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…..”
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.
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?