You need one counter and a dice (a dice with numbers 1, 2 and 3 is ideal but you can play with an ordinary 1 – 6 dice)

The game is for 2 players – one will be Digit Dog and the other will be Calculating Cat.

Put the counter on Start. Both players move the same counter BUT Digit Dog moves towards the bone and Calculating Cat moves towards the fish. Take turns to throw the dice and see who gets their food first. There will be a lot of moving back and fro.

When children throw the dice ask them to say how many spots there are without counting in ones – this is called subitising.

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 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…..”

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.

Ask:

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.

Digit Dog and Calculating Cat enjoyed the game so much that they made their own version of the game.

The game is for two players – one is Digit Dog, the other Calculating Cat.

You need: One dice, one counter.

Digit Dog wants to get to the bone, Calculating Cat wants to get to the fish.

Put the counter on start.

Take turns to throw the dice and move the counter. Both players move the same counter – Digit Dog moves the counter towards the bone, Calculating Cat moves it towards the fish.

The winner is the one who gets to the food first.

Variations

Use two dice – throw the two dice and choose which dice you want to use.

Use two dice – add the numbers on the dice and use the total for your move.

Use two dice – find the difference between the numbers on the two dice and use the difference for your move.

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.

Small objects such as pennies, buttons or counters.

To play:

One player is the leader and has the ten frame cards in a pile, face down.

Other players have a blank ten frame and ten small objects each.

The leader turns over the top card for a few seconds and then turns it back again.

Other players make the pattern they saw with objects on their ten frame.

The leader turns over the card again to check the patterns. Players who were correct score one point.

Play until all cards have been turned over, or one player reaches 10 points.

The winner is the player with most points.

Variations

Make the number on your ten frame one more than the number on the card.

Make the number on your ten frame two more than the number on the card.

Make the number on your ten frame one less than the number on the card.

Make the number on your ten frame two less than the number on the card.

2. Who has more?

You need:

For 2 players

A set of Digit Dog ten frames for each player, in a pile face down.

To play:

On the count of 3, players turn over their top card. The player with more dogs wins the two cards and says “I have …….dogs. I have more dogs than you”. The other player says “I have ……. dogs. I have fewer dogs than you”.

The game ends when all cards have been turned over. The winner is the player with more cards.

Variation

The player with the fewer dogs wins the cards.

Say how many more and how many fewer dogs there are.

A few sets of Digit Dog ten frame flash cards – large or small

To play:

Place the cards in a pile face down.

One player shows the top card and then turns it back again, the other players have to say how many dogs were on the card. The length of time that the card is revealed can get shorter as learners get better at recognising the patterns.

Encourage learners to recognise patterns and to work out the number without counting each dog.

How did you know how many there are? Explain your thinking.

Variations

For learners still practising counting accurately, turn over the cards and count each dog. Place an object on each dog and count the objects.

For a challenge: turn over the card, show the dogs and then hide them again. This time say one more than the number of dogs or one less than the number, e.g. if there were 4 dogs on the card, you would say “one more is 5” or “one less is 3”.

Show these slides for a couple of seconds to practise saying how many objects there are without counting in ones.

To play:

Open slideshow.

Click once to reveal an image, click again for it to disappear.

Ask: “How many Digit Dogs can you see?”

At first learners will want to count each dog and you will need to leave the image on the screen. Practise recognising the groups of dogs and saying how many there are without having to count each one. How quickly can you do this?

Being able to look at a small set of objects (up to 5) and say how many there are without counting in ones is called subitising. Once children can count objects accurately we want them to move onto subitising, this is an important step in the development of number sense.

It is easier to subitise if objects are arranged in recognisable patterns, such as the dice dot patterns or on ten-frames. The frames are used so that learners can relate numbers to 5 and 10, an important understanding for calculation.

Perceptual subitising – instantly recognising a small group of objects, usually up to 5 or 6.

How many Digit Dogs can you see?

Conceptual subitising – seeing smaller groups of objects within a larger group to say how many there are without counting in ones. We do this when there are more than 5 or 6 objects.

I know there are 7 because I see 5 and 2 more.

I know there are 7 because I can see 4 and 3 more.

Digit Dog and Calculating Cat have been practising their counting. Play their game by downloading it here.

You need one counter and a dice (a dice with numbers 1, 2 and 3 is ideal but you can play with an ordinary 1 – 6 dice)

The game is for 2 players – one will be Digit Dog and the other will be Calculating Cat.

Put the counter on Start. Both players move the same counter BUT Digit Dog moves towards the bone and Calculating Cat moves towards the fish. Take turns to throw the dice and see who gets their food first. There will be a lot of moving back and fro.

When children throw the dice ask them to say how many spots there are without counting in ones – this is called subitising.

The aim of the activity is to encourage learners to think and talk mathematically – to have a mathematical conversation and use their knowledge of additive relationships. This structure of problem is more difficult than the usual “I had 2 bones and then ate 2 more, how many did I eat altogether?”

Ask:

What has Digit Dog been doing? Can you tell me in your own words? What is Calculating Cat wondering?

How many bones could Digit Dog have had in the beginning? How many could he not have had? Explain your thinking.

Take suggestions for numbers of bones.

Is there just one answer?

Use one number as an example.

If Digit Dog started with 3 bones, how many bones did he eat?

Explain how you can find out.You might want to use bones, drawings, Numicon shapes, cubes to help.

Can you write a number sentence? 3 – ? = 2

Try some other numbers of bones. Record your answers. Can you put your answers in order? What do you notice?

Use this speaking frame to explain your work:

Digit Dog started with ______ bones, he ate _____ bones, now he has 2 bones left.

What if……….

He had a different number of bones left?

Make up your own problem like this about Calculating Cat and some fish.

The five proficiences

Learners will use:

strategic competence to make sense of the problem, work out what is known and what needs to be found out and to decide on a way of solving it.

logical reasoning to explain their thinking and work systematically to find possible numbers.

conceptual understanding of, and fluency with, number bonds to recognise that they need numbers with a difference of 2 or to see this pattern as they try out numbers, to see that 1 or 2 are not possible numbers to start with and to be efficient and accurate with the basic calculations.

communication using symbols and correct mathematical vocabulary to show and explain their thinking .

Learners will need to be competent in all five proficiencies to make up their own problems.

The idea of equal value is fundamental to mathematical understanding. Children need to understand that the “=” symbol means “equal value” and not “here is the answer”.

Ask:

How can you make the scales balance?

Which Numicon® shape could go in the pan balance?

What about this one?

How are you going to solve it? Explain your thinking.

What if ………..you changed the shapes?

Now using numerals.

Can you model this with the pan balance and Numicon® shapes?

What’s the missing number? Explain how you know. Record the sentence.

Make up some of your own.

Make sets of problems like this to put with a pan balance in your enhanced provision.