Category: Problem solving

Posted in Chinese New Year, Logical reasoning, Numicon, Problem solving

Chinese Year of the Tiger

Posted on by Digit Dog

February 1st 2022 is the beginning of the Year of the Tiger

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

You will need the tiger picture (download here – make sure you print at 100% so that it is the right size for the shapes) and a set of Numicon® shapes. If you don’t have the plastic shapes you can download a set of printable Numicon® shapes here. 

Use the Numicon® shapes to cover the tiger in any way you can. You could copy Digit Dog and Calculating cat.

What do you notice about the ways they have covered the tiger? Which shapes did they use? How many shapes? What is the same and what is different?

How many different ways can you cover the tiger? Describe what you’ve done.

Compare your tiger 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?

Questions to ask:

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

Can you cover the tiger again, 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?

Play What’s missing? with Digit Dog.

Digit Dog and Calculating Cat have removed one shape from their tiger. Which shape do you think it is? Why do you think that?

Could you fill that space with more than one shape? Which ones?

Play the game with a friend. Cover your tigers with shapes. Player 1 close your eyes, player 2 take away one shape. Player 1 say which shape is missing and explain how you know.

Feely bag challenge

Put some shapes in a feely bag, take them out one at a time and place on the tiger. Can you find the shapes you want by touch alone?  This helps with visualising the shapes.

Challenge learners to:

  • describe and explain what they are doing, to reason why they have chosen certain shapes.
  • have a strategy for choosing shapes rather than do it randomly.
  • swap shapes for other equivalent shapes each time they look for a new arrangement rather than starting from the beginning.
  • put all their completed tigers together and ask “what is the same?” “what is different?”

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

IMG_0849

Posted in Christmas, Logical reasoning, Numicon, Problem solving, Strategic competence

Cover Rudolph’s head

Posted on by Digit Dog

This is the latest addition to the popular Cover with Numicon® series.

You can explore the other activities here: Santa’s Sleigh, Christmas Tree, Baubles and Presents.

For this activity you will need a Rudolph (download and print) and Numicon® shapes.

How many shapes do you think Calculating Cat needs to finish covering Rudolph’s head? Is there more than one way she can do it?

Get some Numicon® shapes and see if you can cover Rudolph’s head.

Can you explain how you did it? Which shapes did you choose first and why? What did you notice? Are some shapes more useful than others?

How many different ways can you find to cover Rudolph’s head? Compare your Rudolph with your friend’s. What’s the same and what’s different about the two Rudolphs?

How many shapes have you used? Who has used most shapes? Who has used fewest?

What is the total of all the shapes you have used?

Can you cover Rudolph using only odd shapes? Why or why not? What about even shapes?

Can you use one shape repeatedly to cover Rudolph? Which shapes will work? Which won’t? Why?

Look for learners who:

Show strategic competence by understanding and tackling the task; by trying different ways of doing it and seeing which ways work.

Use logical reasoning to try different shapes and explain their thinking; are becoming systematic in their choices of shapes; can reason about which shapes will/will not fit; substitute shapes so that they have more or fewer, rather than starting from scratch each time; talk about similarities and differences.

Communicate mathematically about what they are doing; can describe the shapes and say which are bigger/smaller, too big/too small.

Can confidently and fluently choose shapes to fit the spaces on the board; can recognise the spatial patterns and find the shapes that fit.

Posted in Additive relationships, Calculating, Conceptual understanding, Fluency, Logical reasoning, Mathematical language, Number sense, Problem solving

Exploring inverse relationships with the Bottle Top Bugs

Posted on by Digit Dog

Play Under the Leaf

How many spots are under the leaf?bug under the leaf

Digit Dog is using the bottle top bugs and leaves to create some number problems.

This type of problem encourages learners to think and talk mathematically and use the  link between addition and subtraction.

Ask children to:

  • Explain what the problem is about in their own words.
  • Explain what information they know and what they are trying to find out. How many spots are there altogether? How many spots are on the bug you can see? What number of spots cannot be under the leaf?
  • Find a way to work out how many spots are on the bug under the leaf.
  • Describe the strategy they have used. They might:
    • use concrete representations to work out how many more they need to make 10, for example,Screenshot 2021-09-08 at 09.57.08Put counters on a ten frame to represent the total amount and the number of spots you can see. Screenshot 2021-09-08 at 09.48.35Use Numicon shapes to represent the total and spots. Either use the pegs or shapes. Make sure that learners can explain what the resources represent. The pink shape represents the number of spots Calculating Cat can see. Using concrete resources helps learners to explain their thinking.
    • draw pictures of the bugs and spots.
    • find the numbers on a number line and count on or find the difference.
    • use number bonds – the numbers that add together to make 10.
      • I know that 7 + 3 = 10 so there must be a 3-spot bug under the leaf.
      • I know that 10 – 7 = 3 so there must be a 3-spot bug under the leaf.
  • Convince everyone that their answer is correct. Use sentence starters such as:
    • I know the answer is 3 because ….
    • First of all I…………then I………
    • I know that …….. so…………
  • Write a number sentence
  • Change the bugs – choose two different bugs, work out the total number of spots and then hide one under a leaf.

