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…..”
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.
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?
It’s the Chinese year of the ox and Digit Dog and Calculating Cat are using the Numicon® shapes to cover the picture of the ox.
You will need the ox picture (download here – make sure you print at 100% so that it is the right size for the shapes) and a set of Numicon® shapes. If you don’t have the plastic shapes you can download a set of printable Numicon® shapes here.
Use the Numicon® shapes to cover the ox in any way you can.
How many different ways can you do it? Describe what you’ve done.
Compare your ox with your friend’s. What’s the same and what’s different? How did you check that your way was different from your friend’s?
How did you cover the ox? How many shapes did you use? Talk about how you chose the shapes. Which shapes were most useful?
Can you cover the ox again, using different shapes?
How many different ways can you do it?
What is the fewest number of shapes you can use? The most?
Can you just use odd shapes? Even shapes?
What if you weren’t allowed to use the same shape more than once? How many ways can you do it? Is this more difficult? What are you thinking?
When the ox is covered, player 1 closes their eyes, player 2 takes away one shape. Player 1 says which shape is missing and explains how they know.
Feely bag challenge
Put some shapes in a feely bag, take them out one at a time and place on the ox. Can you find the shapes you want by touch alone? This helps with visualising the shapes.
Challenge learners to:
describe and explain what they are doing.
have a strategy for choosing shapes rather than do it randomly.
swap shapes for other equivalent shapes each time they look for a new arrangement rather than starting from the beginning.
put all their completed rats together and ask “what is the same?” “what is different?”
Digit Dog and Calculating Cat have some red and blue baubles to put on their tree. They can only put 5 baubles on the tree and have to decide how many of each colour they use. How many different ways can they do it?
Look at the picture. What do you notice? Describe what you see.
What has Digit Dog done? What is Calculating Cat thinking?
How many different ways do you think they can put the baubles on the tree? Why do you think that?
Try it yourself. How are you going to record your different ways? How will you remember what you have done?
How do you know you have found all the different ways? Convince me.
Have you found any patterns?
Look for children who are starting to organise their work and systematically look for all the combinations. The activity is about exploring the combinations and reasoning about choices and patterns.
Ways to record
Provide enough baubles and trees so that each combination can be kept and checked. Children can then look at all the trees and say what is the same and what is different. Ask them to put the trees in order and look for a pattern.
Have number sentences on card and ask children to match the number sentence to the trees.
What does the 5 represent? It is the 5 blue baubles. The 0? There are no red baubles.
Write number sentences for each tree on separate post-it notes. These can then be sorted and put in order.
Use Numicon shapes to represent the number pairs.
There was a different number of baubles on the tree? Explore other numbers.
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
What patterns can you see on the grids? Describe the patterns on each grid. What do you notice?
If we added another row, can you predict which square you would colour in? Why do you say that? Explain your thinking.
Try your own name and look for patterns.
Print the 6 x 6 grid here. Write your name in the grid, one letter in each square, repeating it until all the squares are filled. Now colour in the squares which have the first letter of your name in them. What patterns have you made? Can you think of a way to describe the patterns?
Ask people you know to try it. What is the same and what is different about the patterns different names make?
What if you tried a larger grid?
What has changed?
What about a smaller grid? What patterns can you see then?