Stars on crackers
What do you think? How can you solve Calculating Cat’s problem?
Numicon® shapes might help. Use the shapes to represent the stars.
Or use the Cuisennaire rods to find ways to make the 19 stars.
………..Calculating Cat wanted a differen tnumber of stars on the tree? What about 21? 22? or a larger number?
………there was a different number od stars on each cracker?
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?
……….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?
How many in the box?
Digit Dog is playing a game with Calculating Cat. He has 6 tree decorations and has hidden some of them in his box. Calculating Cat has to work out how many he has hidden.
Calculating Cat is thinking about the Numicon
® shape to help her work out how many are in the box.
She knows the whole is 6 – that’s the number of decorations Digit Dog had to start with.
She knows one of the parts is 3 – that’s the number of decorations not in the box.
Now she can work out the unknown part – that’s the number of decorations in the box – by thinking about the spaces in the Numicon
She could have solved the problem by using number bonds. If she knows 3 + 3 = 6, she can work out the missing number.
……….Digit Dog put a different number of decorations in the box?
………..he had more decorations to start with? Fewer decorations?
Try out the game for yourself. One person hides objects in a box, their partner works out how many are hidden. Remember to explain how you work it out.
Digit Dog and Calculating Cat have been using
pattern blocks to make snowflake patterns.
What do you notice?
Can you copy their patterns?
Are the patterns symmetrical?
Can you design your own snowflake patterns?
What if …………
……….we give a value to one of the shapes?
……….the green triangle is 1 what is the value of the other shapes?
……..you had to make a snowflake that is worth 20?
………the blue rhombus is worth 1?
………the red trapezium is worth 1?
What’s the value?
Work out the value of the tree, the snowman and Santa.
What is each picture worth?
What do you notice? Where would be a good place to start? Which row would help us to solve the problem?
Encourage children to use their reasoning skills and make deductions rather than use trial and improvement. Talk aloud and model your thinking.
Is Digit Dog right? Does using Numicon® help solve the problem? What do you think about Calculating Cat’s idea?
What are you going to do next? What do we know?
Does using pegs make it easier? What do you think about Calculating Cat’s idea? Can you work out the value of Santa? How?
Could you look at a different column instead of the middle one?
What if.……..you changed the totals?
This challenge was inspired by Bernie Westacott in his conversation with Craig Barton. Watch the podcast – it’s well worth it.
Which one doesn’t belong?
Digit Dog and Calculating Cat were decorating their Christmas tree when they thought they’d make up a
Which one doesn’t belong? question.
What do you think?
It doesn’t matter which you choose as long as you can give a reason for your choice.
Look at each Santa in turn and think of a reason why it doesn’t belong.
How many different reasons can you think of?
Make up your own
Which one doesn’t belong?
“What is the same about all the Santas?” “What is different?
Check out this
Digit Dog and Calculating Cat are decorating their
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.
………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?
Digit Dog was looking at the Christmas wrapping paper and noticed some patterns.
What do you notice? What is the pattern?
What will the next picture be? And the next? And the one after that? How do you know?
What will the 20th picture be? What about the 35th? How can you work it out? Challenge older children to use their knowledge of multiples to work out the answer.
What about this pattern?
What is the same and what is different?
Both patterns have 4 pictures that repeat over and over and over……………
They are ABCD patterns.
Digit Dog has used multilink cubes to make an ABCD pattern. He has used a different colour cube for each picture. What colour will be next?
Calculating Cat has done the same.
What do you notice?
Next Digit Dog and Calculating Cat cut their strips into smaller pieces and rearranged them to make new patterns. What is the same and what is different? Which picture would come next? Which colour multilink cube?
8 rooms – collecting presents
Santa has asked Digit Dog to help him collect presents from his store. Here is a map of the
store. ( download and print your store here)
Digit Dog counters
There are 8 rooms and the number tells you how many presents are in each room. Digit Dog has to go into the rooms and collect the presents BUT he can only go into each room ONCE.
How many presents can Digit Dog collect?
How many different ways can he go though the store?
Can you record his routes? How might you do this?
Can you do it a different way, Digit Dog, and collect more presents?
What’s the most presents you can collect?
What’s the smallest number of presents?
Look for children who are planning the routes and can explain their thinking.
Simplify the task
Numicon® shapes in each room so that Digit Dog can collect a shape when he has gone through the room. These can then be added together to find the total number of presents.
I went to rooms 1, 2, 3, 7 and 8. How many presents did I collect altogether?
I have put the shapes on the number line so that I can see the total without counting in ones.
Calculating Cat says that you can make 10s with the shapes and that makes it easy to find the total. 10, 20, 21
2. Use the
blank store and put just numbers 1, 2 and 3 in the rooms.
3. Put just
Numicon® shapes in the rooms – no numerals.
Extend the challenge
blank store and put higher numbers in each room.
Challenge children to find all possible routes and to explain how they know they have found them.
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
Numicon® purse to help you. Which coins are you going to use?
The chocolate coin cost 7p
……..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.
6 Christmas stars – a puzzle
Download the tree
Look at the picture. What do you notice?
What are Digit Dog and Calculating Cat trying to do?
What are you going to do first?
Check that each side totals 9.
What do you think? Can you do it another way?
To simplify the task
Numicon® shapes instead of numerals.
Use numbers /
Numicon® shapes 1 to 6 and make each side total 9. Then try totals of 10, 11 and 12. See Number Round Up on https://nrich.maths.org/188
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?
Download tree and stars
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.
There was a different number of stars on the tree? Explore any number.
There were more than two colours of stars?