Posted in Calculating, Making totals, Number sense

Using Numicon® to explore equivalences

equivalent shapes

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?

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What about this one?

How are you going to solve it? Explain your thinking.

What if ………..you changed the shapes?

 

Now using numerals.

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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.

Posted in Calculating, Making totals, Numicon

Using Numicon® to find pairs that make 10…..again

Balancing 10

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:

  1. 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?

Screenshot 2019-10-17 18.09.55

 

2. Use a pan balance working board (download here) to record the shapes on.

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3. Select a written number sentence (download here) that matches their shapes.

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4. Record in their own way.

5. Record number sentences.

Posted in Making totals, Numicon

Using Numicon® to find pairs that make 10

Digit Dog is looking for two Numicon® shapes that are equal to the 10 shape. Calculating Cat is challenging him to find another two shapes, and then another two, and then another two.

Making 10 with Numicon

 

Find one example, then another, then another, then one your friend hasn’t found is a good strategy to encourage learners to use their reasoning skills. Once they have found one pair of shapes challenge them to find another pair, ask:

Is this pair different?

How will you know when you have found all the pairs?

How are you going to record your work?

Look at the pairs that your friend has found. Are they the same? Different?

Are there any shapes you haven’t used? Why?

Encourage learners to check their pairs by putting them on the 10 shape.

Screenshot 2019-09-26 17.48.19Screenshot 2019-09-26 17.48.11

Can you put your pairs of shapes in order?

Why can’t you use the 5 shape?

What if……….

You choose three shapes to total 10? How many ways can you do it?

 

 

Posted in Making totals

Find a pair of cards that make 10, and another, and another……..

Digit Dog and Calculating Cat are finding pairs of digit cards that make 10.

Digit Dog has found two cards that total 10. Calculating Cat is challenging him to find another two cards, and then another two, and then another two.

Making 10

 

Find one example, then another, then another, then one your friend hasn’t found is a good strategy to encourage learners to use their reasoning skills. Once they have found one pair of cards challenge them to find another pair, ask:

Is this pair different?

How will you know when you have found all the pairs?

How are you going to record your work?

Look at the pairs that your friend has found. Are they the same? Different?

Look for learners who:

  • are systematic when looking for all the pairs that make 10.
  • can explain how they know they have found all the pairs.
  • are looking for patterns.
  • can organise their work.

What if……….

You choose three digit cards to total 10? How many ways can you do it?

Download a set of Digit Dog’s 0 – 9 cards here  Print double-sided to have DIgit Dog on the back!

Download a baseboard here

Posted in combinations, Easter, Making totals, Money

Coin combinations

Buying an egg

Screenshot 2019-04-08 16.30.42

Digit Dog has bought a chocolate egg for 50p. He paid for it using silver coins. Which coins do you think he used? Which coins did he definitely not use? Why?

How many different ways do you think he could pay? Convince me that you have found all the different ways. Explain your thinking.

What is the least number of coins he could use? What is the most?

What if…………..

……..Digit Dog bought something for 50p, 75p, £1……..any amount you like?

……..he could use any coins? How many ways to pay would there be then?

Make up some questions like this for your friends.

 

 

Posted in 2-sided beans, Making totals, Visualising

Two-sided beans – Under the Cup

Under the Cup

beans under cup

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?

 

Play Under 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.

Step 1

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.

beans under cup 2

Step 2

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”.

Step 3

Remove the frame but visualise it. Visualise the frame and moving the beans onto it.

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Use Numicon shapes in the same way as the frames to help visualise the problem.

IMG_1584.jpg

 

IMG_1583.jpg

 

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Screenshot 2019-03-22 09.12.08

Download the challenge card here

Posted in 2-sided beans, Making totals, Problem solving, Subitising

New Challenge Cards

Here are the first two of Digit Dog’s new challenge cards with ideas for exploring the two-sided beans.

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Download Shake and Spill

Download Recording

Let us know what you think.

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

Posted in Calculating, Chinese New Year, Making totals

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.

red envelope

Extend the challenge with ideas in the latest challenge card – click here or download from www.primarytreasurechest.com

Posted in 2-sided beans, Calculating, Making totals

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

5 beans

5 ffa

 

 

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.

    Screenshot 2018-03-05 14.05.35
    Recording the two-sided beans

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

Posted in Christmas, Making totals

Christmas challenge – day 15

How many in the box?

Screenshot 2018-12-12 18.09.58.png

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.

Screenshot 2018-12-12 18.18.47.png

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.

Posted in Christmas, combinations, Making totals, Money

Christmas challenge – Day 7

7p to spend – combinations of coins

Screenshot 2018-12-05 12.02.42

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?

 

Screenshot 2018-12-03 17.50.40

Screenshot 2018-12-03 17.51.18
The chocolate coin cost 7p

 

What if…………..

……..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?

presentVary the amounts and the coins you can use.

Screenshot 2018-12-03 18.01.40

Posted in Christmas, combinations, Making totals

Christmas challenge – Day 5

5 Christmas stars – investigating 5

stars on treeAn 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

Ask:

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.

Screenshot 2018-12-03 08.32.20

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.

What if…………

There was a different number of stars on the tree? Explore any number.

There were more than two colours of stars?