If you want more ideas for Foundation Phase mathematics, join us on March 13th in the Future Inn, Cardiff to explore ways of developing firm foundations in mathematical concepts. Book here www.collectivelearning.co.uk

It’s the Chinese year of the pig and Digit Dog and Calculating Cat are using the Numicon® shapes to cover the picture of the pig.

You will need the pig picture (download and print on pink paper) and a set of Numicon® shapes. Ask learners to use the Numicon® shapes to cover the pig in any way they can.

How many different ways can you do it? Describe what you’ve done.

Compare your pig 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?

When the pig is covered, one child closes their eyes, another takes away one shape. Which one is missing? How do you know?

Put some shapes in a feely bag, take them out one at a time and place on the pig. Can you find the ones you want by touch alone? This helps with visualising the shapes.

Ask:

How did you cover the pig? How many shapes did you use? Talk about how you chose the shapes. Which shapes were most useful?

Can you cover the pig 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?

Can you use one shape repeatedly to cover the pig? Which shapes will work? Which won’t? Why?

Encourage learners to describe and explain what they are doing.

Look for those learners who had a strategy for choosing shapes and those who did it randomly.

Look for learners who swap shapes for other equivalent shapes each time they look for a new arrangement rather than starting from the beginning.

Encourage learners to put all their completed pigs together and ask “what is the same?” “what is different?”

Try the same activities with the other animals (download here).

There are many versions of the story about the order of animals in the Chinese zodiac. They all involve a race with the order of the zodiac animals being chosen according to the order in which the animals finished the race.

This is a problem solving activity for groups of 3 or 4 children, or it can be used as a class/group activity with younger children to encourage discussion, reasoning, logical thinking and use of mathematical language.

The 14 clue cards have all the information needed to solve the problem. Cut out the cards and share them between the children in the group.

Ask children to:

read the cards;

find the card that tells them what to do (Find the order of the animals)

organise the cards – which ones are most useful to start? which have redundant information?

Use children themselves and the animal masks from www.primarytreasurechest.com to solve the problem. Read the clues and children can move around to find the right order.

Encourage children to check their solution by reading through the clues again.

When Digit Dog saw that this year was the Chinese Year of the Pig, it reminded him of the dice game PIG.

Play PIG

PIG is a game for 2 – 6 players

You need one dice.

Rules

The aim of the game is to get to 50.

Players take turns to roll the dice as many times as they like, adding the numbers as they go. A player can end their turn at any time and “bank” their points.

BUT if a player rolls a 1, they lose all their unbanked points and their turn is over. When you roll a 1 you shout PIG!

The first player to score 50 or more points wins.

For example:

It is Digit Dog’s turn and he throws a 2, 5, 4 and 3. His total so far is 14.

What shall he do now? Shall he throw again and hope that he doesn’t throw a 1? If he throws a 1 he will lose all 14 points. Or shall he bank his 14 points so that they are safe and end his go?

Calculating Cat has banked 20 points from her first turn. On her next turn she throws 2, 6 and 5 so she has 13 points unbanked. What shall she do? Bank the 13 points and add them to her 20 points so that she has a total of 33? Or throw again? If she throws a 1 she will lose her 13 points.

Variations:

Change the target score – make it lower or higher. The first player to score 100 or more points wins. The first player to score 30 or more wins.

Use a 1 – 3 dice and a lower target score.

Make the calculating more accessible by collecting Numicon shapes each time you roll and put them on the number line.

Use 2 dice. If a player rolls one 1, their turn ends and they lose their points for that turn. If a player rolls double 1 , their turn ends and they lose all banked points as well as points from that turn.

Use 2 dice. Rolling one 1 ends the turn and all unbanked points. Throwing a double earns double score – so double 2 = 8 etc. and double 1 scores 25.

Making a set of two-sided beans is quick and easy. Take a bag of dried butter beans (available in any supermarket), lay on newspaper and spray on one side with non-toxic spray paint in your chosen colour. Leave to dry and you’re ready to go.

Shake and Spill

Using the beans to investigate ways to partition the number 5

Take 5 beans and put in a cup. Shake the cup and spill the beans.

Say “I have….red beans and ……white beans. I have 5 beans altogether”.

Keep shaking and spilling and counting the number of red beans and the number of white beans.

How many different ways do the beans spill?

Ask children to think about how they can record what they have done. “How are you going to remember all the different ways?”

Record by using the beans themselves – put them on a large piece of paper, draw a circle around each combination.

Draw pictures of the beans.

Use digit cards and place them alongside the beans.

Match to Numicon shapes.

Match a number sentence.

Write a number sentence.

Use a part-whole diagram.

Encourage children to say how many of each colour there are without counting in ones – tosubitise.

How many gold coins can Digit Dog collect? Digit Dog is trying to collect the pirate’s gold coins. Here is a map of where the pirate keeps the coins (download and print your map here)

Use the Digit Dog pirate counters to move on the board (download here)

There are 8 rooms and the number tells you how many coins are in each room. Digit Dog has to go into the rooms and collect the coins BUT he can only go into each room ONCE.

How many coins can Digit Dog collect?

How many different ways can he go though the rooms?

Can you record his routes? How might you do this?

What’s the most coins you can collect?

What’s the smallest number of coins?

Look for children who are planning the routes and can explain their thinking.

Simplify the task

Put gold coins in each room so that Digit Dog can collect them as he goes through. He can then count them at the end to find out how many he has.

Put 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 coins. Using the shapes encourages children to calculate rather than count in ones.

I went to rooms 1, 2, 3, 7 and 8. How many coins did I collect altogether?

I have put the shapes on the number line so that I can see the total without counting in ones.

Encourage children to use number bonds to find the totals.

3. Use the blank store and put just numbers 1, 2 and 3 in the rooms.

4. Put just Numicon® shapes or coins in the rooms – no numerals.

Extend the challenge

Use the 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.

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?

What about………

…….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?

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® shape.

She could have solved the problem by using number bonds. If she knows 3 + 3 = 6, she can work out the missing number.

What if………

……….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.