CPA and Bar modelling

Session 1: Wednesday 13th FebruarySession 2: Wednesday 27th February

Session 3: Wednesday 6th MarchSession 4: Wednesday 20th March

Rachel Bradley: head@lyne.surrey.sch.ukKaren Marsden: Karen@burpham.surrey.sch.uk

Gap Task Feedback

This can be completed after either Session 3 or 4 Plan and teach a lesson/task/activity using either

the PPW or Multiplicative bar model Assess the impact of using the bar model Ask the children for feedback! Take photos as evidence if possible Complete reflection sheet and bring to next

session/email me

Aims Today

To gain an insight into bar modelling and how it can help children to reason and solve problems

To be aware of how bar modelling can be used to solve problems involving multiplication, division, fractions, percentages, ratio and proportion

What could this model be showing?

Ratio of green to blue is 3:1

3 x 1/3 = 1

9 sweets shared between 3 bags 3 + 3 + 3 = 9

3 x 4 = 12

1/3 + 1/3 + 1/3 = 1

27 ÷ 3 = 9

Multiplication

5

6 6 6 6 6

6 12 18 24 30

5 lots of 6 = 30

6 + 6 + 6 + 6 + 6 = 30

5 x 6 = 30

Multiplicative reasoning

6

Factors

12

6 6

4 4 4

3 3 3 3

2 2 2 2 2 2

1 1 1 1 1 1 1 1 1 1 1 1

Multiplicative reasoning

• Jane has 3 books. Penny has five times as many books as Jane. How many books has Penny got?

8

3

3 3 3 3 3

Jane

Penny

Multiplication

The farmer has 24 animals.

There are three times as many sheep as cows.

How many sheep and how many cows?

Sheep

Cows

24

18

6

Multiplication

Another farmer has 42 animals There are twice as many ducks as cows and three times as many sheep as cows. How many sheep, cows and ducks?

Helen has 9 times as many football cards as Sam. Together they have 150 cards. How many

more cards does Helen have than Sam?

S

H

150

150 ÷ 10 = 15

8 x 15 = 120

Vary the Language!

The sum of 2 numbers is 64. One number is 7 times as big as the other. What is the larger number?

And again!

The difference between two numbers is 27. If the larger number is 4 times the smaller number, find the sum of the two numbers.

Division

24 Year 3 children are going on a field trip to the art museum. 6 minibuses have been booked. How many children does each minibus carry.

24

24 ÷ 6 = 4

Fractions

30

Find 1/5 of 30

6

30÷ 5 = 6

Fractions

30

Find 3/5 of 30

6

Can you find the rule?

½ of the sweets in the tin were chocolates.

¼ were toffees.

The rest were strawberry creams.

There were 12 strawberry creams.

How many sweets were in the tin?

Fractions – Problem Solving

12

¼½ ¼

1224

Lauren has some cherries.

She eats 2 of them.

Then she eats half of what is left.

She now has 6 cherries.

How many did she start with?

KS1

KS2 SATS

Boys Girls Girls Girls

18

6

Total in class = 4 x 6 = 24

In a class, 18 of the children are girls and one quarter are boys. How many children are in the class?

In a Year 6, of the children are boysThere are 30 girls.How many children are in Year 6?

14

Charlotte spent 2/5 of her pocket money on a book. The book cost £10.How much money did she start off with?

Fractions

Sample Y6 test question:

• On Saturday Lara read 2/5 of her book. On Sunday she read the other 90 pages to finish the book. How many pages are there in Lara’s book?

90 ÷ 3 = 30

30 x 5 = 1502/5Sat

90Sun

5/8 of a group of boys chose the lion as their

favourite animal.

2/3 of the rest chose the elephant.

The remaining 18 boys chose the cheetah.

How many boys were there in the group?

Fractions

A computer game is £24 in the sale. This is one quarter off its original price. How much did it cost before the sale?

£24 ÷ 3 = £8£8 x 4 = £32

Ratio

26

Tim and Sally share marbles in the ratio of 2:3If Sally has 36 marbles, how many are there altogether?

Ratio

27

Tim and Sally share marbles in the ratio of 2:3If Sally has 36 marbles, how many are there altogether?

Tim

Sally

36

5 x 12 = 60

12

28

Ralph posts 40 letters, some of which are first

class, and some are second.

He posts four times as many second class letters as first.

How many of each class of letter does he post?

Problem Solving

Solution using the bar model

40

F

S

8

5 x ? = 40

Sam and Tom have football stickers in the ratio of 2 to 5.

Altogether they have 98 stickers.

If Sam gives half of his stickers to Tom. How many will Tom have?

Ratio

Percentages

A computer game is reduced in a sale by 30%. Its reduced price is £77. How much was the original price?

Percentages

A computer game is reduced in a sale by 30%. Its reduced price is £77. How much was the original price?

£77 ÷ 7 = £11£11 x 10 = £110

In a library, 40% of the books are science books, 80% of the remaining books are English books and the remaining 120 books are maths books. How many books in total are in the library?

40% 60%

80% 20%

120

10% = 60100% = 600

60% = 60010 % = 100100% = 1000

Mrs Smith is three times as old as her daughter, Pam, who is twice as old as her brother, Tom. The sum of their ages is 54 years. How old is Pam?

Mrs S

Pam 54

Tom

54 ÷ 9 = 6

6 x 2 = 12 Pam is 12 years old.

Mrs Smith is three times as old as her daughter, Pam, who is twice as old as her brother, Tom. The sum of their ages is 54 years. How old is Pam?

Comparison Model

Mandy packs her clothes into a suitcase and it weighs 20 kg. Nat packs his clothes into an identical suitcase and it weighs 12kg. Mandy’s clothes weigh twice as much as Nat’s clothes. How much does the suitcase weigh?

s c c

s c

Mandy

Nat

20

12

20 – 12 = 8 = c

12 – 8 = 4 = s

Independent practice

Four consecutive even numbers add up to 92. Find the largest of these four numbers.

92

92 – (6 x 2) = 80

80 ÷ 4 = 20

20 + 2 + 2 + 2 = 26

Perimeter of Regular Shapes

• If one side of a regular octagon measures 5cm, what is the perimeter of the shape?

5

Gap Task

This can be completed after either Session 3 or 4 Plan and teach a lesson/task/activity using either

the PPW or Multiplicative bar model Assess the impact of using the bar model Ask the children for feedback! Take photos as evidence if possible Complete reflection sheet and bring to next

session/email me

Thank you!