The document provides information about a parental workshop on Mathematics Mastery. It aims to help parents understand what Mathematics Mastery is, its core principles, and how parents can support their children. Mathematics Mastery focuses on developing a deep conceptual understanding through cumulative learning and representing concepts in multiple ways, rather than acceleration. It emphasizes problem solving, mathematical thinking and communication. Parents can support their children by fostering a growth mindset, encouraging reasoning and making links, and engaging in further reading on teaching mathematics concepts.
2. Aims
• Understand what Mathematics
Mastery is
• Understand the core principles
of Mathematics Mastery
• Know how you can support your
child
3. • Brief answer
• Or the odd bullet point
What is
Mathematics
Mastery?
4. Mathematics Mastery
The programme that we are involved
with has been inspired by
internationally recognised practice,
particularly drawing on evidence from
Singapore and Shanghai.
More than 475 schools are subscribed
nationally.
6. What is Mathematics Mastery?
Understanding concepts in depth
Cumulative learning
Challenge through depth, not acceleration
Number sense and place value come first
Learning ‘rules’ or ‘tricks’
Practising 50 times
7. “In mathematics, you know you’ve
mastered something when you can
apply it to a totally new
problem in an unfamiliar
situation”
Dr Helen Drury, “Mastering Mathematics” OUP 2014
What is Mathematics Mastery?
8. • Brief answer
• Or the odd bullet point
Understand the
core principles of
Mathematics
Mastery
11. Claire spent 65p on an apple and an orange.
Her orange cost 23p.
How much did her apple cost?
Idris also spent 65p on an apple and an orange.
His orange cost 23p less than his apple.
How much did the apple cost?
Do Now
Can you create another question with the same
numbers but a different answer?
Draw bar models to support your answers.
12. Claire’s fruit
65
23 42
Which model do you prefer?
Does it make a difference?
42 23
65
Claire spent 65p on an apple and an orange.
Her orange cost 23p.
How much did her apple cost?
13. Idris’s fruit
65
23
?
Where does the 42
come from?
What can now be
worked out?
65
23
42
How does this model
help? What can you
work out now?
Idris also spent 65p on an apple and an orange.
His orange cost 23p less than his apple.
How much did the apple cost?
44p
14. Tree B is 80 cm taller than tree A
Tree B is 120 cm shorter than tree C
Tree A is 215 cm tall.
Draw a bar model to represent this information.
Use your bar model to work out how tall trees B and C are.
Trees
? ? ?
A
B
C
120 cm
215 cm
80 cm215 cm
295 cm
415 cm
15. Draw two bar models to support answering the following two
problems.
Subtle wording
Alicia had £6 more than
Bobby. If Bobby had
£10, how much did they
have altogether?
Alicia had £6 more than
Bobby. If they had £10
altogether, how much did
each person have?
£10
£16
£26 £10
£6
£6
Alicia
Bobby
Alicia
Bobby
?
?£2
£2
16. Do Now
Sticker problem
Helen had 157 stickers. Sahar had 43 fewer than Helen.
Ian had 23 fewer than Sahar.
Draw bar models to show how to solve the questions below.
1) How many stickers does Ian have now?
2) Ian then gave 16 stickers to Helen. How many more stickers does
Helen now have than Ian?
17. Solving Problems
Helen had 157 stickers. Sahar had 43 fewer than Helen.
Ian had 23 fewer than Sahar.
157
114
91
157
43
23?
Helen
Sahar
Ian
2) Ian gave 16
stickers to Helen.
How many more
stickers does
Helen now have
than Ian?
157 16
43
2316
?
Helen
Sahar
Ian
1) How many
stickers does
Ian have now?
98
How could you solve this part of the
problem without using subtraction?
75
18. The three little pigs went shopping.
The first little pig spent £23 on a bundle of straw and a stack of wood.
The second little pig spent £35 on a stack of wood and a pile of bricks.
The third little pig spent £42 on a bundle of straw and a pile of bricks.
Use bar models and / or concrete manipulatives to work out how much
each item cost (assuming the bundles, stacks and piles were the same
size for each little pig)?
Challenge!
19. The three little pigs
First little pig Second little pig
Third little pig
How does this help solve the problem?
Is there more than one way to solve this?
£23 £35
£42
20. The three little pigs
First little pig Second little pig
Third little pig
£58
£42
?£42
£8£8
£58
How does
this help to
solve the
problem?
£16
21. The three little pigs
First little pig Second little pig
Third little pig
£23 £35
£42
£27£8
£15 £27
£15 £8
25. Bar model problems
Between them, Sam and Tim have collected 32 shells from the beach.
