# 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.

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…..”