## 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…..”

## Counting and comparing with Bottle Top Bugs

Count, order and compare with Bottle Top Bugs.

To play the game you need:

A set of Bottle Top Bugs

A feely bag, box or cloth

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.

Ensure learners are using correct mathematical language.

Who has more spots? Who has fewer spots?

Who has more? Who has less?

Say:

I have more spots. I have fewer spots.

I have more. I have less.

Make sure that learners practise using fewer/less as well as more.

Practise subitising (saying how many spots there are without counting in ones). Seeing patterns and arrangements of objects is an important skill that helps with rearranging, combining, breaking up and putting together amounts in number.

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 7 spots because she saw 5 plus 2 more.

Match the numeral

Say how many spots you have and find that number on a number line.

Say how many spots you have and find a digit card to match that amount.

Extend the game

Ask Who has more spots? How many more?

Who has fewer spots? How many fewer?

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

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

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 difference captures the four bugs.

## Practising number bonds with the Christmas flik-flak

Make practising counting and remembered facts part of your daily routine.

In order for children to develop fluency they need to have a daily routine where they practise:

• Counting;
• Remembered facts;
• Using number relationships to do calculations.

Children need the opportunity to:

• Talk mathematically;
• Discuss and solve problems;
• Be creative;
• Use reasoning skills.

Use the flik flak to practise number bonds

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:

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:

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.

## Have you seen Digit Dog’s challenge card packs?

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.

There are currently two packs available.

The first pack has activities using my favourite resource – the Two-sided Beans

Packs can be purchased from Collective Learning

The second pack has activities that focus on solving non-routine 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.

Packs are available to purchase at Collective Learning

## 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 2-sided beans, Conceptual understanding, Fluency

## NEW! Challenge card packs

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 first pack contains activities using the Two-sided Beans

Packs are available to purchase at www.collectivelearning.co.uk

## Making 10

Look at the Numicon shapes and find pairs of shapes that make 10. Check that you are correct by placing each pair on top of the ten shape.

Put your pairs in order.

What do you notice? What patterns can you see?

Say an addition sentence for each pair e.g. 1 add 9 equals 10.

Write an addition sentence e.g. 1 + 9 = 10.

Say a subtraction sentence e.g. 10 take away 1 equals 9.

Write a subtraction sentence e.g. 10 – 1 = 9.

Play What’s Missing?

Set out your pairs like Digit Dog and Calculating Cat.

Player 1 closes their eyes, Player 2 removes one shape and says “what’s missing?”

Player 1 works out what shape is missing and explains how they know.

For more Numicon activities visit Oxford Owl for Home Maths.

Download and print the free Numicon shapes and the Numicon at Home Activity Kit for Years 1 and 2.

## Largest number

2 – 4 players

You need:

Digit cards 1 – 9  (one set per player, shuffled) or a pack of playing cards, Ace to 9 only.

To play:

Deal 2 cards to each player.

Players turn over their cards and make the largest 2-digit number they can with the cards they have been dealt.

The player with the largest number scores a point.

Play ten rounds. The winner is the player with most points.

Variations

• Deal 3 cards to each player and make 3-digit numbers.
• Try 4 or 5- digit numbers.
• Get a point for the smallest number rather than the largest.
• Play more than 10 rounds.
Posted in Conceptual understanding, Counting, Games

## Target board 4 – counting and recognising numbers

An important part of learning mathematics is using and understanding mathematical vocabulary. Children need this vocabulary to talk about their work, to ask questions and to explain their thinking.

Target boards are grids with numbers or pictures that can be used to practise using mathematical language.

Counting and recognising numbers with Target Board 4

Print Target Board 4. Point at any box on the target board and ask children to say the number. Point to a number and ask children to say the number of tens and number of ones in that number.

Find the number 12, or 50 or……….

Put the numbers in the first row in order. Which number is the smallest? Which number is the largest?

Find the largest number on the board.

Find the number that is one more than 35, one more than 11………

Find the number that is two more than 22, two more than 43………

Find the number that is one less than 12, one less than 28……….

Find the number that is two less than 38, two less than 10………

Find all the odd numbers. Find all the even numbers.

Does every column have an even number?

Does every column have an odd number?

Find the number that is ten more than 14, ten more than 40…….. What do you notice?

Find the number that is ten less than 55, ten less than 37…….. What do you notice?

Point at, or put counters on, two numbers. Count from the smallest number to the biggest number and back again.

Choose a number. Count from that number in 2s up to 60 or beyond. Now count back in 2s  to your number.

Choose a number. Count in tens from your number. How far can you count?

Now get children to ask their own questions so that they learn to use the correct vocabulary.

Make your own target board.

Posted in Conceptual understanding, Counting, Games

## Target board 3 – counting and recognising numbers

An important part of learning mathematics is using and understanding mathematical vocabulary. Children need this vocabulary to talk about their work, to ask questions and to explain their thinking.

Target boards are grids with numbers or pictures that can be used to practise using mathematical language.

