Posted in Calculating, Fluency, Making totals, Strategic competence

Bottle Top Bugs – Making tens

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 Calculating, Making totals, Numicon

Total 6

Total 6 is an extension of Investigating totals

Put the shapes on the grid but this time each row, column and diagonal has to total 6.

6 grid

You might want to start by:

  1. Just making each row total 6. Then try
  2. Just making each column total 6. Follow this by
  3. Making both the rows and columns total 6, and finally
  4. Include the diagonals too.

Which shapes are you using in each row / column? Why?

Is there more than one way of completing the grid?

Look at your partner’s grid. What is the same and what is different?

Make the task more challenging:

  1. Use digit cards instead of the shapes.
  2. Don’t give the total – Can you put the Numicon shapes on the grid so that each row, column and diagonal add to the same total?

What do you think the total might be? Why?

How are you going to start? What are you going to try first?

What if.……..you used three different consecutive shapes?

3 twos, 3 threes and 3 fours                                 3 threes, 3 fours and 3 fives

Screenshot 2018-09-26 14.28.32or   Screenshot 2018-09-26 14.28.43

What will the totals of each row be now?

Screenshot 2018-09-26 15.51.01

Posted in Calculating, Making totals, Numicon

Investigating totals

Digit Dog has got a 3 x 3 grid and 9 Numicon shapes – 3 one shapes, 3 two shapes and 3 three shapes. He is going to put the shapes on the grid and investigate the totals he can make.

Screenshot 2018-09-23 15.50.21

This is what he does first:

Screenshot 2018-09-23 15.50.32

Copy what Digit Dog has done.

Digit Dog says that the sum of the shapes in the first row is 6. Do you agree with Digit Dog? Why or why not? Are you sure?

Expecting learners to explain their thinking helps develop their reasoning skills.

If you agree, convince me that Digit Dog is correct. If you don’t agree, explain why you think he is wrong.

Encourage learners to explain why the total of the first row is 6. Use the Numicon shapes to show that the 3 shapes in the first row are equivalent to a six-shape. Explanations are much easier when you use concrete apparatus.

Screenshot 2018-09-23 18.01.53     Screenshot 2018-09-23 18.01.40

Screenshot 2018-09-23 18.07.13

Use the pan balance to explain.

Calculating Cat says that the total of the shapes in the third column is 6 too. Is she right? How do you know?

What is the same and what is different about Digit Dog’s row and Calculating Cat’s column?

Can you find any other rows or columns that total 6? Are there any that total more than 6? What about less than 6?

Can you find a row or column that totals 1 more than 6? What about 1 less than 6?

What else do you notice?

Find a way to record the totals you have found?

Now arrange the shapes on the grid in any way you want and investigate the totals that you make. What do you notice? What is the largest total you can make? The smallest total?

Look at a grid your friend has done. What is the same? What is different?

What if you used other shapes?

Posted in Additive relationships, Calculating, Logical reasoning, Making totals

Finding pairs

Digit Dog and Calculating Cat are using one set of digit cards 1 – 10 and looking for pairs that make 10.

Screenshot 2020-06-15 09.32.44

Download a set of digit cards here. You will need cards 1 to 10. Print double-sided to have Digit Dog on the back!

Download a baseboard here. Print two.

How many pairs that make 10 can you make? Put the cards on the baseboard.

Can you use all the cards? Which cards are left over? Why?

Try making some other totals – remember you can only use one set of cards from 1 – 10.

What if you make 9? Which cards are left over? Why?

What about 8?  or 12?  or 13?  or 11? Investigate the number of pairs and the cards that you cannot use.

Record your work. Write down the pairs of numbers and their totals.

 

Posted in Calculating, Logical reasoning, Making totals

Making totals

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, Making totals

Making more tens

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

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, Games, Logical reasoning, Making totals

Which Square?

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, Making totals, Number sense

Using Numicon® to explore equivalences

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?

Screenshot 2019-11-11 10.43.28

What about this one?

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

What if ………..you changed the shapes?

 

Now using numerals.

Screenshot 2019-11-13 11.41.26

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.