Category: Fluency

Posted in Additive relationships, Calculating, Fluency, Problem solving

Calculating with target boards 2

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 2

Print Target Board 2

  • Say each number out loud.
  • Put objects on each number – check that you have the correct amount.
  • Say the numbers in order.

Practise addition with the target board.

Ask children to:

Find two numbers that total 5.

  • 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.

Find numbers that total 10.

  • 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. 3 + 2 = 5 Digit Dog ate 3 bones for breakfast and 2 bones for dinner. He ate 5 bones altogether. How many different stories can you make?

Find other totals and make up stories to go with them.

 

Find the total of the numbers in the first column. How did you work it out?

Find the sum of the numbers in the bottom row.  How did you do that?

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………..

 

Point at a number and say what double that number is e.g. point at 5 and say “double 5 is 10”

Problem solving with the target board

My total is 8 – 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 5. When I add it to another number, my total is 7. What is my second number?

I am thinking of a number. I count on 3 and get to 8. What number did I start with?

I am thinking of a number. I doubled it to make 8. What is my number?

 

 

 

 

 

 

 

Posted in Additive relationships, Calculating, Fluency

Calculating with target boards

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 1

Print Target Board 1 and a set of dog cards.

Match the dog cards to your target board.

Find two groups of dogs that make 5 altogether.

How do you know you are correct? How did you work it out? Explain your thinking. Can you find a different way of making 5?

Use the cards to record your pairs.

dog cards

What do you think? Will Calculating Cat be able to find more pairs of cards that total 5?

Write a number sentence for each of your pairs.

dog cards sentences

Can you put your pairs of cards in order? What patterns can you see?

Look at the target board again. Can you make some other totals? Can you use more than 2 groups of dogs to make some totals?

Posted in Calculating, Conceptual understanding, Counting, Fluency

Yet more flik-flaks: counting in steps of more than 1

Posted on by Digit Dog

Try using the flik-flaks to practise and use multiplication facts.

Practise counting in 2s by folding the Digit Dog flik-flak in half and asking:

  • How many dogs can you see?
  • How many eyes can you see?
  • How do you know? Tell me a number sentence.

Each dog has 2 eyes – 2, 4, 6, 8, 10

Five 2s equal 10,  5 lots of 2 equal 10, 5 groups of 2 equal 10, 2 five times equals 10,           5 x 2 = 10

1 dog has 2 eyes  1 x 2 = 2

2 dogs have 4 eyes  2 x 2 = 4

3 dogs have 6 eyes 3 x 2 = 6………..and so on

What patterns can you see? What do you notice about the number of eyes?

 

Repeat but this time count number of ears.

Challenge:

You can see 5 dogs but how many dogs are hidden? How many eyes are hidden? How did you work it out? Explain your thinking.

If I can see 12 eyes, how many dogs can I see?

Counting in steps of more than 2

You can practise counting in different steps by choosing different flik-flaks and repeating these activities. There are a range of flik-flaks available on www.primarytreasurechest.com

Use the star flik-flak to count in 5s.

Screenshot 2020-04-23 11.54.17

How many stars can you see? How many points? How did you work it out? What is the multiplication sentence?

If I can see 30 points, how many stars can I see?

Or the 10p coin flik-flak to count in 10s.

Screenshot 2020-04-23 11.58.51

How many coins? How many pence? How did you work it out? What is the multiplication sentence?

 

Posted in Additive relationships, Calculating, Conceptual understanding, Counting, Fluency

More flik-flaks: number bonds

Posted on by Digit Dog

What do children need to practise daily?

In order for children to develop fluency they need to have a daily routine where they practise:

  • Counting;
  • Remembered facts;
  • Using number relationships to do calculations.

Children need the opportunity to:

  • Talk mathematically;
  • Discuss and solve problems;
  • Be creative;
  • Use reasoning skills.

Follow Digit Dog for ideas to engage children in mathematical conversations.

Using flik-flaks

Print your own flik – flaks from www.primarytreasurechest.com

Flik-flaks available to download from www.primarytreasurechest.com

Use flik-flaks to practise:

  • Counting
  • Subitising (recognising small amounts without counting)
  • Number bonds
  • Multiplication facts
  • Using mathematical language
  • Using reasoning skills

Number bonds

Look for patterns within numbers and help children understand that numbers are composed of smaller numbers e.g. fold the Digit Dog flik-flak in half as shown, ask How many dogs can you see? What else can you see? I can see 4 and 1, and 3 and 2……..Explain your thinking. Repeat by folding to show other numbers.

 

Use the flower flik-flak, fold it in half to show 6 flowers.

