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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, Counting, Mathematical language

How many?

Posted on by Digit Dog
Design by Cordelia Hutchinson Ling Design produced for National Trust www.nationaltrust.org.uk

Look at the card and see what you can count.

How many cats are smiling? How many are not?

How many cats are not wearing hats?

How many cats have stripes?

How many more cats have hats than have scarves?

How many fewer scarves are there than hats?

How many legs? How did you count them? Did you count in 2s or 4s?

How many eyes? Ears? Whiskers?

How many holly leaves?

How many more hats do they need so that all the cats are wearing one?

Make up some word problems

Ten cats are coming to the party, how many haven’t arrived yet?

At the beginning of the day there were 8 cats, how many have gone home?

Some cats were playing in the snow, 4 cats ran away and now only 6 are left. How many were there to start with?

Write some number sentences to go with the picture.

6 = 4 + 2 There are six cats altogether. Four cats standing plus 2 that are not.

6 = 1 + 5 There are 6 cats altogether. 1 cat holding holly and 5 not or 1 cat sleeping and 5 awake.

What if……..?

What if Calculating Cat joined in? How many cats would there be then?

What if 3 cats ran away? How many would be left?

What if two more cats fell asleep? How many would then be sleeping?

What if two more cats put on a scarf?

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 Christmas, Mathematical language

Christmas card questions

Posted on by Digit Dog

Choose a Christmas card and see how many mathematical questions you can ask about it.

Card by Louise Cole for DementiaUK (2020) http://www.dementiauk.org

How many sheep are wearing headphones? How many are not wearing them?

How many sheep are upside down? How many are the right way up?

Use concrete resources and number sentences to explain your answers.

One sheep is holding a present, 9 sheep are not. There are 10 sheep altogether. 1 + 9 = 10, 10 – 1 = 9.

Use the words more than, fewer than, less than in your questions.

How many fewer sheep are upside down than are the right way up?

How many more presents do they need so that all the sheep have one?

What’s the difference between the number of sheep with scarves and the number without?

How many legs are there? How do you know? How did you count them?

How many eyes?

Ask some what if questions:

What if one more sheep came along? How many would there be?

What if 3 sheep ran away?

What if 2 more sheep put a hat on?

How many more sheep would you need to make a larger triangle? Explain your thinking. What do you notice?

Posted in Counting, Games, Number sense, Subitising

Counting with Digit Dog

Posted on by Digit Dog

Digit Dog and Calculating Cat have been practising their counting. Play their game by downloading it here.

If you want more ideas like this then book onto Mathematics and Numeracy in PS1 (Nursery and Reception) on October 13th 2021.

IMG_1591.jpg

You need one counter and a dice (a dice with numbers 1, 2 and 3 is ideal but you can play with an ordinary 1 – 6 dice)

The game is for 2 players – one will be Digit Dog and the other will be Calculating Cat.

Put the counter on Start. Both players move the same counter BUT Digit Dog moves towards the bone and Calculating Cat moves towards the fish. Take turns to throw the dice and see who gets their food first. There will be a lot of moving back and fro.

When children throw the dice ask them to say how many spots there are without counting in ones – this is called subitising.

If you enjoyed the game why not try the Incey Wincey Spider game from www.nrich.org

IMG_1590.jpg

Download drainpipes here.

Posted in Uncategorized

“Making Connections” Between the Mathematics and Numeracy and Language, Literacy and Communication AoLEs

Posted on by Digit Dog

Lynwen Barnsley and Helen Bowen are doing another full-day LIVE ONLINE ZOOM session of this popular course on September 30th 2021

The day will be full of practical ideas for making links between the Mathematics and Numeracy and the Language, Literacy and Communication AoLEs. As we begin to embed the new curriculum over the next few years, schools will need to explore how they can make manageable links between AoLEs. How can we use literacy skills in a meaningful way to develop and improve mathematical understanding? Where is the natural overlap?

We will explore and discuss:

  •  Where is the literacy in mathematics? Where are the opportunities for developing literacy skills?
  • What are the good speaking, listening and reading strategies that can help make sense of mathematics and develop reasoning skills?
  • Do you have a toolkit to support talk in mathematics and numeracy? Is it consistent? Is it progressive? Are pupils able to use the toolkit independently, at home as well as in school?

