Posted in Chinese New Year, Logical reasoning, Numicon

Chinese Year of the Ox

2021 is the Year of the Ox

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

screenshot-2021-02-10-at-09.02.21

You will need the ox 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 ox in any way you can.

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

Compare your ox 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?

Ask:

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

Can you cover the ox 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?

What’s missing?

When the ox is covered, player 1 closes their eyes, player 2 takes away one shape. Player 1 says which shape is missing and explains how they know.

Feely bag challenge

Put some shapes in a feely bag, take them out one at a time and place on the ox. 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.
  • 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 rats together and ask “what is the same?” “what is different?”

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

IMG_0849

Posted in Logical reasoning, Patterns, Shape

Patterns with tiles

Use 4 of the pattern tiles (download here) to make as many different designs as you can.

Digit Dog and Calculating Cat have arranged the tiles into a square.

What do you notice about the patterns they have made? Can you think of a way of describing the patterns?

What is the same? What is different?

How many different patterns do you think you could make by arranging the tiles in a square?

Try it. Take some pictures of your designs.

How will you know you have found all the ways?

Is there a way of being systematic? Explain your thinking.

What if……..

…….. you only made symmetrical designs?

…….. you arranged the tiles in a straight line?

…….. you used more than 4 tiles?

…….. you designed your own tile?

Posted in Calculating, Christmas, Logical reasoning

5 Christmaths baubles

An activity to explore numbers that total 5.

Screenshot 2020-12-09 at 08.51.42

Digit Dog and Calculating Cat have some red and blue baubles to put on their tree. They can only put 5 baubles 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 baubles

Ask:

Look at the picture. What do you notice? Describe what you see.

What has Digit Dog done? What is Calculating Cat thinking?

How many different ways do you think they can put the baubles on the tree? Why do you think that?

Try it yourself. 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 baubles 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 2020-12-08 at 17.39.58

What does the 5 represent? It is the 5 blue baubles. The 0? There are no red baubles.

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 baubles on the tree? Explore other numbers.

There were more than two colours of bauble?

Posted in Communication using symbols, Conceptual understanding, Fluency, Logical reasoning, Mathematical language, Strategic competence

Have you seen Digit Dog’s challenge card packs?

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.

There are currently two packs available.

The first pack has activities using my favourite resource – the Two-sided Beans

Packs can be purchased from Collective Learning

The second pack has activities that focus on solving non-routine 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.

Packs are available to purchase at Collective Learning

Posted in Logical reasoning, Mathematical language, What do you notice?

Bottle Top Bugs – What do you notice?

 

Digit Dog and Calculating Cat have arranged their bugs in 4 rows of 4.

What do you notice?

How many ways can you finish the sentence?

I notice that……….

Screenshot 2018-06-06 12.20.39

Is Calculating Cat correct? Or has she made a mistake? Convince me. Explain your thinking.

What can you say about:

  • the rows?
  • the columns?
  • the number of bugs?
  • patterns in the numbers on the bugs’ backs?
  • diagonal patterns?
  • odd ones out?
  • totals of spots?
  • their eyes?
  • anything else?

Digit Dog is also asking What do you wonder?

Look at the bugs and finish the sentence – I wonder…………..

How many ways can you finish the sentence? You might say things like:

I wonder what the total of each row is……

I wonder which row has the lowest total……..

I wonder if I can arrnage the bugs in order………

Collect the I wonder statements to use as challenges and activities.

Posted in Logical reasoning, Patterns

Patterns in names

What patterns can you see on the grids? Describe the patterns on each grid. What do you notice?

Screenshot 2020-06-23 09.31.57

Screenshot 2020-06-23 09.51.40Screenshot 2020-06-23 09.50.21

If we added another row, can you predict which square you would colour in? Why do you say that? Explain your thinking.

Try your own name and look for patterns.

Print the 6 x 6 grid here. Write your name in the grid, one letter in each square, repeating it until all the squares are filled. Now colour in the squares which have the first letter of your name in them. What patterns have you made? Can you think of a way to describe the patterns?

Ask people you know to try it. What is the same and what is different about the patterns different names make?

What if you tried a larger grid?

Screenshot 2020-06-23 09.53.25

What has changed?