What do you notice? How many flowers can you see? How many purple? How many red? How many yellow? How many altogether?

Repeat by folding to show other numbers.

Download flower flik-flak here

Use the flik-flaks as a quick way to practise number bonds to 10 (the pairs of numbers that add togther to make 10).

 

Show children the flik-flak and ask:

“How many dogs can you see?” “How did you count them?”

Explore the numbers of dogs in each row and column. Ask questions such as “Which row has most dogs?” “Which row has the fewest dogs?” “Which row has one more than the bottom row?”

Explore the groups of dogs you can see. I can see 5 dogs on the top half and 5 dogs on the bottom, 5 + 5 = 10

Before continuing, make sure children are confident that there are 10 dogs altogether.

Fold the flik-flak:

 

Ask:

“How many dogs can you see now?”

“How many dogs are hidden?” “How many dogs can’t you see?” “How do you know?” “Explain your thinking”.

“How many dogs altogether?”

You want children to realise that they know there are 10 dogs altogether, that they can see 5 of them and need to work out how many of the dogs they can’t see. They might:

  • Count on from 5 to 10
  • Take away the 5 from 10
  • Use their knowledge that  5 and 5 equals 10

Expect children to explain their thinking.

Fold the flik-flak in a different way:

Ask the same questions.

“How many dogs can you see now?”

“How many dogs are hidden?” “How do you know?” “Explain your thinking”.

“How many dogs altogether?”

 

Keep folding the flik-flak to explore all the combinations of numbers to make 10.

I can see 1 dog. 9 dogs are hidden. 9 + 1 = 10
I can see 3 dogs. I know 7 are hidden because 3 +7 = 10.
I can see 7 dogs, so 3 dogs must be hidden because 3 + 7 = 10

 

 

 

 

 

 

 

 

 

Posted in Conceptual understanding, Counting, Fluency, Subitising

Practising maths with Digit Dog

Posted on by Digit Dog

What do children need to practise daily?

In order for children to develop fluency they need to have a daily routine where they practise:

  • Counting;
  • Remembered facts;
  • Using number relationships to do calculations.

Children need the opportunity to:

  • Talk mathematically;
  • Discuss and solve problems;
  • Be creative;
  • Use reasoning skills.

Follow Digit Dog for ideas to engage children in mathematical conversations.

Using flik-flaks

Print your own flik – flaks from www.primarytreasurechest.com

Flik-flaks available to download from www.primarytreasurechest.com

Use flik-flaks to practise:

  • Counting
  • Subitising (recognising small amounts without counting)
  • Number bonds
  • Multiplication facts
  • Using mathematical language
  • Using reasoning skills.

Counting

Hold up the Digit Dog flik-flak and ask how many dogs can you see? You can fold the flik-flak along the black lines to show all the numbers from 0 to 10. This allows children to practise counting sets of objects up to 10.

Give children their own flik-flak and ask them to:

  1. Show a single digit number – 1, 2, 3, 4 ……etc.
  2. Show the numbers 0 – 10 in order. How many ways can you show each number?
  3. Show the same number of dogs as you are showing.
  4. Show one less / one more e.g. show me one less than 3, one more than 5….etc. How did you work it out? Can you do it without counting?
  5. More/fewer than I am showing. Explain your answer. e.g. How many dogs am I showing? Can you show me more dogs? Can you show me fewer dogs?

Subitising

Once children can confidently count the dogs by pointing at each one and not making mistakes, encourage them to subitise i.e. to recognise amounts without counting. When they see 3 dogs, they can say it is 3 without counting 1, 2, 3. They should be able to do this with numbers up to 5.

Counting in 2s

Use the flik-flaks as a quick way to practise counting in 2s.

 

Show children the flik-flak and ask:

How many dogs can you see?  How many eyes can you see?  How many ears can you see?  How did you count them?

Fold the flik-flak:

 

 

 

 

 

 

 

Ask:

How many eyes can you see now? How did you count them? Did you count in 2s? Did you say “3 lots of 2”?

Challenge:

I can see 10 eyes. Show me 10 eyes with your flik-flak. How many dogs are there if there are 10 eyes?

 

 

 

 

 

 

 

Posted in Additive relationships, Calculating, Fluency

Under the leaf

Posted on by Digit Dog

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 on the bug they 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 counters to represent the spots and work out how many more they need to make 10
    • draw pictures of the bugs
    • 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 it with 3 bugs? Work out the total and then hide one bug under a leaf.

……..you tried multiplying the numbers? Hide one bug under a leaf but this time say “the product of my numbers is…..”

 

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 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.