Year 5 Term 3 Unit 6b

Year 5 Term 3 Unit 6b

Day 1

L.O.1

To be able to recall multiplication facts and derive division facts from the six times

table

We are going to say the 6x table

1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10

Now back to the 6x table

Let’s say it again!

1 2 3 4 5 6 7 8 9 10

Here are the multiples of 6

1 2 3 4 5 6 7 8 9 10

6 12 18 24 30 36 42 48 54 60

Q. What is this multiplication fact?

1 2 3 4 5 6 7 8 9 10

6 12 18 24 30 36 42 48 54 60

1 2 3 4 5 6 7 8 9 10

6 12 18 24 30 36 42 48 54 60

6 x 4 = 24 or 4 x 6 = 24

6 x table

Q. What are the associated division facts?

1 2 3 4 5 6 7 8 9 10

6 12 18 24 30 36 42 48 54 60

6 x table

1 2 3 4 5 6 7 8 9 10

6 12 18 24 30 36 42 48 54 60

24 ÷ 6 = 4 and 24 ÷ 4 = 6


1 2 3 4 5 6 7 8 9 10

6 12 18 30 36 42 48 54 60

6 x table

1 2 3 4 5 6 7 8 9 10

6 12 18 30 36 42 48 54 60

42 ÷ 6 = 7 and 42 ÷ 7 = 6


1 2 3 4 5 6 7 8 9 10

6 12 18 30 36 48 54 60

6x table

1 2 3 4 5 6 7 8 9 10

6 12 18 30 36 48 54 60

54 ÷ 6 = 9 and 54 ÷ 9 = 6


1 2 3 4 5 6 7 8 9 10

6 12 18 30 36 48 60

6 x table

1 2 3 4 5 6 7 8 9 10

6 12 18 30 36 48 60

30 ÷ 6 = 5 and 30 ÷ 5 = 6


1 2 3 4 5 6 7 8 9 10

6 12 18 36 48 60

6 x table

1 2 3 4 5 6 7 8 9 10

6 12 18 36 48 60

12 ÷ 6 = 2 and 12 ÷ 2 = 6


1 2 3 4 5 6 7 8 9 10

6 18 36 48 60

6 x table

1 2 3 4 5 6 7 8 9 10

6 18 36 48 60

48 ÷ 6 = 8 and 48 ÷ 8 = 6


1 2 3 4 5 6 7 8 9 10

6 18 36 60

6x table

1 2 3 4 5 6 7 8 9 10

6 18 36 60

6 ÷ 6 = 1 and 6 ÷ 1 = 6


1 2 3 4 5 6 7 8 9 10

18 36 60

6x table

1 2 3 4 5 6 7 8 9 10

18 36 60

60 ÷ 6 = 10 and 60 ÷ 10 = 6


1 2 3 4 5 6 7 8 9 10

18 36

6x table

1 2 3 4 5 6 7 8 9 10

18 36

36 ÷ 6 = 6 and 36 ÷ 6 = 6


1 2 3 4 5 6 7 8 9 10

18

6x table

1 2 3 4 5 6 7 8 9 10

18

18 ÷ 6 = 3 and 18 ÷ 3 = 6

6x table

1 2 3 4 5 6 7 8 9 10

Now write down all the division facts you can remember.

6x table

1 2 3 4 5 6 7 8 9 10

6 12 18 24 30 36 42 48 54 60

L.O.2

To be able to solve mathematical problems or puzzles, recognise and explain patterns and relationships.

is 3 is 4 is 5

Q. What are the totals in the 8 boxes?

What strategies will you use?

is 3 is 4 is 6

Q. How many totals change now that represents a 6 instead of a 5?

is 2 is 4 is 6

Q. If represents 2, how many totals will change?

4 will change

is 2 is 4 is 6

8 will change

is _ is _ is _

This time I have given you some totals and left you to work out the others!

23

15

24

is _ is _ is _

Q. Which of the three totals did you use to help you first?

How did this help you?

23

15

24

is 6 is _ is _

First you should have worked out that = 6 because 4 x 6 in the last column gives the total 24.

Q. Which total did you use next?

23

15

24

is 6 is 5 is _

Next you should have worked out that = 5 because on the top row 3x6=18 + 5 =23

Q. Which total did you use last?

23

15

24

is 6 is 5 is 2

Last you should have worked out that = 2.

In the row totalling 15 you already have 6 + 5 = 11.

15 – 11 = 4 , there are 2 so each must be worth 2.

