Transcript 1 2 3 4 5 6 7 8 9 10

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
We are going to say the 3x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 7x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 9x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 8x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 4x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 5x table
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
6
12
18
24
30
36
42
48
54
10
60
6 x table
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
Q. What are the associated division facts?
1
2
3
4
5
6
7
8
9
6
12
18
24
30
36
42
48
54
10
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
Q. What are the associated division facts?
1
2
3
6
12
18
4
5
6
7
8
9
10
30
36
42
48
54
60
6 x table
1
2
3
6
12
18
4
5
6
7
8
9
10
30
36
42
48
54
60
42 ÷ 6 = 7 and 42 ÷ 7 = 6
Q. What are the associated division facts?
1
2
3
6
12
18
4
5
6
30
36
7
8
9
10
48
54
60
6x table
1
2
3
6
12
18
4
5
6
30
36
7
8
9
10
48
54
60
54 ÷ 6 = 9 and 54 ÷ 9 = 6
Q. What are the associated division facts?
1
2
3
6
12
18
4
5
6
30
36
7
8
48
9
10
60
6 x table
1
2
3
6
12
18
4
30 ÷ 6 = 5
5
6
30
36
and
7
8
9
48
30 ÷ 5 = 6
10
60
Q. What are the associated division facts?
1
2
3
6
12
18
4
5
6
36
7
8
48
9
10
60
6 x table
1
2
3
6
12
18
4
12 ÷ 6 = 2
5
6
36
and
7
8
9
48
12 ÷ 2 = 6
10
60
Q. What are the associated division facts?
1
6
2
3
18
4
5
6
36
7
8
48
9
10
60
6 x table
1
6
2
3
4
18
48 ÷ 6 = 8
5
6
36
and
7
8
9
48
48 ÷ 8 = 6
10
60
Q. What are the associated division facts?
1
6
2
3
18
4
5
6
36
7
8
9
10
60
6x table
1
6
2
3
4
18
6÷6=1
5
6
7
8
36
and
9
10
60
6÷1=6
Q. What are the associated division facts?
1
2
3
18
4
5
6
36
7
8
9
10
60
6x table
1
2
3
4
5
18
60 ÷ 6 = 10
6
7
8
9
36
and
10
60
60 ÷ 10 = 6
Q. What are the associated division facts?
1
2
3
18
4
5
6
36
7
8
9
10
6x table
1
2
3
4
18
36 ÷ 6 = 6
5
6
7
8
9
36
and
36 ÷ 6 = 6
10
Q. What are the associated division facts?
1
2
3
18
4
5
6
7
8
9
10
6x table
1
2
3
4
5
6
7
8
9
18
18 ÷ 6 = 3
and
18 ÷ 3 = 6
10
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
6
12
18
24
30
36
42
48
54
10
60
L.O.2
To be able to solve mathematical
problems or puzzles, recognise and
explain patterns and relationships.
Q. What are the
totals in the 8
boxes?
What strategies
will you use?
is 3
is 4
is 5
Q. How many totals
change now that
represents a 6
instead of a 5?
is 3
is 4
is 6
4 will change
Q. If
represents 2, how
many totals will
change?
is 2
is 4
is 6
8 will change
is 2
is 4
is 6
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?
23
15
How did this help
you?
24
is _
is _
is _
First you should
have worked out
that
=6
because 4 x 6 in
the last column
gives the total 24.
23
15
Q. Which total did
you use next?
is 6
24
is _
is _
Next you should
have worked out
that
=5
because on the top
row 3x6=18 + 5 =23
23
15
Q. Which total did
you use last?
24
is 6
is 5
is _
Last you should
have worked out
that
= 2.
23
15
In the row totalling
15 you already
have 6 + 5 = 11.
15 – 11 = 4 , there
are 2
so each
must be worth 2.
is 6
24
is 5
is 2
Q. What are the
other totals?
20
What strategies
will you use?
18
12
is _
is _
is _
You should have
found these
answers.
15
23
20
18
20
is 3
is 6
21
23
12
is 7
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?
is _
is _
is _
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.
=__
=__
=__
Q. What do these
totals tell us about
what the shapes
represent?
18
20
is _
is _
is _
The 20 means that
18
= 10.
+
If this is so then
on the top line,
=8
+
so
20
=4
With one more total
we can find
is _
is _
is _
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.
