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?
http://www.nctm.org/about/content.aspx?id=34
791
Read the article
Agree a definition for Fluency
What else do you know?
21÷3=7
210÷70=
3
3x7=21
7x3=21
70x3 =210
3x70=210
17 x 3 = 57
21÷7=3
210÷3=70
KS1 What else do you know?
100 – 30 = 70
10 – 7 = 3
10 – 3 = 7
10 = 7 + 3 17 + 3 = 20
70+
30
=
100
30 + 70 =100
3 + 7 = 10
7 + 3 = 10
10 = 3 + 7
100 = 70 + 30
What does problem solving
mean?
• Does it mean word problems?
Representing
Word Problems
Enquiring
 plan
 decide
 organise
 Interpret
 reason
 justify
Problem solving
and reasoning
Reasoning

create
 deduce
 analyse
 record
 do
 check
 confirm
Communicating
Explain methods
and solutions

 apply
 choices
 explore
 decisions
 predict
 reasoning
 hypothesise
 test
NCETM – new curriculum
resources
NCETM – new curriculum resources
NCETM – new curriculum
resources
What does reasoning mean?
• Close your eyes and think of ….
I noticed a connection
between...
This is true
here
because…
Reasoning Mat
I
noticed
that...
This
reminded
me of ...so
I...
What if…
This is
always true
because…
I tested
I wondered
why...
When I looked at
the
table/result/grap
h I noticed that...
I used ...
method
because...
I decided
to.........
because
........
I can
see a
pattern
...
I already
know
that ...
so....
This didn’t work
so...
Using the
numbers in
my table I
looked at .....
This
worked
so...
Reasoning Mat KS1
I
noticed
I can see a
pattern...
that...
I tried …
What
if…
I decided
to.........
because
........
I
wondered
why…
This didn’t
work so...
This
worked
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…
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 answers
Key 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.
Questioning techniques – right or
wrong?
Using your reasoning mat,
discuss these sequences or
number sentences
10, 8, 5, 1, -4
7 – 10 = -7
3, 6, 10, 16, 22, 29
7 – 10 = -3
KS 1 Questioning techniques –
right or wrong?
Using your reasoning mat,
discuss these sequences or
number sentences
2, 4, 6, 8, 10
7 + 4 = 11
5, 10, 16, 20, 23
7 – 4 = 11
Doing and Undoing
• Doing
Find the area of these rectangles
6cm
8cm
7cm
2cm
8cm
4cm
Doing and Undoing
• The area of a rectangle is 48cm 2.
• What could the dimensions be?
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
•
•
•
•
•
•
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
Fluency
Reasoning
Problem Solving
Fluency
Reasoning
Problem Solving
New sample
questions July
2014
Aims
• To
develop an understanding of the new
mathematics curriculum
•To develop ideas for fluency, problem
solving and reasoning