23

15

24

is _ is _ is _

Q. What are the other totals?

20

18

12

What strategies will you use?

is 3 is 6 is 7

You should have found these answers.

20

18

12

23

15

232120

is _ is _ is _

Q. Does it matter which three totals you are given?

is _ is _ is _

Work in pairs to choose your own number for each shape. Find the 8 totals.

Then give 3 totals to another pair for them to find the missing totals.

is _ is _ is _

Q. So, does it matter which three totals you are given?

Are there any awkward ones?

You will do ACTIVITY Sheet 6b1 for

HOMEWORK this week but we will look

at the first grid now.

WARNING You may find you need to change your

strategy when you do the last 2 grids.

Let’s try this as a class.

=__ =__ =__

is _ is _ is _

Q. What do these totals tell us about what the shapes represent?

18

20

is _ is _ is _

The 20 means that 18

20

+ = 10.

If this is so then on the top line,

so = 4

+ = 8

With one more total we can find

Now try the first question only on

Self-assessment sheet 6b1.

By the end of the lesson the children should be able to:

Solve puzzles and problems

involving missing totals.


Day 2

L.O.1

To be able to recall multiplication facts and derive division facts from the seven times

table


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10



1 2 3 4 5 6 7 8 9 10

This shows the multiples of 7

1 2 3 4 5 6 7 8 9 10

7 14 21 28 35 42 49 56 63 70


1 2 3 4 5 6 7 8 9 10

7 14 21 28 35 42 49 56 63 70

1 2 3 4 5 6 7 8 9 10

7 14 21 28 35 42 49 56 63 70

8 x 7 = 56 or 7 x 8 = 56

7 x table


1 2 3 4 5 6 7 8 9 10

7 14 21 28 35 42 49 56 63 70

7 x table

1 2 3 4 5 6 7 8 9 10

7 14 21 28 35 42 49 56 63 70

56 ÷ 7 = 8 and 56 ÷ 8 = 7


1 2 3 4 5 6 7 8 9 10

7 14 21 28 35 42 49 63 70

7 x table

1 2 3 4 5 6 7 8 9 10

7 14 21 28 35 42 49 63 70

49 ÷ 7 = 7 and 49 ÷ 7 = 7


1 2 3 4 5 6 7 8 9 10

7 14 21 28 35 42 63 70

7 x table

1 2 3 4 5 6 7 8 9 10

7 14 21 28 35 42 63 70

28 ÷ 7 = 4 and 28 ÷ 4 = 7


1 2 3 4 5 6 7 8 9 10

7 14 21 35 42 63 70

7 x table

1 2 3 4 5 6 7 8 9 10

7 14 21 35 42 63 70

35 ÷ 7 = 5 and 35 ÷ 5 = 7


1 2 3 4 5 6 7 8 9 10

7 14 21 42 63 70

7 x table

1 2 3 4 5 6 7 8 9 10

7 14 21 42 63 70

14 ÷ 7 = 2 and 14 ÷ 2 = 7


1 2 3 4 5 6 7 8 9 10

7 21 42 63 70

7 x table

1 2 3 4 5 6 7 8 9 10

7 21 42 63 70

63 ÷ 7 = 9 and 63 ÷ 9 = 7


1 2 3 4 5 6 7 8 9 10

7 21 42 70

7 x table

1 2 3 4 5 6 7 8 9 10

7 21 42 70

70 ÷ 7 = 10 and 70 ÷ 10 = 7


1 2 3 4 5 6 7 8 9 10

7 21 42

7 x table

1 2 3 4 5 6 7 8 9 10

7 21 42

21 ÷ 7 = 3 and 21 ÷ 3 = 7


1 2 3 4 5 6 7 8 9 10

7 42

7 x table

1 2 3 4 5 6 7 8 9 10

7 42

7 ÷ 7 = 1 and 7 ÷ 1 = 7


1 2 3 4 5 6 7 8 9 10

42

7 x table

1 2 3 4 5 6 7 8 9 10

42

42 ÷ 7 = 6 and 42 ÷ 6= 7

7 x table

1 2 3 4 5 6 7 8 9 10


7 x table

1 2 3 4 5 6 7 8 9 10

7 14 21 28 35 42 49 56 63 70

L.O.2

To be able to solve mathematical puzzles and problems.

To be able to explain methods and reasoning

.Q. What fraction of these 8 shapes are circles?

Half the shapes are circles : 4/8 ½

Q. What fraction of the shapes are circles now?

Three quarters of the shapes are circles: 6/8 ¾


five eighths of the shapes are circles now: 5/8


One eighth of the shapes are circles : 1/8

Now I shall give you the fractions but not the total number of shapes:

½ the shapes are squares

½ the shapes are circles.

