CPA and Bar modelling
Session 1: Wednesday 13th FebruarySession 2: Wednesday 27th February
Session 3: Wednesday 6th MarchSession 4: Wednesday 20th March
Rachel Bradley: [email protected] Marsden: [email protected]
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!
