Download Solving problems

Solving
problems
The three strands of Using and
Applying
Problem solving
purely mathematical; based on real life
Communicating
includes interpreting; formulating; discussing and
recording maths and presenting findings
Reasoning
includes making and testing hypotheses; spotting
patterns; generalising; explaining and justifying
How do you teach problem solving?
Give children a method they
can always use?
Read
Underline (or Understand)
Calculate (or Choose)
Solve
Answer
Check
Y3/4
Read the problem
Underline (or understand)
Calculate (or choose the
operation)
Solve the problem
Answer the problem
Check the answer
1.
2.
3.
4.
5.
6.
What do I know?
What do I want to know?
What can I work out?
Give it a try out!
Is that the problem done?
If not go back to number 1.
1. What do I know? Tripods have 3 legs, Bipods have 2 legs and the
total number of legs is 23
2. What do I want to know? How many Tripods and Bipods there
have to be if their legs add up to 23
3. What can I work out? I know it’s more than 1 Tripod and 1 Bipod
because that only adds up to 5 legs. I can work out how many legs
there are on 2 Tripods and 2 Bipods.
4. Give it a try out! Argh…That only adds up to 10.
5. Is that the problem done? No
6. If not go back to number 1.
1. What do I know? That there are more than 2 Tripods and 2 Bipods
2. What do I want to know? How many legs on 3, 4, 5…Tripods and
Bipods
3. What can I work out? Multiples of 3 and multiples of 2 that add up
to 23
4. Give it a try out!
Tripods
1
3 legs
2
6 legs
3
9 legs
4
12 legs
5
15 legs
6
18 legs
7
21 legs
Answer:
3 Tripods (9 legs) and 7 Bipods (14 legs),
or
5 Tripods (15 legs) and 4 Bipods (8 legs).
Bipods
1
2 legs
2
4 legs
3
6 legs
4
8 legs
5
10 legs
6
12 legs
7
14 legs
8
16 legs
9
18 legs
10
20 legs
11
22 legs
Y3
Read the problem
Underline (or understand)
Calculate (or choose the
operation)
Solve the problem
Answer the problem
Check the answer
Read
1. What
do I know?
Underline
(or Understand)
2. What do I want to know?
Calculate (or Choose)
3. What can I work out?
Solveit a try out!
4. Give
5. Is
that the problem done?
Answer
6. If
not
go
back
to
number
1.
Check
Types of problems

One step problems

Multi step word problems

Problems that require the interpretation of pictures, tables
or graphs, interpolating and extrapolating, within and
beyond what is known.

Problems that require lists to identify patterns within which
relationships or totals can be found

Puzzle-type problems that require some reasoning and
involve some train of logical thought

Puzzle-type problems that require some reasoning and
employ deduction from known facts
72-18
54
£5.00 - £1.05 = £3.95
£7.00 - £3.95 = £3.05
3.05
All the angles would be
108° if it was regular
cheetah
leopard and wildcat
2
4
banana
13
15
Work out how much the class spends in a
week, a month and a year on chocolate.
Extrapolate how much the whole school
spends in a year.
Comic Relief/Fairtrade resources
Lesson plan: http://www.papapaa.org/pdf/ks2_1a_plan.pdf
Website: http://www.papapaa.org/
‘A goldfish costs £1.80 and an angel fish
costs £1.40. Nasreen paid £20 for some
fish. How many of each fish did she buy?’
Goldfish at £1.80 each
Angel fish at £1.40 each
1 £1.80
2 £3.60
3 £5.40
4 £7.20
5 £9.00
6 £10.80
7 £12.60
8 £14.40
9 £16.20
10 £18.00
11 £19.80
1
2
3
4
5
6
7
8
9
10
11
12
13
14
£1.40
£2.80
£4.20
£5.60
£7.00
£8.40
£9.80
£11.20
£12.60
£14.00
£15.40
£16.80
£18.20
£19.60
A solution in under 3 minutes could get you a job with Microsoft!
U2 has a concert that starts in 17 minutes and they must all cross a bridge to get
there.
All four men begin on the same side of the bridge. It is night. There is one
flashlight.
A maximum of two people can cross at one time.
Any party who crosses, either 1 or 2 people, must have the flashlight with them.
The flashlight must be walked back and forth, it cannot be thrown, etc.
Each band member walks at a different speed.
Bono takes 1 minute to cross
Edge takes 2 minutes to cross
Adam takes 5 minutes to cross
Larry takes 10 minutes to cross
How can the band get to the concert in time?
Solution
Bono and Edge go over,
Bono comes back
Bono takes 1 minute to cross
Edge takes 2 minutes to cross
Adam takes 5 minutes to cross
Larry takes 10 minutes to cross
= 3 mins
Larry and Adam go over,
Edge comes back
= 12 mins
Bono and Edge go over
= 2 mins
Total time taken = 17 mins
What is a smile worth?
A smile is worth £15.
(A frown is worth £10 and a neutral face is
worth £12)
Here is some information about my four friends:
Nicky is older than Jason,
Jason is older than Nathan,
Nathan is younger than Nicky
and Sam is older than Nicky.
Can you list my friends from oldest to youngest?
Sam
Nicky
Jason
Nathan
Types of problems