What if you tried a more difficult problem?

  • Use 3 bugs. Work out the total and then hide one bug under a leaf. What strategies will you use now?
  • Use two bugs but try multiplying the numbers. Hide one bug under a leaf but this time say “the product of my numbers is…..”
Posted in Christmas, Numicon, Problem solving

Baubles again

Posted on by Digit Dog

These baubles have a larger space to cover with Numicon shapes.

Ask learners to use the Numicon shapes to cover the space in any way they can.

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

What is the total of the shapes you have used? Can you wite a number sentence to record what you have done?

Digit Dog didn’t use any shape more than once? Can you try this? How many ways can you do it? Is this more difficult? What are you thinking?

Can you use one shape repeatedly to cover the bauble? Which shapes will work? Which won’t? Why?

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

What if you use only odd shapes? Only even shapes?

Look for learners who:

  • can reason about which shapes to use,
  • can discuss what they are doing and explain their thinking,
  • can work systematically,
  • can see patterns and discuss why they are choosing particular shapes,
  • can substitute shapes so that they have more or fewer, rather than starting from scratch each time,
  • can talk about similarities and differences.

Posted in Christmas, Numicon, Problem solving

Christmas Baubles

Posted on by Digit Dog

 

If you enjoyed Cover Santa’s Sleigh and Cover the Christmas Tree, here’s another version of the activities.

You need:

  • copies of the baubles (download and print – make sure you set the print scale at 100% so that the shapes are the corect size)
  • a set of Numicon® shapes.

Match the shapes to the spaces on the bauble.Cover the bauble

  1. Give learners a limited number of shapes to choose from to match the spaces on the bauble.  Can they find the shapes they need?
  2. Have a complete set of shapes for children to choose from.
  3. When the bauble is covered, one partner closes their eyes, the other takes away one shape. Which one is missing? Can you find it in the pile of shapes?
  4. For an extra challenge, put the shapes in a feely bag and find the ones you need by touch alone.
  5. Ask: Why does Calculating Cat think there might be more than one way of covering the shapes?

As learners are working, ask them to explain their thinking.

Why did you choose that shape?

How many shapes do you need?

Which shape do you think will fit here…..? Is it bigger than the orange shape?

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

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

 

Posted in Christmas, Numicon, Problem solving

Cover the Christmas Tree

Posted on by Digit Dog

Can you use the Numicon shapes to cover the Christmas tree?

This is a variation on the popular Cover Santa’s Sleigh activity.

You will need a Christmas tree (download and print) and Numicon® shapes.

Screenshot 2020-11-26 at 18.54.03

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

Ask learners to explain how they covered the tree. Which shapes did they choose first and why? What did they notice? Are some shapes more useful than others?

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

How many shapes have you used? Who has used most shapes? Who has used fewest?

Can you cover the tree using only odd shapes? Why or why not? What about even shapes?

Can you use one shape repeatedly to cover the tree? Which shapes will work? Which won’t? Why?

Can you cover the tree using each shape at least once?

Look for learners who:

  • can reason about which shapes to use,
  • can explain their thinking,
  • can work systematically,
  • can see patterns and discuss why they are choosing particular shapes,
  • can substitute shapes so that they have more or fewer, rather than starting from scratch each time,
  • can talk about similarities and differences.
Posted in Additive relationships, Calculating, Conceptual understanding, Fluency, Number sense, Problem solving

NEW! Challenge card pack – Exploring Additive Relationships

Posted on by Digit Dog

New from Digit Dog Challenges – the challenge cards are extended versions of Digit Dog’s popular posts and are now available in packs of 5 with links to Curriculum for Wales 2022.

Each pack has 5 challenge cards, linked to a theme, concept or resource. There is also an overview of how Digit Dog Challenges address the five proficiencies, and links to the relevant Descriptions of Learning in the Mathematics and Numeracy Area of Learning and Experience.

The latest pack contains activities that focus on solving problems that involve additive relationships. They are aimed at Progression Step 2 level descriptions:

Statement of What Matters 1

I have explored additive relationships, using a range of representations. I can add and subtract whole numbers, using a variety of written and mental methods.

Statement of What Matters 2

I can find missing numbers when number bonds are not complete.

Digit Dog and his bones are used as a context for exploring additive relationships and solving non-routine problems that focus on missing numbers.

Packs are available for purchase at https://www.collectivelearning.co.uk/product/digit-dog-challenges-exploring-additive-relationships-lynwen-barnsley/

Posted in Logical reasoning, Problem solving

100 square jigsaw

Posted on by Digit Dog

Digit Dog and Calculating Cat are doing a 100 square jigsaw. They are looking at each piece and deciding where it goes on the grid.

Screenshot 2020-06-18 12.37.30

Have a go at completing the puzzle.

Download the blank grid here. Download this 100 square and cut along the thicker lines to create the jigsaw pieces.

