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…..”
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?
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
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.
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…..”
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
You play Go Fish 10 in the same way as Go Fish but the aim of the game is to make pairs that add up to 10.
Print Digit Dog’s cards here. You need 4 sets for 2 -3 players.
To play:
Deal each player 7 cards and spread out the remaining cards face down on the table. The aim of the game is to find pairs of cards that add up to 10.
Each player takes a turn. During a turn the player:
Looks at the cards in their hand, if they have any pairs that add up to 10, they put them in front of them, face up.
They then ask another player if they have a particular card so that they can make another pair. For example, player 1 might have a 4 in their hand and so ask aplayer 2 “do you have a 6?” – the card they need to make a pair that adds to 10. If player 2 has a 6 card, then they must give it to player 1. If they don’t have a 6 card, they say “go fish” and player 1 takes a card from the pool of cards on the table.
If the player gets the card they asked for, either from the pool or from the other player, then they put their pair of cards in front of them, face up.
The game ends when one player runs out of cards or there are no more cards in the pool. The winner is the player with most pairs in front of them.
What if………
………….you played the game by making pairs of cards with a difference of 1?
Put counters on a 
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.
Digit Dog Challenges 