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Category: Calculating
6 stars on a puzzle
It’s day 6. Have you tried the puzzle? More ideas and resources here.
Using Numicon® to explore equivalences
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.
Using Numicon® to find pairs that make 10…..again
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.
4. Record in their own way.
5. Record number sentences.
Calculating Chicks
The chicks are hiding
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?
…….the story wasn’t about chicks?
Exploring 10 with 2-sided beans – Fill the frame
Fill the frame game
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.
New challenge card – Fill the Frame
Fill the frame game
Play this game with children so that they practise:
- counting
- subitising small numbers
- using mathematical language – how many more?
- seeing 5 as a benchmark number
Fill the frame to 5
You need two-sided beans and a 5-frame for each player.
Each player takes a turn to:
- Put 3 beans in their cup.
- Shake and spill the beans.
- Put the red beans on the 5-frame and say “I have ….. red beans. I need …..more to make 5”.
Keep playing until someone has 5 red beans.
Note: at the beginning of each turn a player checks they have 3 beans in their cup.
Download the Challenge Card here.
Play PIG
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.
2019 is the Chinese Year of the Pig
Digit Dog is getting ready to celebrate Chinese New Year which begins on February 5th and ends on February 19th.
He has given Calculating Cat a lucky red envelope with some coins in it. See if you can work out how much money could be in the envelope.
Extend the challenge with ideas in the latest challenge card – click here or download from www.primarytreasurechest.com
Reasoning about 5
Explore the number 5 using the 2-sided beans.
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 – to subitise.
Treasure Hunt
Collect the gold coins
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.
Christmas challenge – Day 6
6 Christmas stars – a puzzle
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
Use Numicon® shapes instead of numerals.
Variation
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