Think about which piece you are going to put in first. Why have you chosen that one? Which piece has the lowest number on it? Where does that go? How do you know?

Where does the highest number go?

Whenever you place a piece on the board, explain why you are placing it there.

Can you see patterns to help you?

Challenge yourself

  • Turn all the pieces face down. Turn over one piece at a time and work out where it goes on the grid. Explain your thinking.
  • If you want to try an interactive version of this puzzle, go to https://nrich.maths.org/5572
  • Print this 100 square and cut out your own puzzle pieces for a friend to solve.

 

 

 

Posted in Calculating, Logical reasoning, Money, Problem solving

How much is in the purse?

Posted on by Digit Dog

5 coins

Calculating Cat has 5 coins in her purse.

Think about which coins they could be. Get some coins and work out the possibilities.

What is the largest amount that could be in the purse? Which coins would that be?

What is the smallest amount that could be in the purse? Which coins would that be?

Digit Dog thinks that Calculating Cat might have 6p in her purse. Which coins is he thinking of? What about 10p?

Explore which coins could be in the purse. How many different amounts could there be?

Record the different amounts you have found.

Organise your answers so that you can be systematic and work out all the possible amounts.

What if there were fewer coins in the purse? Try it with just 2 or 3 coins.

What if the coins in the purse were silver coins?

What if there were only 1p, 2p, 5p and 10p coins in the purse?

What if no coin was worth more than 20p?

 

Posted in Additive relationships, Calculating, Fluency, Problem solving

Counting and calculating with target boards – numbers to 100

Posted on by Digit Dog

Develop fluency with the target boards. Use the target boards to:

  • recall and remember useful number facts;
  • use number facts to calculate mentally;
  • explain thinking and methods of calculating.
  • use mathematical language correctly

Target board 4

Print Target Board 4

  • Say each number out loud.
  • Say the numbers in order – from smallest to largest and back again.
  • Point at a number – how many tens and how many ones make that number?
  • Point at a number – what is 10 more than that number?
  • Point at a number and count in 10s from that number. How far can you count?

Look at the target board and:

Find two numbers that total / add up to 30 / 40 / 50.

Find more than two numbers that make those totals.

Choose your own totals to make.

Record your work.

  • How do you know you are correct?
  • How did you work it out? Explain your thinking.

Find two numbers with a difference of 10, a difference of 12………… What other differences can you find?

 

Find the column with the highest total. Which column is easiest to add up? Why?

Find the number that is double 14, double 7, double 20………..

Find the number that is half of 80, half of 36………

Find the answer to 5 x 2, 9 x 5, 3 x 4…………..make up some questions of your own.

 

Find numbers that are multiples of 5 (are in the 5 times table), multiples of 2, multiples of 10……..

 

 

 

 

 

 

 

 

Posted in Additive relationships, Calculating, Fluency, Problem solving

Calculating with target boards (4)

Posted on by Digit Dog

Develop fluency with the target boards. Use the target boards to:

  • recall and remember useful number facts;
  • use number facts to calculate mentally;
  • explain thinking and methods of calculating.
  • use mathematical language correctly.

 

Target board 3

Print Target Board 3

  • Say each number out loud.
  • Say the numbers in order.
  • Point at a number and then find that number of objects.
  • Point at a number – what is 10 more than that number?

Ask children to look at the target board and:

Find two numbers that total / add up to 20.

  • How do you know you are correct?
  • How did you work it out? Explain your thinking.
  • How many pairs of numbers can you find?
  • Make a list of the pairs you find.
  • Make up a number story to go with your pairs of numbers e.g. 13 + 7 = 20 There were 13 ladybirds sitting on a leaf, 7 more came along and now there are 20.

Find more than two numbers that total 20?

Find numbers that make other totals.

 

Find the total of the numbers in the first column. How did you work it out? Which numbers did you add first? What did you notice? Did you notice that 18 + 2 = 20? How does this help?

Find the sum of the numbers in the bottom row.  How did you do that? Which numbers did you add first? What did you notice? What is the easiest way to add up the numbers?

Find the column with the highest total. Which column is easiest to add up? Why?

Find the number that is double 1, double 2, double 3………..

Find the number that is half of 10, half of 12………

 

Find two numbers with a difference of 2, a difference of 4…………

Make a list of your numbers. Put them in order. What do you notice? Can you find any patterns?

Problem solving with the target board

My total is 16 – find two numbers that you can add together to make my total.  Can you find three numbers to make my total?

One of my numbers is 7. When I add it to another number, my total is 13. What is my second number?

I am thinking of a number and when I count on 5, I say 14. Find the number I started with.

I am thinking of a number and when I count back 3, I say 8.  Find the number I started with. 

I am thinking of a number. I doubled it to make 16. What is my number?

My difference is 5 – find two numbers on the target board that have a difference of 5.

I am thinking of two numbers. When I take away the smaller from the larger my answer is 4. What numbers could I be thinking of? How many pairs of numbers can you find? How do you know you have found them all?

One of my numbers is 15. When I subtract another number, I am left with 9. What is my second number?

Make up some of your own problems like this.