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Posted in Christmas, Problem solving

Christmaths advent calendar

 

Digit Dog has got a Christmaths challenge for each school day in December.

Click on the images to reveal the first week’s challenges.

December 2ndScreenshot 2019-11-17 13.41.26

December 3rd Screenshot 2019-11-17 13.43.19

 

 

 

 

Screenshot 2019-11-17 13.44.42December 4thScreenshot 2019-11-17 13.46.21

                                                                                                December 5th

Screenshot 2019-11-17 13.49.21December 6th

 

 

 

 

 

 

Posted in Christmas, Numicon, Problem solving

Start planning your Christmaths with Digit Dog

One Santa’s sleigh – put the presents on Santa’s sleigh

You will need Santa’s sleighs (download and print) and a set of Numicon® shapes. Match the shapes to the spaces on the sleigh.

Screenshot 2018-11-30 16.27.13

  1. Give children just the shapes they need and let them match them to the spaces on the sleigh.
  2. Have a complete set of shapes for children to choose from.
  3. When the sleigh is covered, one partner closes their eyes, the other takes away one shape. Which one is missing?
  4. For an extra challenge, put the shapes in a feely bag and find the ones you need by touch alone.

Ask:

How many shapes do you need?

Which shape will fit here…..?

Is the shape that goes here big or small? Bigger / smaller than a red one?

Can you take away one shape and put two in its place?

Which shapes are easy to find?

5. Start with the blank sleigh and ask learners to use the Numicon shapes to cover it in any way they can.

How many different ways can you do it? Compare your sleigh with your friend’s. What’s the same and what’s different?

 

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 sleigh? Which shapes will work? Which won’t? Why?

What is the fewest number of shapes you can use? The most?

You use only odd shapes? Only even?

Find more ideas in the Santa’s Sleigh Challenge Booklet

 

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.

Screenshot 2019-11-13 11.41.26

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.

Screenshot 2019-10-17 18.10.54

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 Easter, Numicon, Problem solving

Collect the Easter Eggs

Collecting eggs

Digit Dog is collecting eggs from the Easter Bunny’s store. Here is a map of the store. (download and print your store here

Digit Dog counters

Screenshot 2019-04-03 15.31.31

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

How many presents can Digit Dog collect?

How many different ways can he go though the store?

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

Screenshot 2019-04-03 15.49.25

Can you do it a different way, Digit Dog, and collect more eggs?

What’s the most eggs you can collect?

What’s the smallest number of eggs?

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

Simplify the task

  1. 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 eggs.

Screenshot 2018-12-04 16.58.53

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

Screenshot 2018-12-04 17.01.28

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

Calculating Cat
Calculating Cat says that you can make 10s with the shapes and that makes it easy to find the total. 10, 20, 21

 

Screenshot 2018-12-04 16.59.30

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

3. Put just Numicon® shapes in the rooms – no numerals.

4. Put mini-eggs in the rooms. Instead of counting in ones, put the eggs in the Numicon® ten-shapes to find the total.

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 all.

Posted in Easter, Numicon, Problem solving

Cover the animals

Easter animals

Digit Dog and Calculating Cat are using the Numicon® shapes to cover the picture of the Easter Chick .

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

Screenshot 2019-04-03 13.39.12

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

Compare your chick 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?

Play What’s missing?

  1. When the chick is covered with shapes, one child closes their eyes, another takes away one shape. Which one is missing? How do you know?
  2. Put some shapes in a feely bag, take them out one at a time and place on the chick. Can you find the shapes you want by touch alone?  This helps with visualising the shapes.

Ask:

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

Can you cover the chick 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 chick? Which shapes will work? Which won’t? Why?

Encourage learners to describe and explain what they are doing.

Look for those learners who have a strategy for choosing shapes and those who use trial and improvement.

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 chicks together and ask “what is the same?” “what is different?”

 

Try the same activities with the Easter Bunny  (download here).

 

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Posted in Uncategorized

Spring Chicks

Digit Dog and Calculating Cat are trying one of the Numicon Ideas for Spring resources that they found on www.oxfordowl.co.uk

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How can Calculating Cat share the chicks between the 3 nests? Try it.

How many chicks will be in each nest? Convince your friend that you are right.

Write a dividing calculation to go with your representation.

Try different numbers of nests – can you share the 12 chicks equally between 2 nests? What about 4 nests, 5 nests, 6 nests? What do you notice?

Try a different number of chicks. What happens?

Posted in Calculating, Easter

Calculating Chicks

The chicks are hiding

Screenshot 2018-03-22 23.20.51

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?

 

Posted in Easter, Games

Easter Race to 10

A game for any number of players.

You will need:

  • A Numicon 10 shape each
  • A 1 – 3 dice
  • Mini eggs for each player

Take turns to throw the dice. Count the number of eggs and put them on the 10 shape. The first person to get to 10 wins.

As you play describe how many eggs you have:

“I have ……… eggs. I need ……….more to make 10”.

During the game take time to look at each other’s shapes and talk about similarities and differences.

IMG_1593

How many eggs does Digit Dog have?

How many eggs does Calculating Cat have?

Who has fewer eggs? How many fewer? Explain how you know.

Who has more eggs? How many more?

How many more eggs does Digit Dog need to make 10? What about Calculating Cat?