Additive relationships – Digit Dog Challenges

Additive relationships, Calculating, Conceptual understanding, Fluency, Logical reasoning, Mathematical language, Number sense, Problem solving

Exploring inverse relationships with the Bottle Top Bugs

Posted on September 14, 2021September 8, 2021 by Digit Dog

Play Under the Leaf

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.

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…..”

Additive relationships, Calculating, Games, Logical reasoning

Reasoning with the Bottle Top Bugs

Posted on September 12, 2021September 7, 2021 by Digit Dog

Collect the bugs

You need:

A set of bottle top bugs (0 – 12)

A set of leaves to put the bugs on (optional)

2 dice

Set out the leaves with one bug on each leaf. Take turns to roll both dice and use either addition or subtraction to capture a bug. For example, if you throw a 5 and a 3 you can either add the numbers together, 5 + 3 = 8, and capture the 8 bug, or you can subtract the numbers, 5 – 3 = 2, and capture the 2 bug.

collect the bugs

Explain your reasoning like Digit Dog.

When all the bugs have been captured, the player who has most bugs is the winner.

Which bugs are easiest to capture? Why do you think that?

Which bugs are more difficult to capture?

Additive relationships, Calculating, Christmas, Conceptual understanding, Fluency

Practising number bonds with the Christmas flik-flak

Posted on December 3, 2020 by Digit Dog

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:

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.

Screenshot 2020-12-03 at 08.15.22

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).

screenshot-2020-12-02-at-10.11.43

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:

Screenshot 2020-12-03 at 08.23.25

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:

Screenshot 2020-12-03 at 08.25.40

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.

Additive relationships, Calculating, Conceptual understanding, Fluency, Number sense, Problem solving

NEW! Challenge card pack – Exploring Additive Relationships

Posted on October 21, 2020October 21, 2020 by Digit Dog

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.

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

Additive relationships, Calculating, Fluency

Bottle Top Bugs – Under the leaf

Posted on October 3, 2020September 30, 2020 by Digit Dog

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.

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…..”

Additive relationships, Calculating, Conceptual understanding, Fluency, Numicon

Making 10

Posted on July 8, 2020 by Digit Dog

Numicon pairs to 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.

Numicon pairs to 10 pattern

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.

Additive relationships, Calculating, Fluency, Strategic competence

I wish I had……..

Posted on July 3, 2020July 1, 2020 by Digit Dog

Screenshot 2020-07-01 09.48.30

Digit Dog is counting his bones. “One, two, three.” But 3 bones are not enough.

Reason about numbers by asking questions about the number of bones:

What if Digit Dog found 1 more bone? How many would he have then? How do you know that? Can you convince me?

What if he found 2 more bones?

What if he ate one bone?

Screenshot 2020-07-01 09.51.41

What does Digit Dog have to do to make his wish come true? How many more bones does he need? How can you work it out?

Screenshot 2020-07-01 10.11.16

Use a five-frame or ten-frame to help learners work out how to make Digit Dog’s wish come true and explain their thinking.

Explore other numbers of bones.

Additive relationships, Calculating, Logical reasoning, Making totals

Finding pairs

Posted on June 15, 2020 by Digit Dog

Digit Dog and Calculating Cat are using one set of digit cards 1 – 10 and looking for pairs that make 10.

Screenshot 2020-06-15 09.32.44

Download a set of digit cards here. You will need cards 1 to 10. Print double-sided to have Digit Dog on the back!

Download a baseboard here. Print two.

How many pairs that make 10 can you make? Put the cards on the baseboard.

Can you use all the cards? Which cards are left over? Why?

Try making some other totals – remember you can only use one set of cards from 1 – 10.

What if you make 9? Which cards are left over? Why?

What about 8? or 12? or 13? or 11? Investigate the number of pairs and the cards that you cannot use.

Record your work. Write down the pairs of numbers and their totals.

Additive relationships, Calculating, Fluency, Problem solving

Counting and calculating with target boards – numbers to 100

Posted on May 13, 2020 by Digit Dog

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

Target board 4

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.

Record your work.

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……..

Additive relationships, Calculating, Fluency, Problem solving

Calculating with target boards (4)

Posted on May 12, 2020May 13, 2020 by Digit Dog

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.

Target board 3

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.

Additive relationships, Calculating, Fluency

Calculating with target boards 3

Posted on May 11, 2020 by Digit Dog

Use the target boards to develop fluency. Use them to:

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

Target board 2

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.

Subtraction and the target board.

Ask children to:

Choose a number and take away 1. Write a number sentence to show what you have done e.g. 4 – 1 = 3. Use objects to help if you need to. Try taking away other numbers.

Choose two numbers and take the smallest number away from the largest. Write a number sentence to show what you have done.

Choose two numbers and find the difference between the numbers e.g. the difference between 10 and 2 is 8. Use bottle tops to help work this out.

difference between

Or use the number line.

number line difference — The difference between 2 and 5 is 3.

Find two numbers on the board with a difference of 1.

How do you know you are correct?

How did you work it out? Explain your thinking.

How many pairs of numbers with a difference of 1 can you find? Make a list of the pairs you find.

Practise counting back. Choose two numbers and count back from the larger to the smaller e.g. if you choose 4 and 9, you start at 9 and say 9, 8, 7, 6, 5, 4.

Use a number line to count back. Choose a number on the target board, count back 2, what number are you on now?

number line -2 — I chose 10: 10 count back 2 is 8; 10, then 2 less is 8; 10 – 2 = 8

Make up a number story to go with your pairs of numbers, e.g. if you choose 4 and 6 you might say:

“Digit Dog had 6 bones in his dish. He ate 4 of them. How many does he have left?”

“Calculating Cat had 6p in her purse and she spent 4p. How much does she have left?”

“Digit Dog has 6 bones and Calculating Cat has 4. How many more bones does Digit Dog have?”

Make up some problems for someone else to solve.

Problem solving with the target board

My difference is 3 – find two numbers on the target board that have a difference of 3.

I am thinking of two numbers. When I take away the smaller from the larger I am left with 2. What numbers could I be thinking of?

One of my numbers is 7. When I subtract another number, I am left with 5. What is my second number?

I am thinking of a number. I count back 3 and get to 4. What number did I start with?

Additive relationships, Calculating, Fluency, Problem solving

Calculating with target boards 2

Posted on May 8, 2020May 7, 2020 by Digit Dog

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.

Target board 2

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.

Ask children to:

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?