Posted in Additive relationships, Calculating, Fluency

Calculating with target boards

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. 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. 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. 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?

More flik-flaks: number bonds

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

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.

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: “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: 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 Additive relationships, Calculating, Fluency

Under the leaf

How many spots are 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.

• 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 Additive relationships, Counting, Easter, Games

Easter Race to 10

A game for any number of players.

You will need:

• A dice with numbers 1 – 3, or a set of digit cards (download here double sided to have Digit Dog on the back) that are placed face down in a pile and then the top one is turned over for each turn
• 10 eggs for each player (cut out eggs here or use mini chocolate eggs)

Take turns to throw the dice. Count the number of eggs and put them on the 10 frame. The first person to get 10 eggs wins.

As you play describe how many eggs you have:

“I have ……… eggs. I need ……….more to make 10”.

During the game take time to look at each other’s frames and talk about the numbers of eggs on each frame.

Use the sentences like Calculating Cat:

“I have ……… more eggs than you. You have …….fewer eggs than me.”

“I have …….fewer eggs than you. You have ……..more eggs than me.” How many eggs does Digit Dog have?

How many eggs does Calculating Cat have?

Who has fewer eggs? How many fewer? Explain how you know.

Who has more eggs? How many more?

How many more eggs does Digit Dog need to make 10? What about Calculating Cat?

Now play Race from 10

Start with 10 eggs. Throw the dice and take away that number of eggs. The first person to have no eggs is the winner.

Calculating Chicks

How many chicks are hiding? 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.

• 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.

How many bones? 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?”

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.

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

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.

Calculating Chicks

How many chicks are hiding? 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.

• 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.