Welcome to St Margaret’s

Year 7 Mathematics Mastery

Information Evening

The Importance of Maths (as told by an English teacher…)

Do we have a Mathematics problem in the UK?

“I’m not able to read properly…”

Do we have a Mathematics problem in the UK?

“I’m not able to read properly”

Do we have a Mathematics problem in the UK?

“I’m just not good at maths…”

Do we have a Mathematics problem in the UK?

• Numeracy skills have got worse, not better

• International Top 40 (PISA tests)

• Mathematics:

1. Sigapore

2. Hong Kong (China)

3. Macao (China)

4. Chinese Taipei

5. Japan

Do we have a Mathematics problem in the UK?

27: United Kingdom

(also beaten by Estonia, Slovenia, Ireland, Poland, Vietnam, New Zealand, Australia)

Do we have a Mathematics problem in the UK?

Do we have a Mathematics problem in SMA?

Grade SMA%

9

33 8

7

6

57 5

4

3

10 2

1

And there is always room for improvement…

• Are we getting enough top grades?

• Do our boys have a real confidence with number?

• Are they ready for the world of work?

• Have we taught them to pass an exam at the expense of being mathematically able?

Do the maths – true or false?

Even + Even = Even

Even + Odd = Even

Odd + Odd = Even

• Can you explain why?

• Can you prove why… – Using algebra?

– Without using algebra?

m

m

n

n

2m 2n

2m + 1 2n + 1

2m + 1 + 2n + 1

2m + 1 + 2n + 1

2m + 2n + 2

2(m + n + 1)

Our shared vision

• Every school leaver to achieve a strong foundation in mathematics, with no child left behind

• A significant proportion of pupils to be in a position to

choose to study A-level and degree level mathematics and mathematics-related sciences

A belief and a frustration

• Success in mathematics for every child is possible

• Mathematical ability is not innate, and is increased through effort

Mastery member schools wanted to ensure that their aspirations for every child’s mathematics success become

reality

Effort-based ability – growth mindset

Innate ability

Intelligence can grow

Intelligence is fixed

Effort leads to success

Ability leads to success

When the going gets tough ... I

get smarter

When the going gets tough ... I

get found out

When the going gets tough ... dig in

and persist

When the going gets tough ... give

up, it’s hopeless

I only need to believe in

myself

I need to be viewed as

able

Success is the

making of

targets

Success is doing better than

others

NC 2014

“Decisions about progression should be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content in preparation for key stage 4. Those who are not sufficiently fluent should consolidate their understanding, including through additional practice, before moving on”

• Fewer topics in greater depth

• Mastery for all pupils

• Number sense and place value come first

• Problem solving is central

Curricular principles

Y7 differentiation through depth

Half term 1

Number sense

Half term 2

Multiplication & division

Half term 3

Angle and line properties

Half term 4

Fractions

Half term 5

Algebraic representation

Half term 6

Percentages & pie charts

KEY

Half term topic

Big idea Substantial new knowledge

mastered

Year 7

Place value

Multiplication and division

Using scales

Angle and line properties

Area

Perimeter

Addition and subtraction

Algebraic notation

Calculating with fractions

Fractions, decimals and percentages

Mathematical problem solving

Conceptual understanding

Language and communication

Mathematical thinking

Conceptual understanding Pupils deepen their understanding by representing concepts using objects and pictures, making connections between different representations and thinking about what different representations stress and ignore.

Language and communication Pupils deepen their understanding by explaining, creating problems, justifying and proving using mathematical language. This acts as a scaffold for their thinking deepening their understanding further.

Mathematical thinking Pupils deepen their understanding by giving an examples, by sorting or comparing, or by looking for patterns and rules in the representations they are exploring problems with.

Mathematics Mastery key principles

Mastering mathematical understanding

Concrete - DOING At the concrete level, tangible objects are used to approach and solve problems. Almost anything students can touch and manipulate to help approach and solve a problem is used at the concrete level. This is a 'hands on' component using real objects and it is the foundation for conceptual understanding. Pictorial - SEEING At the pictorial level, representations are used to approach and solve problems. These can include drawings (e.g., circles to represent coins, tally marks, number lines), diagrams, charts, and graphs. These are visual representations of the concrete manipulatives. It is important for the teacher to explain this connection. Abstract –SYMBOLIC At the abstract level, symbolic representations are used to approach and solve problems. These representations can include numbers or letters. It is important for teachers to explain how symbols can provide a shorter and efficient way to represent numerical operations.

Concrete-Pictorial-Abstract (C+P+A) approach

What are manipulatives?

Language and communication

Mathematical thinking

Conceptual understanding

Mathematical problem solving

Bar models

Dienes blocks

Cuisenaire rods

Multilink cubes

Fraction towers

Bead strings

Number lines

Shapes

100 grids

Abe, Ben and Ceri scored a total of 4,665 points playing a computer game. Ben scored 311 points fewer than Abe. Ben scored 3 times as many points as Ceri. How many points did Ceri score?

4,665

Ceri

Ben

311

Abe

4,665 – 311 = 4,354

4, 354

4, 354 ÷ 7 = 622 Ceri scored 622

Check: 622 + 1,866 + 2, 177 = 4,665

Problem solving – a pictorial approach

• Jake is 3 years older than Lucy and 2 years younger than Pete.

• The total of their ages is 41 years old.

Find Jake’s age.

What else can you find?

Do the maths!

41 years

3 years

2 years

Jake ?

Lucy ?

Pete ?

41 – 8 = 33 33/3 = 11 ? = 11 years Jake is 11 + 3 = 14 years

39 years 33 years

Lucy is 11 years Pete is 11 + 5 = 16 years

Problem solving

Mastering mathematical

thinking “Mathematics can be terrific fun; knowing

that you can enjoy it is psychologically and intellectually empowering.” (Watson, 2006) We believe that pupils should: • explore, wonder, question and conjecture • compare, classify, sort • experiment, play with possibilities, modify an

aspect and see what happens • make theories and predictions and act

purposefully to see what happens, generalise

What number is half of 6?

6 is half of what number?

What number is half of 6?

6 is half of what number?

What comes next…?

• Thousands

• Hundreds

• Tens

• Ones!!!!!!!

Why is this important?

Consider:

• One Hundred = Ten Tens • Ten Tens = One Hundred Similarly:

• One Ten = Ten Ones • Ten Ones = One Ten

Fractions – a “talk task”

Challenging high attainers

• What number is 70 hundreds, 35 tens and 76 ones?

• Which is bigger, 201 hundreds or 21 thousands?

• How many bags each containing £10 000 do you need to have £3 billion?

• How many ways can you find to show/prove your answers?

True or False?

A B C  D E I D E F  G H C G H I  A B F

A B C  B A C D E F  E F D G H I  I G H

Can you make your own true or false statements like these?

=

=

Does it work?

Evidence from successful schools: • Pupil collaboration and discussion of work • Mixture of group tasks, exploratory activities and

independent tasks • Focus on concepts, not on teaching rules • All pupils tackled a wide variety of problems • Use of hands on resources and visual images • Consistent approaches and use of visual images and

models • Importance of good teacher subject-knowledge and

subject-specific skills • Collaborative discussion of tasks amongst teachers

What would OfSTED think?