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Posted in Easter

Easter counting competition

How many objects can you fit in the egg?

Digit Dog and Calculating Cat are trying to fill their plastic eggs with as many objects as they can.

Give each child an empty plastic Easter egg and ask them to fill it with as many objects as they can.

fill the egg

 

 

 

Fill the egg Cy

Count the objects to see who has the most. Ask children to organise the objects so that they can see how many there are without counting in ones.

They can do this by:

  1. Putting the objects into the holes on Numicon ten-shapes. How many do you have?  “I have one ten and seven”.
IMG_2475
Calculating Cat’s objects.
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Digit Dog’s objects.

How many objects does Digit Dog have? Don’t count in ones.

Does he have more or fewer objects than Calculating Cat? Explain how you know.

2. Organising the objects into the Numicon shape patterns to help organise the count.

Screenshot 2018-03-23 08.27.30

Screenshot 2018-03-23 08.27.39

3. Putting the objects on a 10-frame.

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Calculating Cat
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Digit Dog

Who collected the most objects? How do you know?

How many more objects does Calculating Cat need so that she has 20? How can you work it out by looking at the 10-frame?

4. Putting the objects in egg boxes.

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Calculating Cat
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Digit Dog

Who won the competition? Who had more objects? Who had fewer objects? Can you quickly count the objects?

What is the largest number of objects that you could fit in the egg?

Can you write the number? Can you build the number with Numicon or Base 10 resources?

Make a class list to record the number of objects each child collects. Compare the numbers. Order the numbers.

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.

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Screenshot 2019-03-22 09.12.08

Download the challenge card here

Posted in 2-sided beans, Calculating, Games

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.

Screenshot 2018-03-05 14.47.23

 

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.

Screenshot 2019-03-21 17.52.09

Download the Exploring 10 – Fill the Frame challenge card here.

 

 

 

 

Posted in 2-sided beans, Calculating, Games

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.

Screenshot 2018-03-05 14.37.42

Download the Challenge Card here.Screenshot 2019-03-21 11.08.15

 

 

 

 

 

 

 

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.

Screenshot 2019-03-06 09.39.44Screenshot 2019-03-06 09.40.02

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.

Screenshot 2019-02-05 14.55.59

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, Games

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 PIGpig

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:

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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:

  1. 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.
  2. Use a 1 – 3 dice and a lower target score.
  3. Make the calculating more accessible by collecting Numicon shapes each time you roll and put them on the number line. screenshot 2019-01-30 09.31.58
  4. 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.
  5. 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.
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 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?

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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

 

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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

The last Christmas challenge of 2018

Stars on crackers

crackers 2.png

What do you think? How can you solve Calculating Cat’s problem?

Using the Numicon® shapes might help. Use the shapes to represent the stars.

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Or use the Cuisennaire rods to find ways to make the 19 stars.

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What if……

………..Calculating Cat wanted a differen tnumber of stars on the tree? What about 21? 22? or a larger number?

………there was a different number od stars on each cracker?