How can you work out how many beans are under Digit Dog’s cup?
Explain how you know.
Convince me you’re right.
How do you think Calculating Cat used the 5-frame to help her work it out?
What if Digit Dog had 3 beans on top? How many would be underneath?
PlayUnder the Cup
Each player has a cup and 5 beans and takes turns to hide some of their beans under their cup.
Everyone closes their eyes and Player 1 puts some beans on top of their cup and some underneath. Everyone opens their eyes and Player 1 says “I have 5 beans altogether. I have ….beans on top of my cup. How many are hidden?” The other players work out how many beans are under the cup and explain how they know. Convince me that you’re right.
Encourage learners to visualise the beans under the cup. How many more do you need to make 5?
Use the 5-frames to help children begin to visualise. They need an action and an image before they can work out this problem mentally.
Move the beans from the top of the cup and put them on the frame and say how many more are needed to make 5.
Have the frame in front of learners but visualise the beans on it rather than actually move them. Imagine that the beans are moving. Describe what you can “see”.
Remove the frame but visualise it. Visualise the frame and moving the beans onto it.
Use Numicon shapes in the same way as the frames to help visualise the problem.
Play this game with children so that they practise:
subitising small numbers
using mathematical language – how many more?
seeing 5 and 10 as benchmark numbers
Fill the frame to 10
Work with a small group. You need two-sided beans and a 10-frame for each player. Each player takes a turn to:
Put 5 beans in their cup.
Shake and spill the beans.
Put the red beans thrown onto the 10-frame and say “I have ……..red beans. I need ……more to make 10”.
Keep playing until someone has 10 beans.
At the beginning of each turn children will need to put more beans in their cup and check they have 5 beans.
During the game, make sure that learners describe the number of beans using full sentences.
What do you notice about Digit Dog and Calculating Cat’s game? Who has most red beans? How many red beans will Digit Dog have when he puts his last throw on his frame?
How can he work it out? Encourage children to fill the top row first and talk about how they are partitioning the beans – I can split the 5 beans I have thrown into 2 and 3, use the 2 to make 5 on the top row and have 3 more on the bottom.5 and 3 equals 8. This shows the importance of 5 as a benchmark number – numbers greater than 5 can be described as 5 and some more.
How many more will he need to make 10? How do you know?
Talk about the number of spaces left to fill. I have 8 red beans altogether and need 2 more to make 10.The 10-frame provides a good visual image of numbers and their relationship to 5 and 10.
Download the Exploring 10 – Fill the Frame challenge card here.
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
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?
When Digit Dog saw that this year was the Chinese Year of the Pig, it reminded him of the dice game PIG.
PIG is a game for 2 – 6 players
You need one dice.
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.
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.
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.