One step problems

Multi step word problems

Problems that require the interpretation of pictures, tables
or graphs, interpolating and extrapolating, within and
beyond what is known.

Problems that require lists to identify patterns within which
relationships or totals can be found

Puzzle-type problems that require some reasoning and
involve some train of logical thought

Puzzle-type problems that require some reasoning and
employ deduction from known facts
Not just word problems!

Children need to experience a wide variety of
problem types.

Children need to be taught how to recognise,
access and solve each problem type

Children need to be taught how to justify and
communicate their understanding and reasoning

Reasoning, justifying and communicating should
be integral to problem solving lessons
Communicating
includes interpreting; formulating;
discussing and recording maths and
presenting findings
True or false?
Convince yourself (mental justification)
Convince a friend (oral justification)
Convince a friend in writing (informal written justification)
Convince the teacher (formal written justification)
Convince Scenario: The Mathematical Association
A heptagon is a 7 sided polygon with
interior angles that add to 720
degrees
Is this true or false?
More ‘true/false’ questions in
separate PowerPoint!
A heptagon is a 7 sided polygon with interior angles
that add to 720 degrees
FALSE
• A heptagon is a seven sided
polygon.
• It can be divided into 5 triangles.
• The sum of the interior angles in
a triangle is 180.
180°
180°
180°
180°
180°
• 5 x 180 = 900
Therefore, a heptagon is a 7 sided
polygon with interior angles that
add to 900 degrees.
Why do angles in a triangle always add up to 180°?
Reasoning
includes making and testing hypotheses;
spotting patterns; generalising; explaining and
justifying
Identifying patterns
Pattern objectives…
From YR
 Use shapes to describe and make models, pictures and
patterns.

Count in twos.
…to Y6
 Recognise and extend number sequences such as square
and triangular numbers.

Count on and back in steps of 0.1, 0.2, 0.25, 0.5 and
then back.

Solve mathematical problems or puzzles. Recognise
patterns and generalise.
Solve mathematical problems or puzzles.
Recognise patterns and generalise.
Pascal’s triangle
 Square and triangular numbers
 Perfect numbers
 Prime numbers
 Consecutive numbers
 Shape
 Number sequences

Identifying patterns and
relationships
If it takes 4 women 6 days to plough
five fields how long will it take the
men to collect the potatoes?
-32 – 45 = -77
-77 ÷ 7 = -11
45 + 22 = 67
67
98
T = 2R - 2
Points to note

Teach children the skills to recognise and access different problem
types.

Use a range of closed, open problems and investigations

Encourage children to be systematic in their recording

Teach children how to communicate their understanding

Teach or consolidate other mathematical topics through pattern
If children are having difficulty solving problems you need to find out:

is it the underlying maths they are struggling with?

are they able to identify the problem type and have they been
taught the skills to access it?

are they having difficulty, recording, reasoning or communicating
their thoughts?

do they know how to work systematically?
Children will not learn how to
problem solve, communicate or
reason simply through answering
word problems.
Children will not become
proficient problem solvers simply
because they understand what
RUCSAC stands for.