Posted in combinations, Easter, Making totals, Money

## Coin combinations

Digit Dog has bought a chocolate egg for 50p. He paid for it using silver coins. Which coins do you think he used? Which coins did he definitely not use? Why?

How many different ways do you think he could pay? Convince me that you have found all the different ways. Explain your thinking.

What is the least number of coins he could use? What is the most?

What if…………..

……..Digit Dog bought something for 50p, 75p, Ā£1……..any amount you like?

……..he could use any coins? How many ways to pay would there be then?

Make up some questions like this for your friends.

Posted in Christmas, combinations

## Christmas treats – how many ways?

How many different ways could Digit Dog eat his treats?

Which one will he eat first, second, third?

How many ways do you think there could be?

How will you know when you have found all the different ways he could do it?

How are you going to record the different ways?

…….using the pictures of the treats?

…….drawing pictures of the treats?

…….writing the names or initials of the treats?

…….using a table to organise your work?

Think about how you can organise your work. How can you be systematic so that you can convince everyone that you have found all the different ways?

What if…..

……….he had a lollipop as well?

Would there then be more ways or fewer ways?

A lot more? Just a few more? Why do you think that?

Did you try the Christmas Tree Decoration Challenge on Day 11? What is the same and what is different about the two challenges? What skills and strategies did you use in both of them?

Posted in Christmas, combinations

## Christmas challenge – Day 11

Digit Dog and Calculating Cat are decorating their Christmas tree.

They have three decorations to put on the tree. How many different ways can they do it?

What do you notice? What has Digit Dog done? Where has he put his decorations?

What is Calculating Cat thinking? What would her tree look like? How would hers be different from Digit Dog’s? How would it be the same?

Calculating Cat is wondering how many different ways they could put the decorations on the tree.

What do you think? Is it more than 2? Would it be as many as 10? Explain your thinking.

How shall we find out?

How are you going to record you work?

How will you know when you have found all the ways?

Look for children who:

• can describe what they are doing.
• can convince you that they have found all the different ways.
• can explain using objects or drawings.
• are starting to work systematically.

What if………

………there were more than 3 decorations?

…….there were 4 decorations? Will there now be more ways to put them on the tree? How many more ways? Just a few? A lot more?

Posted in Christmas, combinations, Making totals, Money

## 7p to spend – combinations of coins

Digit Dog has bought a chocolate coin for 7p. He paid for it exactly, so which coins did he use?

How many different ways do you think he could do it? Convince me that you have found all the ways.

What is the least number of coins he could use? What is the most?

Which coins do you think he used? Which coins did he definitely not use? Why?

You might want to use your NumiconĀ® purse to help you. Which coins are you going to use?

What if…………..

……..Digit Dog bought something for 8p, 9p, 10p………..any amount you like?

…….he didn’t have the exact money but only had a 10p coin. How much change would he have? Which coins might he be given?

………you used larger amounts?

Vary the amounts and the coins you can use.

Posted in Christmas, combinations, Making totals

## 5 Christmas stars – investigating 5

An activity to explore numbers that total 5.

Digit Dog and Calculating Cat have some yellow and purple stars to put on their tree. They can only put 5 stars 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?

What has Digit Dog done? What is Calculating Cat thinking?

How many different ways do you think they can put the stars on the tree? Why do you think that?

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 stars 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 yellow stars. The 0? – there are no purple stars.

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.

What if…………

There was a different number of stars on the tree? Explore any number.

There were more than two colours of stars?