Two squares are replaced with two circles so now

1/3 of the shapes are squares and

2/3 of the shapes are circles.

Q. How many shapes did we start with?

2 minutes

What answers do you have?

What strategies did you use?

Q. If 1/3 of the total number of shapes were squares what multiplication table will the total number of shapes be in?

Q. If 1/3 of the total number of shapes were squares what multiplication table will the total number of shapes be in?

It must be in the 3x table.

Total 1/3 Squares 2/3 Circles

3

6

9

12

15

18

21

Let’s fill in the table


3

6

9

12

15

18

21

1

2

3

4

5

6

7

2

4

6

8

10

12

14

Q. As we have replaced two squares with two circles what would the original number of squares and circles be?


3

6

9

12

15

18

21

1

2

3

4

5

6

7

2

4

6

8

10

12

14

Let’s work it out.

+2squares -2 circles

To answer this we need to add 2 more columns.


3

6

9

12

15

18

21

1

2

3

4

5

6

7

2

4

6

8

10

12

14

Q. When were half the shapes squares and half circles?


3

4

5

6

7

8

9

0

2

4

6

8

10

12


3

6

9

12

15

18

21

1

2

3

4

5

6

7

2

4

6

8

10

12

14


3

4

5

6

7

8

9

0

2

4

6

8

10

12

The only time this happens is when there are 12 shapes.

Try these: use the grid to help you.

Q1. 1/3 of the shapes are squares, 2/3 of the shapes are circles.Three circles are replaced with three squares. Now ½ the shapes are squares, ½ the shapes are circles. How many squares and circles did we start with?

Q2. 1/4 of the shapes are squares, 3/4 of the shapes are circles.One circle is replaced by one square.Now 1/3 the shapes are squares, 2/3 the shapes are circles. How many squares and circles did we start with?

What answers do you have?


There are some cubes in a bag.

1/5 of them are red

4/5 of them are blue

Q. How many cubes might be in the bag?

We know that if we are working in 1/5 ’s

we must be using the 5x table.

I take out 6 blue cubes and replace them with

6 red ones.

Now ½ are red and ½ blue.

Q. How many cubes are in the bag?

Let’s do it.

Remember we are working in multiples of

5

This blank screen is for recording the working.

Now try the second question on

Assessment sheet 6b1.


Solve puzzles and problems involving fractions;

Explain methods and reasoning.


Day 3

L.O.1

To be able to recall multiplication facts and derive division facts from the eight times