Counting and recognising numbers with Target Board 3

Print Target Board 3. Point at any box on the target board and ask children to say the number. Point to a number and ask children to collect that number of objects. Put sets of objects more than 10 into groups of 10 and some more, e.g. 17 objects will be organised into one group of 10 and 7 more. Put the objects onto 10 frames to support this idea of a group 10 and some more.

Find the number 12, or 16 or……….

Put the numbers in the first row in order. Which number is the smallest? Which number is the largest?

Find the number that is one more than 13, one more than 8……….

Find the number that is two more than 16, two more than 7………

Find the number that is one less than 15, one less than 19……….

Find the number that is two less than 20, two less than 5………

Find an odd number. Find an even number.

Does every column have an even number?

Does every column have an odd number?

Find the number that is ten more than 6, ten more than 5…….. What do you notice?

Find the number that is ten less than 16, ten less than 15…….. What do you notice?

Now get children to ask their own questions so that they learn to use the correct vocabulary.

Play Bingo.

You need a board each, sets of digit cards 1 – 20 (you will need one set per player) and objects to cover the numbers on the board (use buttons, counters, milk bottle tops, small toys.

Shuffle the digit cards and place in a pile face down. Take turns to turn over the top card, say the number and cover it on your board. The first to cover the board is the winner.

Variations

The winner is the first to complete a row or a column.

Play Ten More / Ten Less Bingo. Use digit cards 0 – 20. Take turns to turn over the top card, but say the number that is either 10 more or 10 less than the number on the card and find the new number on your board.

Posted in Conceptual understanding, Counting, Games

## Target board 2 – counting and recognising numbers

An important part of learning mathematics is using and understanding mathematical vocabulary. Children need this vocabulary to talk about their work, to ask questions and to explain their thinking.

Target boards are grids with numbers or pictures that can be used to practise using mathematical language.

Counting and recognising numbers with Target Board 2

Print Target Board 2. Point at any box on the target board and ask children to say the number. Point to a number and ask children to hold up that number of fingers or do that number of claps, or jump that number of times or collect that number of objects.

Find the number 2, or 6 or……….

Find a number that is more than 4. Now find a number that is less than 8.

Find the largest number. Find the smallest number.

Put the numbers in the first row in order. Which number is the smallest? Which number is the largest?

Find the number that is one more than 5, one more than 9……….

Find the number that is two more than 3, two more than 7………

Find the number that is one less than 5, one less than 9……….

Find the number that is two less than 3, two less than 7………

Find an odd number. Find an even number.

Does every column have an even number?

Does every column have an odd number?

For numbers up to 20, try the same activities with Target Board 3.

Now get children to ask their own questions so that they learn to use the correct vocabulary.

Play Bingo.

You need a board each, sets of digit cards 1 – 20 (you will need one set per player) and objects to cover the numbers on the board (use buttons, counters, milk bottle tops, small toys.

Shuffle the digit cards and place in a pile face down. Take turns to turn over the top card, say the number and cover it on your board. The first to cover the board is the winner.

Variations

The winner is the first to complete a row or a column.

Play One More Bingo. Use digit cards 0 – 19. Take turns to turn over the top card, but say the number that is one more than the number on the card and find the new number  on your board.

Play One Less Bingo. Use digit cards 1 – 21. Take turns to turn over the top card, but say the number that is one less than the number on the card and find the new number on your board.

What about two more and two less bingo?

Posted in Conceptual understanding, Counting, Games

## Target board 1 – counting

An important part of learning mathematics is using and understanding mathematical vocabulary. Children need this vocabulary to talk about their work, to ask questions and to explain their thinking.

Target boards are grids with numbers or pictures that can be used to practise using mathematical language.

Counting with Target Board 1

Print Target Board 1. Point at any box on the target board and ask: How many Digit Dogs can you see?  Do children count the dogs in ones or do they recognise the arrangement and say the number without counting?

Point at 2 dogs, 3 dogs, 1 dog ……….

Point at 4 dogs. Now point at more than 4 dogs. Now point at fewer than 4 dogs.

Point at 3 dogs. Now point at 1 more than 3 dogs. Now point at 1 fewer than 3 dogs.

Which boxes have the most dogs? Which boxes have the fewest dogs?

Which row has most dogs? Which column has fewest dogs?

How many dogs are in the first row altogether? What about the second row? And the third?

Point to some dogs and ask children to hold up that number of fingers or do that number of claps, or jump that number of times.

Now get children to ask the questions and use the correct vocabulary.

Play Match the Dogs. Put 4 sets of the Digit Dog cards face down in a pile. Take turns to turn over the top card and find the matching picture on your board. How many dogs are on your card? The winner is the first to cover their board.

Play Bingo. Have a board each, roll a dice, say the number rolled and cover that number of dogs with a milk-bottle top/ button/ counter. The winner is the first to cover their board.

Put 4 sets of digit cards 1 – 5 in a pile face down. Take turns to turn over the top card and match the number to the dogs on your board. First to cover their board wins.

Play One More Bingo. Put 4 sets of digit cards 0 – 4 in a pile face down. Take turns to turn over the top card, say the number that is one more than the number on the card and match that number to the dogs on your board. First to cover their board wins.