The idea of equal value is fundamental to mathematical understanding. Children need to understand that the “=” symbol means “equal value” and not “here is the answer”.
Ask:
How can you make the scales balance?
Which Numicon® shape could go in the pan balance?
What about this one?
How are you going to solve it? Explain your thinking.
What if ………..you changed the shapes?
Now using numerals.
Can you model this with the pan balance and Numicon® shapes?
What’s the missing number? Explain how you know. Record the sentence.
Make up some of your own.
Make sets of problems like this to put with a pan balance in your enhanced provision.
Numicon® shapes are weighted and so are the perfect resource for exploring equivalences. Make sure that learners have had the opportunity to play with the scales and the shapes before doing the challenge.
Ask:
How are you going to record what you have found?
Learners might:
Use the shapes and an equals sign (download here) as a record. Ask children to explain what they have done. Ask:
Are all the pairs different?
How do you know that your pair of shapes are equal to 10?
2. Use a pan balance working board (download here) to record the shapes on.
3. Select a written number sentence (download here) that matches their shapes.
This type of word problem requires more thinking than the problems where the end result is unknown e.g. “There are 4 chicks in my egg and 4 chicks on the floor. How many chicks are there altogether?”
Ask learners to:
Explain how to find out how many chicks are in the egg.
Describe the strategy they have used:
act it out – with children or toy chicks
use counters to represent the chicks
draw pictures
use an eight Numicon shape
use number bonds
Convince everyone that their answer is correct.
What number sentence can you write about the problem?
Make up some of your own problems like this one for your friend.
What if……….
………there were more than 8 chicks altogether?
………there were more or fewer chicks outside the egg?
Play this game with children so that they practise:
counting
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.
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.
Recording the two-sided beans
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.
Calculating Cat says that you can make 10s with the shapes and that makes it easy to find the total. 10, 20, 21
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.
Two Numicon® shapes – which shapes are in the Christmas sack?
Show me 2 shapes that could be in the sack. Why do you think that? Are you sure? Convince me.
Are they the only 2 shapes it could be?
How many pairs could it be?
If I show you one of the shapes will you know for sure what the other one is?
Encourage children to explain their reasoning. At first, why don’t they know for sure which two shapes are in the sack? How many possible pairs can it be? Show one pair, and another, and another………..
When you know one shape, how can you be sure what the other shape is?
Variations
Put one shape in the sack and give children clues so that they can work out which shape it is. An opportunity to model mathematical language. My shape is:
one more / one less than………
two more/ two less than………
in between……
an odd/even number
If I add …and …..I get this number
If I take my number away from 10, I am left with……
The difference between my number and 6 is………
……more than……
a multiple of ……….
a factor of………Get the children to ask questions about your shape to work out which one it is.
Put 3 shapes in the sack. The total is 15 which shapes could they be? What if I show you 1 shape, how does that change your thinking?
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