a number – what is 10 more than that number?

Ask children to look at the target board and:

Find two numbers that total / add up to 20.

• How do you know you are correct?
• How did you work it out? Explain your thinking.
• How many pairs of numbers can you find?
• Make a list of the pairs you find.
• Make up a number story to go with your pairs of numbers e.g. 13 + 7 = 20 There were 13 ladybirds sitting on a leaf, 7 more came along and now there are 20.

Find more than two numbers that total 20?

Find numbers that make other totals.

Find the total of the numbers in the first column. How did you work it out? Which numbers did you add first? What did you notice? Did you notice that 18 + 2 = 20? How does this help?

Find the sum of the numbers in the bottom row.  How did you do that? Which numbers did you add first? What did you notice? What is the easiest way to add up the numbers?

Find the column with the highest total. Which column is easiest to add up? Why?

Find the number that is double 1, double 2, double 3………..

Find the number that is half of 10, half of 12………

Find two numbers with a difference of 2, a difference of 4…………

Make a list of your numbers. Put them in order. What do you notice? Can you find any patterns?

Problem solving with the target board

My total is 16 – find two numbers that you can add together to make my total.  Can you find three numbers to make my total?

One of my numbers is 7. When I add it to another number, my total is 13. What is my second number?

I am thinking of a number and when I count on 5, I say 14. Find the number I started with.

I am thinking of a number and when I count back 3, I say 8.  Find the number I started with.

I am thinking of a number. I doubled it to make 16. What is my number?

My difference is 5 – find two numbers on the target board that have a difference of 5.

I am thinking of two numbers. When I take away the smaller from the larger my answer is 4. What numbers could I be thinking of? How many pairs of numbers can you find? How do you know you have found them all?

One of my numbers is 15. When I subtract another number, I am left with 9. What is my second number?

Make up some of your own problems like this.

## Calculating with target boards 2

Develop fluency with the target boards. Use the target boards to:

• recall and remember useful number facts;
• use number facts to calculate mentally;
• explain thinking and methods of calculating.
• use mathematical language correctly. Print Target Board 2

• Say each number out loud.
• Put objects on each number – check that you have the correct amount.
• Say the numbers in order.

Practise addition with the target board.

Find two numbers that total 5.

• How do you know you are correct?
• How did you work it out? Explain your thinking.
• How many pairs of numbers can you find?
• Make a list of the pairs you find.

Find numbers that total 10.

• How do you know you are correct?
• How did you work it out? Explain your thinking.
• How many pairs of numbers can you find?
• Make a list of the pairs you find.

Make up a number story to go with your pairs of numbers, e.g. 3 + 2 = 5 Digit Dog ate 3 bones for breakfast and 2 bones for dinner. He ate 5 bones altogether. How many different stories can you make?

Find other totals and make up stories to go with them.

Find the total of the numbers in the first column. How did you work it out?

Find the sum of the numbers in the bottom row.  How did you do that?

Find the column with the highest total. Which column is easiest to add up? Why?

Find the number that is double 1, double 2, double 3………..

Point at a number and say what double that number is e.g. point at 5 and say “double 5 is 10”

Problem solving with the target board

My total is 8 – find two numbers that you can add together to make my total.  Can you find three numbers to make my total?

One of my numbers is 5. When I add it to another number, my total is 7. What is my second number?

I am thinking of a number. I count on 3 and get to 8. What number did I start with?

I am thinking of a number. I doubled it to make 8. What is my number?

Posted in Patterns, Problem solving

## Patterns with bunting

Digit Dog is making some bunting ready for the VE Day celebrations. He has made a pattern with his flags.

Which colour flag will he put next? How do you know?

What colour will the 10th flag be? What about the 16th flag? How did you work it out?

If he uses 30 flags, what colour will the last flag be?

Can you make a pattern like Digit Dog?

Calculating Cat has made a different pattern. What do you notice about Calculating Cat’s pattern?

Which flag will she put next? How do you know?

What will the 12th flag be? What about the 17th? How did you work it out?

If she uses 28 flags, which flag will be last?

Look at both sets of flags.

What is the same about them? What is different?

Try making your own bunting. Make some flags and decide on a pattern. See if someone else can spot your pattern.