Category: Calculating

Posted in Calculating, Counting, Games, Subitising

Who has more?

Posted on by Digit Dog

Digit Dog and Calculating Cat are playing with the bottle top bugs (make them with milk bottle tops).

bugs 1-12 fives   bugs 1 - 12 numicon

Who has more?

Put your bottle top bugs in a feely bag or a box or under a tea towel. 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 the bugs. Keep playing until you have used all the bugs. The winner is the one to have captured most bugs.

Who has more spots? How many more?

Who has fewer spots? How many fewer?

Say how many spots there are without counting in ones. Calculating Cat knows she has 11 spots because she counted 5 + 5 + 1.

What if…….

…….the player with fewer spots wins?

…….players take out two bugs, add the number of spots and compare the totals? The player with the greater total captures the bugs.

 

Posted in Calculating, Games

Collect the bugs

Posted on by Digit Dog

Collect the bugs

collect the bugs

A game for two players.

You need two dice and a set of bottle top bugs (you can make these by drawing on old milk bottle tops. Either use spots or numerals). You can print these leaves to put the bugs on, if you wish.

Screenshot 2020-03-26 19.07.06

Screenshot 2020-03-26 19.07.14

Take turns to roll both dice and use either addition or subtraction to capture a bug e.g. 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.

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?

What if………

…… you could multiply the two numbers?

……you could also divide the numbers?

 

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, Conceptual understanding, Easter, Logical reasoning, Problem solving

Two eggs left

Posted on by Digit Dog

Digit Dog has been eating his Easter mini eggs.

He has 2 eggs left.

Calculating Cat is wondering how many eggs he could have had to start with and how many he could have eaten to be left with 2.

two eggs left

How many eggs could he have had at the start? What if it was 6? How many would he have eaten to be left with 2?

What other numbers could he have started with?

What number do you know he couldn’t have had at the start?

How many different solutions can you find?

How did you work it out? Explain your reasoning.

Can you record your solutions?

Can you put your solutions in order?

What if………..

……………he had a different number of eggs left?

………….he was eating bones not eggs?

………..you made up a problem like this about your Easter eggs?

Posted in Calculating, Logical reasoning, Making totals

Making totals

Posted on by Digit Dog

Digit Dog and Calculating Cat are using 4 bottletop bugs (or you can use digit cards) to make different totals.

make totals with bugs.png

They have got the 2, 3, 4 and 8 bugs.  They have made two totals already and are wondering how many more they can make.

What totals can you make? Which bugs are you using?

How are you going to record what you have done? With a drawing? With a number sentence?

Can you make these totals:

9

10

11

13

14

15

How will you know when you have found all the possible totals?

Can you record your work in a systematic way?

What if…………

…………you choose a different 4 bugs / numbers and do the same thing?

 

 

Posted in Calculating, Conceptual understanding, Easter

Making ten with eggs

Posted on by Digit Dog

Digit Dog has got 10 mini Easter eggs and two baskets. He puts some eggs in one basket and the rest in the other. He’s trying to find out how many ways he can do this.

Try this yourself – if you don’t have eggs and baskets you can use any objects and containers you can find.

eggs in basket

eggs in basket Welsh

Let children try out some different ways of organising the eggs. Say:

I have ……..eggs in one basket and ……..eggs in the other. I have 10 eggs altogether.

…….. plus ……… is equal to 10.

Ask:

How can you record what you have done? Children might take photos, draw pictures or write a number sentence.

How will you know you have found all the different ways? Can you explain how you know?

Do you notice any patterns?

What if………….

……….you put the eggs in the two baskets, then one person closes their eyes and another person takes away some eggs? Person 1 opens their eyes and works out how many eggs are missing. How did you work out how many were missing? Explain your thinking.

………you had three baskets?

……..you had more than 10 eggs?

 

Posted in Calculating, Making totals

Making more tens

Posted on by Digit Dog

Another way to investigate making 10 with 2 numbers using the bottletop bugs. Download the board here.

Making ten bugs

Can you record the pairs that you have found?

You could also use the number pebbles to do the activity.

making ten pebbles

Try turning the pebbles face down. Turn them over one at a time and decide where to place them on the board.

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 Calculating, Counting, Games

Face Up

Posted on by Digit Dog

You need:

4 milk bottle tops with a face drawn on them.

bottle tops

About 50 small objects to keep score – you could use cocktail sticks, counters, buttons, dried beans, small pebbles, Lego pieces.

How to play:

  1. Decide how many rounds you want to play.
  2. Toss the bottle tops in the air and count how many fall with faces up and how many with faces down.

To score:

All 4 face up = 5 points

3 up and 1 down = 2 points

2 up and 2 down = 1 point

1 up and 3 down = 2 points

All 4 down = 5 points

Keep your score with the small objects. The player with most objects at the end of the agreed number of rounds wins.

Dash

Variations

You can keep score with pencil and paper instead of objects.

If you want an Easter theme, you can use mini eggs to keep score.

Use more bottle tops and make up your own scoring system.

Invent your own game.

 

Posted in Calculating, Games, Logical reasoning, Making totals

Which Square?

Posted on by Digit Dog

How to play Which Square?

A game for 2 players.

You need:

A game board (download here), two dice and 12 counters for each player.

Rules:

  • Each player puts their counters on the board. They can put them on any number and more than one counter on a number if they wish.
  • Players take turns to throw 2 dice and to add the two numbers. If they have a counter on the total they have thrown, they can take it off. If they have more than one counter on the total, they just remove one.
  • The winner is the first to remove all 12 counters.

Digit Dog and Calculating Cat are playing the game. They both think that they will win. What do you think?

Which square

Look at where they have placed their counters. Who do you think will win? Why do you think that?

When you are playing the game do you notice that you get some totals more than others?

Which numbers are the best to put your counters on? Are there any numbers you don’t want to put your counters on? Can you explain why you think that?

Play the game a few times to see if your ideas work.

Posted in Calculating, Games

Turn the cards

Posted on by Digit Dog

Digit Dog and Calculating Cat are playing a game of Turn the Cards

Turn the cards

You will need:

A set of digit cards and two dice

You can download some digit cards here  (if you print them double-sided they will have Digit Dog on the back) or you can just write numbers on pieces of paper. If you don’t have dice, there are free rolling dice apps that you can download.

Rules:

  1. Put the cards 1 – 6 in order
  2. Player 1 throws the two dice and turns over the cards that match the dice – Digit Dog threw 2 and 3 so he will turn over the 2 card and the 3 card. Keep throwing the dice until you can’t turn over any more cards. The cards that are left showing are added together and that is Player 1’s score.
  3. It is now the next player’s turn. Put the cards in order again and throw the dice in the same way as Player 1.
  4. The winner is the one with the lower score.

Either play one round to find a winner or play 5 or 10 rounds, adding the scores of each round to give a final score.

Want more of a challenge?

Use digit cards from 1 – 12 and put them in order.

When you throw the dice you can:

  1. turn over the cards that match the numbers on the dice.
  2. add the two numbers and turn over the total.
  3. subtract the two numbers and turn over the answer.

As with the first game, your turn ends when you can’t turn over a card. Find your score by adding together all the cards still facing up.

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.