Year 5 Term 3 Unit 6b
Day 2
L.O.1
To be able to recall multiplication facts and
derive division facts from the seven times
table
We are going to say the 7x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 6x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 8x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 5x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 4x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 9x table
1
2
3
4
5
6
7
8
9
10
Now back to the 7x table
Let’s say it again!
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
7
14
21
28
35
42
49
56
63
10
70
Q. What is this multiplication fact?
1
2
3
4
5
6
7
8
9
7
14
21
28
35
42
49
56
63
10
70
7 x table
1
2
3
4
5
6
7
8
9
7
14
21
28
35
42
49
56
63
8 x 7 = 56 or 7 x 8 = 56
10
70
Q. What are the associated division facts?
1
2
3
4
5
6
7
8
9
7
14
21
28
35
42
49
56
63
10
70
7 x table
1
2
3
4
5
6
7
8
9
7
14
21
28
35
42
49
56
63
56 ÷ 7 = 8
and
56 ÷ 8 = 7
10
70
Q. What are the associated division facts?
1
2
3
4
5
6
7
7
14
21
28
35
42
49
8
9
10
63
70
7 x table
1
2
3
4
5
6
7
7
14
21
28
35
42
49
49 ÷ 7 = 7
and
8
9
63
49 ÷ 7 = 7
10
70
Q. What are the associated division facts?
1
2
3
4
5
6
7
14
21
28
35
42
7
8
9
10
63
70
7 x table
1
2
3
4
5
6
7
14
21
28
35
42
28 ÷ 7 = 4
and
7
8
9
10
63
70
28 ÷ 4 = 7
Q. What are the associated division facts?
1
2
3
7
14
21
4
5
6
35
42
7
8
9
63
10
70
7 x table
1
2
3
7
14
21
4
35 ÷ 7 = 5
5
6
35
42
and
7
8
9
10
63
70
35 ÷ 5 = 7
Q. What are the associated division facts?
1
2
3
7
14
21
4
5
6
42
7
8
9
63
10
70
7 x table
1
2
3
7
14
21
4
14 ÷ 7 = 2
5
6
42
and
7
8
9
10
63
70
14 ÷ 2 = 7
Q. What are the associated division facts?
1
7
2
3
21
4
5
6
42
7
8
9
63
10
70
7 x table
1
7
2
3
4
21
63 ÷ 7 = 9
5
6
42
and
7
8
9
10
63
70
63 ÷ 9 = 7
Q. What are the associated division facts?
1
7
2
3
21
4
5
6
42
7
8
9
10
70
7 x table
1
7
2
3
4
5
21
70 ÷ 7 = 10
6
7
8
9
42
and
10
70
70 ÷ 10 = 7
Q. What are the associated division facts?
1
7
2
3
21
4
5
6
42
7
8
9
10
7 x table
1
7
2
3
4
21
21 ÷ 7 = 3
5
6
7
8
9
42
and
21 ÷ 3 = 7
10
Q. What are the associated division facts?
1
7
2
3
4
5
6
42
7
8
9
10
7 x table
1
2
3
4
7
5
6
7
8
42
7÷7=1
and
7÷ 1 = 7
9
10
Q. What are the associated division facts?
1
2
3
4
5
6
42
7
8
9
10
7 x table
1
2
3
4
5
6
7
8
9
42
42 ÷ 7 = 6 and 42 ÷ 6= 7
10
7 x table
1
2
3
4
5
6
7
8
9
10
Now write down all the division facts
you can remember.
7 x table
1
2
3
4
5
6
7
8
9
7
14
21
28
35
42
49
56
63
10
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
Q. What fraction of the shapes are circles now?
five eighths of the shapes are circles now: 5/8
Q. What fraction of the shapes are circles now?
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
Total
1/3 Squares
2/3 Circles
3
1
2
6
2
4
9
3
6
12
4
8
15
5
10
18
6
12
21
7
14
Q. As we have replaced two squares with two circles what
would the original number of squares and circles be?
To answer this we need to add 2 more columns.
Total
1/3 Squares
2/3 Circles
3
1
2
6
2
4
9
3
6
12
4
8
15
5
10
18
6
12
21
7
14
+2squares
-2 circles
Let’s work it out.
