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

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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?

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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.

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

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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.

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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 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 Chinese New Year, Numicon, Problem solving

Cover the animals

It’s the Year of the Pig

It’s the Chinese year of the pig and Digit Dog and Calculating Cat are using the Numicon® shapes to cover the picture of the pig.

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

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

Compare your pig 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?

  1. When the pig is covered, 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 pig. Can you find the ones you want by touch alone?  This helps with visualising the shapes.

Ask:

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

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

Encourage learners to describe and explain what they are doing.

Look for those learners who had a strategy for choosing shapes and those who did it randomly.

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

 

Try the same activities with the other animals (download here).

 

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Posted in Chinese New Year, Problem solving

Chinese New Year – the 12 zodiac animals problem

the race

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?

Work through the information. Use the numeral cards and picture cards to help.

Use children themselves and the animal masks from www.primarytreasurechest.com to solve the problem. Read the clues and children can move around to find the right order.

Encourage children to check their solution by reading through the clues again.

Posted in Calculating, Problem solving

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)

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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?

screenshot 2019-01-08 08.55.14

 

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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

  1. 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.
  2. 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.

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

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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

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.

Posted in Christmas, Problem solving

Christmas challenge – day 13

What’s the value?

Work out the value of the tree, the snowman and Santa. What is each picture worth?

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What do you notice? Where would be a good place to start? Which row would help us to solve the problem?

Encourage children to use their reasoning skills and make deductions rather than use trial and improvement. Talk aloud and model your thinking.

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Is Digit Dog right? Does using Numicon® help solve the problem? What do you think about Calculating Cat’s idea?

What are you going to do next? What do we know?

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Does using pegs make it easier? What do you think about Calculating Cat’s idea? Can you work out the value of Santa? How?

Could you look at a different column instead of the middle one?

What if.……..you changed the totals?

This challenge was inspired by Bernie Westacott in his conversation with Craig Barton. Watch the podcast – it’s well worth it.

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http://www.mrbartonmaths.com/blog/bernie-westacott-teaching-maths-with-visuals-and-manipulatives/

Posted in Christmas, Numicon, Problem solving

Christmas challenge – Day 8

8 roomscollecting presents

Santa has asked Digit Dog to help him collect presents from his store. Here is a map of the store. (download and print your store here) 

Digit Dog counters

Screenshot 2018-12-03 12.12.49

There are 8 rooms and the number tells you how many presents are in each room. Digit Dog has to go into the rooms and collect the presents 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 2018-12-04 16.45.31

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

What’s the most presents you can collect?

What’s the smallest number of presents?

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 presents.

Screenshot 2018-12-04 16.58.53

I went to rooms 1, 2, 3, 7 and 8. How many presents 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.

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.

Posted in Calculating, Christmas, Numicon, Problem solving

Christmas challenge – Day 6

6 Christmas stars – a puzzle

Christmas tree

Download the tree

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.

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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

Posted in Christmas, Problem solving

Christmas Challenge – Day 3

Three rows and columns

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Place the pictures (download here) on the grid so that no pictures that are the same are placed next to each other in any column or row e.g. you cannot have two snowmen in squares next to each other. An activity that encourages children to think logically, check their work and explain their thinking.

Explain how you did it.  How did you start? Have you checked that you have followed Digit Dog’s rule?

Is there more than one way to do it?

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Digit Dog did this.

 

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Calculating Cat did this.

What do you notice? What is the same and what is different about their grids?

Ask children to compare their solutions.

How many different ways can you find to do it?

Posted in Christmas, Numicon, Problem solving

Christmas Challenge Day 1

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.

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  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 Problem solving

Ladybird Box

Digit Dog saw the Ladybird Box problem on www.nrich.maths.org/144 and thought he’d try it out.

The Challenge

The box has 9 little square compartments. Can you put the 6 ladybirds in the box so that there are just 2 ladybirds in every column and every row?

Ladybird box

I wonder how many ways there are to do the puzzle?

Does it matter which compartment you put the first ladybird in?

What do you need to keep checking? Remember that each row and each column can only have 2 ladybirds in them.

How many empty compartments will there be?

Record your work on this grid

Look at your friend’s solution. What is the same? What is different?