Sam has three times as many shells as Tim.
Can you draw a bar model to show how many does Sam have?
Sam
Tim
32
26. Prize winner!
Kay and Marius won first and second prize in the raffle.
They had to share the prize in the ratio 5 : 3.
Kay received £20 more than Marius.
What was the value of the cash prize?
£20
£80
Marius
Kay
27. On a farm, the ratio of pigs to cows is 2 : 3. The ratio of cows to
sheep is 5 : 7. What is the ratio of pigs to cows to sheep?
1510 21
pigs cows
cows sheep
LCM of 3
and 5 is 15
10 : 15 : 21
28. A pet shop sells mice, rats and gerbils. The ratio of mice to rats is
4 : 3 and the ratio of mice to gerbils is 7 : 4. If there are 32
gerbils in stock at present, how many rats are there?
LCM of 4
and 7 is 28
mice rats
mice gerbils
28 21 16
28 : 21 : 16
56 : 42 : 32
42 rats
30. £0.85
£5.95
£7.65
Seven apples cost £5.95. Each apple costs the same amount.
What is the cost of nine of these apples?
Direct Proportion
Use the bar model to solve the problem.
£0.85 £0.85 £0.85 £0.85£0.85 £0.85 £0.85 £0.85 £0.85
£0.85 £0.85 £0.85£0.85 £0.85 £0.85
31. 85p
£5.95
£11.05
Seven apples cost £5.95. Each apple costs the same amount.
If I spend £11.05 on these apples, how many have I bought?
Use the bar model to solve the problem.
Direct Proportion
32. The fish tank
Michael fills a fish tank.
He has a range of jugs he can use to carry water to the fish tank.
If Michael uses a 4 litre jug, he will need to use 15 jugfuls.
How many jugfuls are needed if he uses a 6 litre jug?
33. Solution approaches (1)
Michael fills a fish tank.
He has a range of jugs he can use to carry water to the fish tank.
If Michael uses a 4 litre jug, he will need to use 15 jugfuls.
How many jugfuls are needed if he uses a 6 litre jug?
The number of jugfuls is inversely
proportional to the capacity of
the jug used.
The product will always be a
constant value.
15 × 4 = 60
6 × 10 = 60
Michael will need 10 jugfuls.
4
15
10
6
Constant area
of 60 squares.
34. Solution approaches (2)
Michael fills a fish tank.
He has a range of jugs he can use to carry water to the fish tank.
If Michael uses a 4 litre jug, he will need to use 15 jugfuls.
How many jugfuls are needed if he uses a 6 litre jug?
The number of jugfuls, 𝑛, is inversely proportional to the
capacity of the jug used, 𝑏 litres.
The product will always be a constant value.
𝑛𝑏 = 60
If 𝑏 = 6, then
𝑛 × 6 = 60
𝑛 =
60
6
= 10
35. The Tall Construction company build skyscrapers.
5 builders can build a sky scraper in 200 days.
How long would 4 builders take to build a sky scraper of the
same size?
200 200 200 200 200
?
Skyscraper
1000 days worth of work to complete job
1000
250 250250 250
36. • Brief answer
• Or the odd bullet point
How can you
support your
child?
37. Supporting your child
Growth mind-set
Reasoning
Making links
Multiple representations
Challenge through depth
Further reading:
Mastering Mathematics – Teaching to transform
achievement; Dr Helen Drury
Maths for parents; Rob Eastaway
Editor's Notes
Parental involvement; Parents to discuss the statements and decide if they are true or false.
Understanding concepts in depth; Use of multiple representations and problem solving to deepen understanding.
Cumulative learning; Topics studied are revisited and integrated into content throughout the programme.
Challenge through depth, not acceleration; Extension tasks delve further into the problem, as opposed to accelerating to Year 8 or 9 content.
Number sense and place value come first; Studied during the first half term as these skills underpin the remainder of the programme.
Learning ‘rules’ or ‘tricks’; Students are able to explain why the maths ‘works’.
Practising 50 times; More focus on exploring the maths and problem solving in a wide variety of situations.
Depth: These strategies build depth of understanding.
Problem solving; At the heart of the programme.
Statements taken from ‘Mastering Mathematics: Teaching to Transform Achievement; Dr. Helen Drury’.
Growth mind-set; Everyone has the potential to succeed in mathematics.
Reasoning; Encourage explanations of how students know, not just accepting the correct answer.
Making links; In their daily lives, what mathematical skills are the students using?
Multiple representations; Can students use a concrete or pictorial manipulative to help them?
Challenge through depth; More maths doesn’t make students better at maths. Consider posing further questions to deepen their understanding.
