Category: Strategic competence

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

Have you seen Digit Dog’s challenge card packs?

Posted on by Digit Dog

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 Calculating, Fluency, Making totals, Strategic competence

Bottle Top Bugs – Making tens

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?

What if.…………

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

numbers on pieces of paper

number pebbles like these.

 

 

number pebbles 2

Posted in Additive relationships, Calculating, Fluency, Strategic competence

I wish I had……..

Posted on by Digit Dog

Screenshot 2020-07-01 09.48.30

Digit Dog is counting his bones. “One, two, three.” But 3 bones are not enough.

Reason about numbers by asking questions about the number of bones:

What if Digit Dog found 1 more bone? How many would he have then? How do you know that? Can you convince me?

What if he found 2 more bones?

What if he ate one bone?

Screenshot 2020-07-01 09.51.41

 

What does Digit Dog have to do to make his wish come true? How many more bones does he need? How can you work it out?

Screenshot 2020-07-01 10.11.16

 

Use a five-frame or ten-frame to help learners work out how to make Digit Dog’s wish come true and explain their thinking.

Explore other numbers of bones.

Posted in Calculating, Conceptual understanding, Games, Strategic competence

Subtract from 10

Posted on by Digit Dog

Here’s a game to practise subtracting numbers from 10.

subtraction game

You need:

  • A game board (download here)
  • Counters for each person (we made some with pictures stuck on milk bottle tops)
  • A dice or pile of digit cards 1 – 6

Take turns to:

  1. Throw the dice;
  2. Subtract the dice number from 10, find the answer on the board and place a counter on it.

If you cannot place a counter, do nothing. You cannot put a counter on a number that already has a counter on it.

When all the hexagons have been covered, the winner is the player who has placed more counters.

Use full sentences and correct mathematical language as you play the game.

I have thrown a 2.  10 subtract 2 is 8.

I have thrown a 2. 10 take away 2 equals 8.

Subtraction is not just take away. Learners find the concept of subtraction as difference between more difficult than take away, so play the game using the language of difference:

I have thrown a 2. The difference between 10 and 2 is 8.

Use bottle tops to illustrate this.

difference between
The difference between 10 and 2 is 8.

Also explore subtraction as counting back. Use jumps on a number line to show this.

number line -2
I threw a 2.  10 count back 2 equals 8.

Posted in Calculating, Fluency, Making totals, Strategic competence

Making tens

Posted on by Digit Dog

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?

What if………….

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

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

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

You can do this activity by making some bottletop bugs. Collect milk bottle tops, draw some eyes and then number them 0 – 10

Screenshot 2020-03-26 19.07.06

or draw spots from 0 – 10

Screenshot 2020-03-26 19.07.14

or you can use digit cards (download here)

or write numbers on bits of paper

or you can make some number pebbles like these.

number pebbles 2

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

Calculating Chicks

Posted on by Digit Dog

How many chicks are hiding?

Screenshot 2018-03-22 23.20.51

Digit Dog is using a hollow plastic egg and some fluffy chicks to create some number problems. This type of word problem requires more thinking than the problems such as “There are 4 chicks in my egg and 4 chicks on the floor.  How many chicks are there altogether?”, where the end result is unknown.

The aim is to encourage learners to think and talk mathematically – to have a mathematical conversation and use their knowledge of additive relationships and the link between addition and subtraction.

Ask learners 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 chicks are not in the egg? What number of chicks cannot be in the egg?
  • FInd a way to work out how many chicks are in the egg.
  • Describe the strategy they have used. They might:
    • act it out – using children themselves (with chick masks)
    • act it out – using toy chicks
    • use counters to represent the chicks
    • draw pictures of the chicks
    • use an eight Numicon shape to lace the chicks on
    • use number bonds
  • Convince everyone that their answer is correct. Use sentence starters such as:
    • I know the answer is 4 because ….
    • First of all I…………then I………
    • I know that …….. so…………
  • Write a number sentence
  • Change the number of chicks in the egg.
  • Think about a What if………?

What if there were more than 8 chicks altogether?

What if the story wasn’t about chicks?

Can learners transfer their thinking to a new problem?

Make up some of your own problems like this one for your friend.

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, to make sense of the problem and to use what they know to work it out.
  • conceptual understanding of, and fluency with, number bonds for 8 in order to use them to solve the problem and to be efficient and accurate with the basic calculations.
  • communication using symbols and correct mathematical vocabulary to write number sentences and explain their thinking .

Learners will need to be competent in all five proficiencies in order to create their own problems.

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

Cover the Chick

Posted on by Digit Dog

Easter animals

For those of you who enjoyed the Chinese New Year activity Cover the animals, here’s an Easter version.

Digit Dog and Calculating Cat are using the Numicon® shapes to cover the picture of the Easter Chick .

You will need the Chick picture (download and print on yellow paper) and a set of Numicon® shapes. Ask learners to use the Numicon® shapes to cover the chick in any way they can.

Screenshot 2019-04-03 13.39.12

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

Compare your chick 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?

Play What’s missing?

  1. When the chick is covered with shapes, 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 chick. Can you find the shapes you want by touch alone?  This helps with visualising the shapes.

Ask:

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

Can you cover the chick again but 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 chick? Which shapes will work? Which won’t? Why?

Encourage learners to describe and explain what they are doing.

Look for those learners who have a strategy for choosing shapes and those who use trial and improvement.

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 chicks together and ask “what is the same?” “what is different?”

 

Try the same activities with the Easter Bunny  (download here).

 

IMG_1332

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

Screenshot 2020-03-16 11.08.55

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 Additive relationships, Calculating, Communication using symbols, Conceptual understanding, Easter, Fluency, Logical reasoning, Strategic competence

Calculating Chicks

Posted on by Digit Dog

How many chicks are hiding?

Screenshot 2018-03-22 23.20.51

Digit Dog is using a hollow plastic egg and some fluffy chicks to create some number problems. This type of word problem requires more thinking than the problems such as “There are 4 chicks in my egg and 4 chicks on the floor.  How many chicks are there altogether?”, where the end result is unknown.

The aim is to encourage learners to think and talk mathematically – to have a mathematical conversation and use their knowledge of additive relationships and the link between addition and subtraction.

Ask learners 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 chicks are not in the egg? What number of chicks cannot be in the egg?
  • FInd a way to work out how many chicks are in the egg.
  • Describe the strategy they have used. They might:
    • act it out – using children themselves (with chick masks)
    • act it out – using toy chicks
    • use counters to represent the chicks
    • draw pictures of the chicks
    • use an eight Numicon shape to lace the chicks on
    • use number bonds
  • Convince everyone that their answer is correct. Use sentence starters such as:
    • I know the answer is 4 because ….
    • First of all I…………then I………
    • I know that …….. so…………
  • Write a number sentence
  • Change the number of chicks in the egg.
  • Think about a What if………?

What if there were more than 8 chicks altogether?

What if the story wasn’t about chicks?

Can learners transfer their thinking to a new problem?

Make up some of your own problems like this one for your friend.

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, to make sense of the problem and to use what they know to work it out.
  • conceptual understanding of, and fluency with, number bonds for 8 in order to use them to solve the problem and to be efficient and accurate with the basic calculations.
  • communication using symbols and correct mathematical vocabulary to write number sentences and explain their thinking .

Learners will need to be competent in all five proficiencies in order to create their own problems.