What about a smaller grid? What patterns can you see then?

Screenshot 2020-06-23 09.53.31

Try some different sized grids with your name.

Download grids

Grids 2 to 8,

Grids 9 and 10.

For more pattern activities go to Digit Dog’s home page, go to Categories and select Patterns

Posted in Logical reasoning, Problem solving

100 square jigsaw

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 Additive relationships, Calculating, Logical reasoning, Making totals

Finding pairs

Digit Dog and Calculating Cat are using one set of digit cards 1 – 10 and looking for pairs that make 10.

Screenshot 2020-06-15 09.32.44

Download a set of digit cards here. You will need cards 1 to 10. Print double-sided to have Digit Dog on the back!

Download a baseboard here. Print two.

How many pairs that make 10 can you make? Put the cards on the baseboard.

Can you use all the cards? Which cards are left over? Why?

Try making some other totals – remember you can only use one set of cards from 1 – 10.

What if you make 9? Which cards are left over? Why?

What about 8?  or 12?  or 13?  or 11? Investigate the number of pairs and the cards that you cannot use.

Record your work. Write down the pairs of numbers and their totals.

 

Posted in Calculating, Fluency, Games, Logical reasoning

Playing with cards 5

Memory addition

Screenshot 2020-06-11 09.14.09

Any number of players or teams of 2.

You need:

A pack of playing cards arranged in a 13 x 4 array, face down. Ace = 1, picture cards = 10.

To play:

Player 1 turns over 2 cards and adds the values. Player 1 then turns over another two cards and adds the values. If the totals match, player 1 keeps the 4 cards and has another turn. If they do not match, the cards are turned face down again and it is player 2’s turn.

The game continues until no more matches can be made.

Can you remember where cards are? How will this help you? Watch carefully when other players are turning over cards.

Variations

  1. Play the same game but subtract the pairs of cards. If the answers match, keep the cards and have another turn. If they don’t, turn them face down again.
  2. On each turn, turn over two cards. If the numbers match, keep the cards and have another turn. If they don’t match turn the cards face down again.
  3. On each turn, turn over two cards. If the numbers and colours match, keep the cards and have another turn. If they don’t match turn the cards face down again.
  4. On each turn, turn over two cards. If both numbers are odd or both even, keep the cards and have another turn. If they don’t match turn the cards back face down.
  5. Make up your own rules!

 

Posted in Conceptual understanding, Fluency, Games, Logical reasoning

Playing with cards 3

Largest number

2 – 4 players

You need:

Digit cards 1 – 9  (one set per player, shuffled) or a pack of playing cards, Ace to 9 only.

To play:

Deal 2 cards to each player.

Players turn over their cards and make the largest 2-digit number they can with the cards they have been dealt.

The player with the largest number scores a point.

Play ten rounds. The winner is the player with most points.

Screenshot 2020-06-08 12.01.45

Variations

  • Deal 3 cards to each player and make 3-digit numbers.
  • Try 4 or 5- digit numbers.
  • Get a point for the smallest number rather than the largest.
  • Play more than 10 rounds.
Posted in Logical reasoning, Patterns

Making patterns 5

Screenshot 2020-06-04 08.30.08

Calculating Cat has made an AB pattern with the sticks:

purple, yellow, purple, yellow, purple, yellow……….

See if you can use her rule to make a pattern with sounds or movements. You could try:

  • Using your hands to clap, click, clap, click, clap, click……….
  • Making sounds such as whistle, shout, whistle, shout………..
  • Using movements such as hop, jump, hop, jump, hop, jump……or
  • stand, sit, stand, sit, stand, sit ……….or
  • wave, stamp, wave, stamp, wave, stamp………….or
  • run, stop, run, stop……..

 

What about this pattern? Look for the rule then use it to make a pattern with sounds or movements.

Screenshot 2020-06-04 08.38.49

 

Screenshot 2020-06-04 08.45.36

 

Play with patterns:

  • One person makes a repeating pattern using objects. Another person works out the rule and uses it to make a pattern with sounds or movements.
  • One person makes a repeating pattern with sounds or movements. Another person copies it.
  • Look for repeating patterns in your environment. Say the rule and use it to make a pattern using sounds or movements.