table


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10


1 2 3 4 5 6 7 8 9 10



1 2 3 4 5 6 7 8 9 10

Here are the multiples of 8

1 2 3 4 5 6 7 8 9 10

8 16 24 32 40 48 56 64 72 80


1 2 3 4 5 6 7 8 9 10

8 16 24 32 40 48 56 64 72 80

1 2 3 4 5 6 7 8 9 10

8 16 24 32 40 48 56 64 72 80

8 x 4 = 32 or 4 x 8 = 32

8 x table


1 2 3 4 5 6 7 8 9 10

8 16 24 32 40 48 56 64 72 80

8 x table

1 2 3 4 5 6 7 8 9 10

8 16 24 32 40 48 56 64 72 80

32 ÷ 8 = 4 and 32 ÷ 4 = 8


1 2 3 4 5 6 7 8 9 10

8 16 24 40 48 56 64 72 80

8 x table

1 2 3 4 5 6 7 8 9 10

8 16 24 40 48 56 64 72 80

56 ÷ 8 = 7 and 56 ÷ 7 = 8


1 2 3 4 5 6 7 8 9 10

8 16 24 40 48 64 72 80

8x table

1 2 3 4 5 6 7 8 9 10

8 16 24 40 48 64 72 80

72 ÷ 8 = 9 and 72 ÷ 9 = 8


1 2 3 4 5 6 7 8 9 10

8 16 24 40 48 64 80

8 x table

1 2 3 4 5 6 7 8 9 10

8 16 24 40 48 64 80

40 ÷ 8 = 5 and 40 ÷ 5 = 8


1 2 3 4 5 6 7 8 9 10

8 16 24 48 64 80

8 x table

1 2 3 4 5 6 7 8 9 10

8 16 24 48 64 80

16 ÷ 8 = 2 and 16 ÷ 2 = 8


1 2 3 4 5 6 7 8 9 10

8 24 42 64 80

8 x table

1 2 3 4 5 6 7 8 9 10

8 24 48 64 80

64 ÷ 8 = 8 and 64 ÷ 8 = 8


1 2 3 4 5 6 7 8 9 10

8 24 48 80

8 x table

1 2 3 4 5 6 7 8 9 10

8 24 48 80

8 ÷ 8 = 1 and 8 ÷ 1 = 8


1 2 3 4 5 6 7 8 9 10

24 48 80

8 x table

1 2 3 4 5 6 7 8 9 10

24 48 80

80 ÷ 8 = 10 and 80 ÷ 10 = 8


1 2 3 4 5 6 7 8 9 10

24 48

8 x table

1 2 3 4 5 6 7 8 9 10

24 48

48 ÷ 8 = 6 and 48 ÷ 6 = 8


1 2 3 4 5 6 7 8 9 10

24

8 x table

1 2 3 4 5 6 7 8 9 10

24

24 ÷ 8 = 3 and 24 ÷ 3 = 8

8 x table

1 2 3 4 5 6 7 8 9 10


8 x table

1 2 3 4 5 6 7 8 9 10

8 16 24 32 40 48 56 64 72 80

L.O.2

To be able to solve problems and puzzles, recognise and explain patterns, relationships and reasoning.

Large batteries cost £1:60

Medium batteries cost £1:10

Q.1 What would ten large batteries cost?

Q.2 What would six medium batteries cost?

Q.3 How many medium batteries could you buy for £10

Q.4 How many large batteries could you buy for £10

Q.5 How much change would you get in Q.3 + Q.4?

Answers are:

1. £16

2. £6:60

3. 9 batteries with 10p. change

4. 6 batteries with 40p. change

5. 50p.

A farmer bought batteries with a £20 note.

Q. How many of each size could the farmer buy?

1 minute

He could have bought up to

12 large batteries

or up to

18 medium batteries.

If he spent exactly £20 how

many batteries did the farmer buy?

2 minutes in pairs

Would it help if we

used a list or a chart

or a table?

Medium 1 2 3 4 5 6 7 8 9 10

Cost £1.10

Large 1 2 3 4 5 6 7 8 9 10

Cost £1.60

This may help:

Complete the table with your partner and use it to solve the problem.

Q. What answers did you get?

8 medium + 7 large batteries is an answer.

Medium 1 2 3 4 5 6 7 8 9 10

Cost £1.10 £2.20 £3.30 £4.40 £5.50 £6.60 £7.70 £8.80 £9.90 £11

Large 1 2 3 4 5 6 7 8 9 10

Cost £1.60 £3.20 £4.80 £6.40 £8.00 £9.60 £11.20 £12.80 £14.40 £16

This is the completed table

Small batteries cost 70p.

Q. How many small and medium batteries

could we buy for exactly £5

Work with a partner to find the answer.

Would it help if you added two extra rows to the table?

Medium 1 2 3 4 5 6 7 8 9 10

Cost £1.10 £2.20 £3.30 £4.40 £5.50 £6.60 £7.70 £8.80 £9.90 £11

Large 1 2 3 4 5 6 7 8 9 10

Cost £1.60 £3.20 £4.80 £6.40 £8.00 £9.60 £11.20 £12.80 £14.40 £16

Small 1 2 3 4 5 6 7 8 9 10

Cost £0.70

Extra rows

Medium 1 2 3 4 5 6 7 8 9 10

Cost £1.10 £2.20 £3.30 £4.40 £5.50 £6.60 £7.70 £8.80 £9.90 £11

Large 1 2 3 4 5 6 7 8 9 10

Cost £1.60 £3.20 £4.80 £6.40 £8.00 £9.60 £11.20 £12.80 £14.40 £16

Small 1 2 3 4 5 6 7 8 9 10

Cost £0.70 £1.40 £2.10 £2.80 £3.50 £4.20 £4.90 £5.60 £6.30 £7


Q. How many small and large batteries could we buy for exactly £9?

Q. How many small, medium and large batteries

could we buy for exactly £8?

For extension work try these:

How many small + large for £11; £12 ; £14 ?

How many medium + large for £7 ; £14 ; £20 ?

How many small + medium for £10 ; £13 ; £14 ?

How many small + medium + large for £11 ; £15 ?

Now do question 3 on

Self-assessment sheet 6b 1.

Now that you have finished the questions on the Self-assessment sheet think about what we have learned this week in maths and decide on what you would like to get better at.

Write it as your target at the bottom of the sheet.


Solve puzzles and problems involving money and lists

Explain methods and reasoning


Day 4

Documents

Year 5 Term 3 Unit 6b