Category: Number sense

Posted in Counting, Games, Number sense

Counting games

Posted on by Digit Dog

Digit Dog and Calculating Cat have been practising their counting skills by playing the Incey Wincey Spider  (Nursery and Reception) game (Year 1 and 2) from www.nrich.org

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Digit Dog and Calculating Cat enjoyed the game so much that they made their own version of the game.

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The game is for two players – one is Digit Dog, the other Calculating Cat.

You need:  One dice, one counter.

Digit Dog wants to get to the bone, Calculating Cat wants to get to the fish.

Put the counter on start.

Take turns to throw the dice and move the counter. Both players move the same counter – Digit Dog moves the counter towards the bone, Calculating Cat moves it towards the fish.

The winner is the one who gets to the food first.

Variations

Use two dice – throw the two dice and choose which dice you want to use.

Use two dice – add the numbers on the dice and use the total for your move.

Use two dice – find the difference between the numbers on the two dice and use the difference for your move.

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 Counting, Number sense, Subitising, Ten frames

Ten frame games

Posted on by Digit Dog

1. Make the number

Screenshot 2020-06-24 11.27.44

You need:

For 3 – 5 players

Two sets of Digit Dog ten frames – large or small

Small objects such as pennies, buttons or counters.

To play:

One player is the leader and has the ten frame cards in a pile, face down.

Other players have a blank ten frame and ten small objects each.

The leader turns over the top card for a few seconds and then turns it back again.

Other players make the pattern they saw with objects on their ten frame.

The leader turns over the card again to check the patterns. Players who were correct score one point.

Play until all cards have been turned over, or one player reaches 10 points.

The winner is the player with most points.

Variations

  • Make the number on your ten frame one more than the number on the card.
  • Make the number on your ten frame two more than the number on the card.
  • Make the number on your ten frame one less than the number on the card.
  • Make the number on your ten frame two less than the number on the card.

 

2. Who has more?

 

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You need:

For 2 players

A set of Digit Dog ten frames for each player, in a pile face down.

To play:

On the count of 3, players turn over their top card. The player with more dogs wins the two cards and says “I have …….dogs. I have more dogs than you”. The other player says “I have ……. dogs. I have fewer dogs than you”.

The game ends when all cards have been turned over. The winner is the player with more cards.

Variation

  • The player with the fewer dogs wins the cards.
  • Say how many more and how many fewer dogs there are.Screenshot 2020-06-24 12.10.41
Posted in Counting, Number sense, Subitising, Ten frames

Ten frame flash

Posted on by Digit Dog

This game practises subitising (see June 24th Post)

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To play Ten Frame Flash you need:

A few sets of Digit Dog ten frame flash cards – large or small

To play:

Place the cards in a pile face down.

One player shows the top card and then turns it back again, the other players have to say how many dogs were on the card. The length of time that the card is revealed can get shorter as learners get better at recognising the patterns.

Encourage learners to recognise patterns and to work out the number without counting each dog.

How did you know how many there are? Explain your thinking.

Variations

  • For learners still practising counting accurately, turn over the cards and count each dog. Place an object on each dog and count the objects.
  • Use the five frame flash cards.
  • For a challenge: turn over the card, show the dogs and then hide them again. This time say one more than the number of dogs or one less than the number, e.g. if there were 4 dogs on the card, you would say “one more is 5” or “one less is 3”.

Try these on-line ten frame games:

https://gregtangmath.com/tenframemania

https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Ten-Frame/

Posted in Counting, Number sense, Subitising, Ten frames

Using ten frames

Posted on by Digit Dog

Show these slides for a couple of seconds to practise saying how many objects there are without counting in ones.

To play:

Open slideshow.

Click once to reveal an image, click again for it to disappear.

Ask: “How many Digit Dogs can you see?”

At first learners will want to count each dog and you will need to leave the image on the screen. Practise recognising the groups of dogs and saying how many there are without having to count each one. How quickly can you do this?

Being able to look at a small set of objects (up to 5) and say how many there are without counting in ones is called subitising. Once children can count objects accurately we want them to move onto subitising, this is an important step in the development of number sense.

It is easier to subitise if objects are arranged in recognisable patterns, such as the dice dot patterns or on ten-frames. The frames are used so that learners can relate numbers to 5 and 10, an important understanding for calculation.

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I know there are 5 spaces in each row, so I can see this 4 in relation to 5. 4 is one less than 5.

 

Perceptual subitising – instantly recognising a small group of objects, usually up to 5 or 6.

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How many Digit Dogs can you see?

 

Conceptual subitising – seeing smaller groups of objects within a larger group to say how many there are without counting in ones. We do this when there are more than 5 or 6 objects.

