Fluency, Problem solving and Reasoning

Maths for NQTs

Mark HattersleyMark.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 multiplesa collaborative gameRules 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?

FluencyIs it simply fast and accurate?

Read the articleAgree a definition for Fluency

What else do you know?

7x3=21

3x7=21

21÷7=3

21÷3=7

70x3 =2103x70=210

210÷70=3

210÷3=7017 x 3 = 57

KS1 What else do you know?

10 = 7 + 3

10 – 3 = 7

10 = 3 + 7

10 – 7 = 3

70+ 30 = 10030 + 70 =100

100 = 70 + 30

100 – 30 = 70

3 + 7 = 10

7 + 3 = 10

17 + 3 = 20

What does problem solving mean?

• Does it mean word problems?

Problem solving and reasoning

Word ProblemsRepresenting analyse record do check confirm

Enquiring plan decide organise Interpret reason justify

Reasoning create

deduce

apply

explore

predict

hypothesise

test

Communicating Explain methods and solutions

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 MatThis 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...

I decided to.........

because ........

This is true here because…

This is always true because…

I wondered why...

Reasoning Mat KS1

What if… This

worked so...

I can see a pattern...

I tried …

This didn’t work so...

I noticed

that...

I decided to.........

because ........

I wondered

why…

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…

• Visualising

• What else do you know? / Use a fact• Fact families• Convince me / Prove it / Generalising /

Explain thinking• 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

What is 432 - 175 ?

Discuss these “answers” using estimation to decide which could

be right and which are wrong.

607, 257, 343, 238 ,

Estimation/ Range of answersKey stage 1 example

63 + ? = 100

Discuss these “answers” using estimation to decide which could

be right and which are wrong.

47 46 37 36

Sometimes, always, or never true?

•The difference between any two odd numbers is an even number

•If you add three consecutive numbers together the answer is always even

•The sum of three odd numbers is divisible by 5

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

10, 8, 5, 1, -4

3, 6, 10, 16, 22, 29

Questioning techniques – right or wrong?

7 – 10 = -7

7 – 10 = -3

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

• DoingFind the area of these rectangles

4cm

8cm

2cm

6cm

8cm

7cm

Doing and Undoing

• The area of a rectangle is 48cm .

• What could the dimensions be?

2

Doing and undoing KS1

• Doing

+ =

Doing and undoing KS1Undoing – 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

• Opening up questions documents

• Pitch and Expectations (year group)

• Reasoning mat

• Levelopaedia

• Nrich Website

• NCETM

Where to go for ideas

• Opening up questions documents

• Reasoning mat

• NCETM reasoning documents

• Levelopaedia Available on

Bradford Schools

Online

New sample questions July 2014

FluencyReasoningProblem Solving

New sample questions July 2014

FluencyReasoningProblem Solving

Aims

• To develop an understanding of the new mathematics curriculum

•To develop ideas for fluency, problem solving and reasoning