Book your place now at www.collectivelearning.co.uk

Collective Learning Zoom meeting

Posted in Calculating, Fluency, Logical reasoning, Making totals, Strategic competence

Making ten with the Bottle Top Bugs

Posted on by Digit Dog

You need a set of Bottle Top Bugs 0 – 10 with spots or numerals

Screenshot 2020-03-26 19.07.14
Screenshot 2020-03-26 19.07.06

Take turns to choose two bugs so that the numbers on their backs add up to 10.

bottletop bugs add to 10

What do you think?

How many pairs of numbers can you find to make 10?

How do you know you have found all the pairs?

Write a number sentence to go with each of your pairs.

Make up word problems using your pairs of numbers.

What if.…………

…….you looked for 3 numbers which, added together, make 10?

……you weren’t making 10?

…….you looked for numbers with a difference of 1? What do you notice?

…….you made up some of your own questions?

If you don’t have Bottle Top Bugs you can do the same activity with:

digit cards (download here)

Numicon shapes

numbers on pieces of paper

number pebbles like these.

 

number pebbles 2

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 Additive relationships, Calculating, Games, Logical reasoning

Reasoning with the Bottle Top Bugs

Posted on by Digit Dog

Collect the bugs

You need:

A set of bottle top bugs  (0 – 12)

A set of leaves to put the bugs on (optional)

2 dice

Set out the leaves with one bug on each leaf.  Take turns to roll both dice and use either addition or subtraction to capture a bug. For example, if you throw a 5 and a 3 you can either add the numbers together, 5 + 3 = 8, and capture the 8 bug, or you can subtract the numbers, 5 – 3 = 2, and capture the 2 bug.

collect the bugs

Explain your reasoning like Digit Dog.

When all the bugs have been captured, the player who has most bugs is the winner.

Which bugs are easiest to capture? Why do you think that?

Which bugs are more difficult to capture?

Posted in Conceptual understanding, Counting, Mathematical language, Number sense, Subitising

Counting and comparing with Bottle Top Bugs

Posted on by Digit Dog

Count, order and compare with Bottle Top Bugs.

Digit Dog and Calculating Cat are playing Who has more?

To play the game you need:

A set of Bottle Top Bugs

A feely bag, box or cloth

Put your bottle top bugs in a feely bag or a box or under a cloth. Each player takes one bug out, puts it in front of them and says how many spots there are. The player with more spots captures both bugs.

Keep playing until all the bugs have been used. The winner is the player who has captured most bugs.

Ensure learners are using correct mathematical language.

Ask:

Who has more spots? Who has fewer spots?

Who has more? Who has less?

Say:

I have more spots. I have fewer spots.

I have more. I have less.

Make sure that learners practise using fewer/less as well as more.

Practise subitising (saying how many spots there are without counting in ones). Seeing patterns and arrangements of objects is an important skill that helps with rearranging, combining, breaking up and putting together amounts in number.

When you turn over a bug, say how many spots there are without counting in ones. How do you know how many spots there are? Calculating Cat knows she has 7 spots because she saw 5 plus 2 more.

Match the numeral

Say how many spots you have and find that number on a number line.

Say how many spots you have and find a digit card to match that amount.

Extend the game

Ask Who has more spots? How many more?

Who has fewer spots? How many fewer?

I have …..spots. I have ……. more spots than my friend.

I have …….. spots. I have …….. fewer spots than my friend.

Vary the game

  • Change the rules so that the player with fewer spots wins.
  • Players take two bugs and add the number of spots together. They then compare their totals. The player with the greater total captures all four bugs.
  • Players take two bugs and find the difference. They then compare their differences. The player with the greater difference captures the four bugs.

Posted in Counting, Mathematical language, Subitising

Exploring number with Bottle Top Bugs

Posted on by Digit Dog

How to make a set of Bottle Top Bugs.

Use the tops from plastic milk bottles.

Draw eyes and spots. Think about the patterns of spots – this arrangement focuses on the pattern of 5. The numbers above 6 are arranged as “5 and some more”.
The spots on these bugs are arranged to match the Numicon shape patterns.
These bugs have “goggly eyes” and the spots are divided into two so that number bonds can be explored.

Explore your bugs.

Ask:

What do you notice?

  • Find bugs with the same number of spots.
  • Count the spots and put the bugs in order.
  • Start to recognise patterns. Say how many spots there are without counting in ones.
  • Find the bug with 5 spots. Now find the one with one more than 5, one less than 5, two more/less than 5.
  • Find two bugs that have 8 spots altogether. Can you find another two with 8 spots? How many different pairs can you find? How do you know you have found them all?