 

I know there are 7 because I see 5 and 2 more.

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I know there are 7 because I can see 4 and 3 more.

 

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.

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.

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

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Download drainpipes here.

Posted in Additive relationships, Calculating, Communication using symbols, Conceptual understanding, Fluency, Logical reasoning, Number sense, Strategic competence

How many bones?

Posted on by Digit Dog

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The aim of the activity is to encourage learners to think and talk mathematically – to have a mathematical conversation and use their knowledge of additive relationships. This structure of problem is more difficult than the usual “I had 2 bones and then ate 2 more, how many did I eat altogether?”

Ask:

What has Digit Dog been doing? Can you tell me in your own words? What is Calculating Cat wondering?

How many bones could Digit Dog have had in the beginning? How many could he not have had? Explain your thinking.

Take suggestions for numbers of bones.

Is there just one answer?

Use one number as an example.

If Digit Dog started with 3 bones, how many bones did he eat?

Explain how you can find out. You might want to use bones, drawings, Numicon shapes, cubes to help.

Can you write a number sentence?    3 – ? = 2

Try some other numbers of bones.  Record your answers. Can you put your answers in order? What do you notice?

Use this speaking frame to explain your work:

Digit Dog started with ______ bones, he ate _____ bones, now he has 2 bones left.

What if……….

He had a different number of bones left?

Make up your own problem like this about Calculating Cat and some fish.

The five proficiences

Learners will use:

  • strategic competence to make sense of the problem, work out what is known and what needs to be found out and to decide on a way of solving it.
  • logical reasoning to explain their thinking and work systematically to find possible numbers.
  • conceptual understanding of, and fluency with, number bonds to recognise that they need numbers with a difference of 2 or to see this pattern as they try out numbers, to see that 1 or 2 are not possible numbers to start with and to be efficient and accurate with the basic calculations.
  • communication using symbols and correct mathematical vocabulary to show and explain their thinking .

Learners will need to be competent in all five proficiencies to make up their own problems.

Posted in Calculating, Making totals, Number sense

Using Numicon® to explore equivalences

Posted on by Digit Dog

equivalent shapes

The idea of equal value is fundamental to mathematical understanding. Children need to understand that the “=” symbol means “equal value” and not “here is the answer”.

Ask:

How can you make the scales balance?

Which Numicon® shape could go in the pan balance?

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What about this one?

How are you going to solve it? Explain your thinking.

What if ………..you changed the shapes?

 

Now using numerals.

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Can you model this with the pan balance and Numicon® shapes?

What’s the missing number? Explain how you know. Record the sentence.

Make up some of your own.

Make sets of problems like this to put with a pan balance in your enhanced provision.

Posted in Calculating, Christmas, Number sense, Numicon

Christmas Challenge – Day 2

Posted on by Digit Dog

Two Numicon® shapes – which shapes are in the Christmas sack?

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Show me 2 shapes that could be in the sack. Why do you think that? Are you sure? Convince me.

Are they the only 2 shapes it could be?

How many pairs could it be?

If I show you one of the shapes will you know for sure what the other one is?

Encourage children to explain their reasoning. At first, why don’t they know for sure which two shapes are in the sack? How many possible pairs can it be? Show one pair, and another, and another………..

When you know one shape, how can you be sure what the other shape is?

Variations

  1. Put one shape in the sack and give children clues so that they can work out which shape it is. An opportunity to model mathematical language.  My shape is:
    • one more / one less than………
    • two more/ two less than………
    • in between……
    • an odd/even number
    • If I add …and …..I get this number
    • If I take my number away from 10, I am left with……
    • The difference between my number and 6 is………
    • ……more than……
    • a multiple of ……….
    • a factor of………Get the children to ask questions about your shape to work out which one it is.
  2. Put 3 shapes in the sack. The total is 15 which shapes could they be? What if I show you 1 shape, how does that change your thinking?
  3. Vary the totals, vary the number of shapes.

 

 

 

 

 

Posted in Counting, Number sense, Subitising

Subitising

Posted on by Digit Dog

Subitising is being able to look at a small set of objects (up to 5) and say how many there are without counting in ones. Once children can count objects reliably we want them to move onto subitising – an important step in the development of number sense.

Perceptual subitising – instantly recognising a small group of objects.

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How many Digit Dogs can you see?

Conceptual subitising – seeing smaller groups within a larger group to say how many there are without counting in ones.

 

I know there are 7 because I see 5 and 2 more.

Screenshot 2018-03-15 17.01.54.pngScreenshot 2018-03-15 17.02.01.png

I know there are 7 because I can see 4 and 3 more.

Show these slides for a couple of seconds to practise subitising. Click once to reveal the image, click again for it to disappear.