Total
1/3 Squares
2/3 Circles
+2squares
-2 circles
3
1
2
3
0
6
2
4
4
2
9
3
6
5
4
12
4
8
6
6
15
5
10
7
8
18
6
12
8
10
21
7
14
9
12
Q. When were half the shapes squares and half circles?
Total
1/3 Squares
2/3 Circles
+2squares
-2 circles
3
1
2
3
0
6
2
4
4
2
9
3
6
5
4
12
4
8
6
6
15
5
10
7
8
18
6
12
8
10
21
7
14
9
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?
What strategies did you use?
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.
By the end of the lesson the children should
be able to:
Solve puzzles and problems involving
fractions;
Explain methods and reasoning.
Year 5 Term 3 Unit 6b
Day 3
L.O.1
To be able to recall multiplication facts and
derive division facts from the eight times
table
We are going to say the 8x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 3x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 7x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 9x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 6x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 4x table
1
2
3
4
5
6
7
8
9
10
We are going to say the 5x table
1
2
3
4
5
6
7
8
9
10
Now back to the 8x table
Let’s say it again!
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
8
16
24
32
40
48
56
64
72
10
80
Q. What is this multiplication fact?
1
2
3
4
5
6
7
8
9
8
16
24
32
40
48
56
64
72
10
80
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 4 = 32 or 4 x 8 = 32
Q. What are the associated division facts?
1
2
3
4
5
6
7
8
9
8
16
24
32
40
48
56
64
72
10
80
8 x table
1
2
3
4
5
6
7
8
9
8
16
24
32
40
48
56
64
72
32 ÷ 8 = 4
and
32 ÷ 4 = 8
10
80
Q. What are the associated division facts?
1
2
3
8
16
24
4
5
6
7
8
9
10
40
48
56
64
72
80
8 x table
1
2
3
8
16
24
4
5
6
7
8
9
10
40
48
56
64
72
80
56 ÷ 8 = 7 and 56 ÷ 7 = 8
Q. What are the associated division facts?
1
8
2
3
16
24
4
5
6
40
48
7
8
9
10
64
72
80
8x table
1
2
3
8
16
24
4
5
6
40
48
7
8
9
10
64
72
80
72 ÷ 8 = 9 and 72 ÷ 9 = 8
Q. What are the associated division facts?
1
2
3
8
16
24
4
5
6
40
48
7
8
64
9
10
80
8 x table
1
2
3
8
16
24
4
40 ÷ 8 = 5
5
6
40
48
and
7
8
9
64
40 ÷ 5 = 8
10
80
Q. What are the associated division facts?
1
2
3
8
16
24
4
5
6
48
7
8
64
9
10
80
8 x table
1
2
3
8
16
24
4
16 ÷ 8 = 2
5
6
48
and
7
8
9
64
16 ÷ 2 = 8
10
80
Q. What are the associated division facts?
1
8
2
3
24
4
5
6
42
7
8
64
9
10
80
8 x table
1
8
2
3
4
5
24
64 ÷ 8 = 8
6
7
48
and
8
9
64
64 ÷ 8 = 8
10
80
Q. What are the associated division facts?
1
8
2
3
24
4
5
6
48
7
8
9
10
80
8 x table
1
8
2
3
4
24
8÷8=1
5
6
7
8
48
and
9
10
80
8÷ 1 = 8
Q. What are the associated division facts?
1
2
3
24
4
5
6
48
7
8
9
10
80
8 x table
1
2
3
4
5
24
80 ÷ 8 = 10
6
7
8
9
48
and
10
80
80 ÷ 10 = 8
Q. What are the associated division facts?
1
2
3
24
4
5
6
48
7
8
9
10
8 x table
1
2
3
4
24
48 ÷ 8 = 6
5
6
7
8
9
48
and
48 ÷ 6 = 8
10
Q. What are the associated division facts?
1
2
3
24
4
5
6
7
8
9
10
8 x table
1
2
3
4
5
6
7
8
9
24
24 ÷ 8 = 3
and
24 ÷ 3 = 8
10
8 x table
1
2
3
4
5
6
7
8
9
10
Now write down all the division facts
you can remember.
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.
2.
3.
4.
5.
£16
£6:60
9 batteries with 10p. change
6 batteries with 40p. change
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?
This may help:
Medium 1
Cost
£1.10
Large
1
Cost
£1.60
2
3
4
5
6
7
8
9
10
2
3
4
5
6
7
8
9
10
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
What strategies did you use?
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.
By the end of the lesson the children
should be able to:
Solve puzzles and problems
involving money and lists
Explain methods and reasoning
Year 5 Term 3 Unit 6b
Day 4