152_Fluency, Problem solving and Reasoning Maths for NQTs

Fluency, Problem solving and Reasoning Maths for NQTs Mark Hattersley Mark.hattersley@bradford.gov.uk @MarkAHattersley Philipa Varley Philipa.varley@bradford.gov.uk @philipav... Aims• To

Fluency, Problem solving and

Reasoning Maths for NQTs

Mark Hattersley Mark.hattersley@bradford.gov.uk

@MarkAHattersley

Philipa Varley Philipa.varley@bradford.gov.uk

@philipav

Aims

• To develop an understanding of the new mathematics curriculum

•To develop ideas for fluency, problem

solving and reasoning

Starter- Strike it out

• How to play ‘Strike it out’

NRich

Player 1 2+3 = 5

Player 2 Must start where player 1 finished

5 + 10 = 15

Player 1 Must start where player 2

finished

15 – 1 is and so on

The loser is the person who can not

complete their go

Play again collaboratively– can you use

as many numbers as possible?

Starter- Factors and multiples

a collaborative game

Rules of the game

• Player 1 chooses a number

• Player 2 must choose a number that is

a factor or multiple of player 1’s number

• Player 1 must choose a number that is

a factor or multiple of player 2’s number

• And so on… How many numbers can

you get in your sequence?

NRich

2 Minute task

• What is important?

What is important?What do

these mean?

What does it look like?

What is the meaning of Fluency?

Fluency

Is it simply fast and accurate?

Read the article

Agree a definition for Fluency

What else do you know?

210÷70=3

210÷3=70

17 x 3 = 57

KS1 What else do you know?

What does problem solving

mean?

• Does it mean word problems?

Problem solving and reasoning

Word Problems Representing analyse

 choices

 decisions

 reasoning

NCETM – new curriculum resources

NCETM – new curriculum resources

NCETM – new curriculum resources

What does reasoning mean?

• Close your eyes and think of ….

Reasoning Mat

This reminded

me of so I When I looked at

the table/result/graph

I noticed that

What if…

This worked so

Using the numbers

in my table I looked at

I can see

a pattern

I already know that

so

I tested

I used

method because

I noticed a connection between

This didn’t work

so

I noticed that

Reasoning Mat KS1

What

worked so

I can see a pattern

I tried …

This didn’t work so

NCETM - Reasoning

• Progression documents with

reasoning questions

www.ncetm.org.uk/resources/44672

Reasoning question styles

• Spot the mistake / Which is correct?

• True or false?

• What comes next?

• Do, then explain

• Make up an example / Write more

statements / Create a question /

Another and another

• Possible answers / Other possibilities

• What do you notice?

• Continue the pattern

• Missing numbers / Missing symbols /

Missing information/Connected

calculations

• Working backwards / Use the inverse /

Undoing / Unpicking

• Hard and easy questions

• The answer is…

• Make an estimate / Size of an answer

• Always, sometimes, never

• Making links / Application

• Can you find?

• What’s the same, what’s different?

• Odd one out

• Complete the pattern / Continue the pattern

• Another and another

• Ordering

• Testing conditions

Estimation/ Range of answers

Estimation/ Range of answers

Key stage 1 example

Sometimes, always, or never true?

•The difference between any two odd numbers

KS1 Sometimes, always, or never true?

•When I add two numbers together I get an

even answer.

•Adding 10 to a 2 digit number changes both digits.

•When I add two lots of odd numbers, the

answer is always odd

Using your reasoning mat, discuss these sequences or number sentences

Using your reasoning mat, discuss these sequences or number sentences

2, 4, 6, 8, 10

5, 10, 16, 20, 23

KS 1 Questioning techniques – right or wrong?

7 + 4 = 11

7 – 4 = 11

Doing and Undoing

Doing and Undoing

• The area of a rectangle is 48cm

• What could the dimensions be?

2

Doing and undoing KS1

• Doing

Doing and undoing KS1

Undoing – How many teddies are hiding in each pot?

Fluency, problem solving and reasoning every day

• Look at the two examples of

worksheets Which allows for

problem solving and reasoning?

• Closed, closed, open

Where to go for ideas

Where to go for ideas

• Opening up questions documents

New sample questions July 2014

Fluency

Reasoning

Problem Solving

Aims

• To develop an understanding of the new mathematics curriculum

•To develop ideas for fluency, problem

solving and reasoning