10 Simple Ways to Solve Even the Most Complex Problems

Problem Solving Strategies

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PROBLEM SOLVING STRATEGIES

• Make a List• Guess and

Check• Draw a Picture

or Diagram• Find a Pattern• Act It Out

• Work Backward• Make a Table,

Chart, or Graph• Simplify• Use Logic• Brainstorm

MAKE AN ORGANISED LIST

An organized list is useful to show all possible solutions.

How many different

outfits can you make ifyou have two shirts

and

four pairs of pants?

Red shirt, blue pants Red shirt, khaki pants

Yellow shirt, blue pants Yellow shirt, khaki pants

Red shirt, green pants Red shirt, black pants

Yellow shirt, green pants Yellow shirt, black pants

GUESS AND CHECKGuess at a problem’s answer

and check it. Keep trying until you are correct.

The sum of two numbersis 27, their product is

180.

What are the two numbers?

Guess: 13 + 14 = 27 13 * 14 = 182

Guess: 12 + 15 = 27 12 * 15 = 180

YES!YES!

DRAW A PICTURE OR DIAGRAM

Use a picture or diagram to solve the problem

What are the possible combinations for families with two children?B G

B G B G

Tree Diagram

A Picture Representation

FIND A PATTERNUse a pattern to get from one

numeral to the next

Lisa is drawing a pyramid.She puts one block in the top row, two

in the second, four in the third, eight in the fourth.

If she continues this pattern, how many blocks will be in the tenth row?

ROWS BLOCKS

1 1

2 2

3 4

4 8

5

6

7

8

9

10 ?

ACT IT OUTAct a problem out or use

manipulatives.Four students sit at each lunch table. Sue is left-handed and doesn’t want to bump

elbows with anyone, but she likes to sit next to her best friend Kate. Kate is to the left of Nancy. Allison likes to be on the end. Where do each of the girls sit during lunch?

WORK BACKWARDUse inverse operations to solve

problems.

Trish went to the mall and spent$23.50 on a new shirt, $6.75 onlunch, and $31.25 on an new skirt. She had $16.50 left when she gothome. How much money did shebring with her to the mall?

$23.50 + 6.75 + 31.50 + 16.50 = $77.25

$23.50 on Shirt$6.75 on Lunch $31.50 on Skirt $16.50 Left

MAKE A TABLE, CHART OR GRAPH

Tables, charts, and graphs help organize data.

There are 100 fifth graders inthe school. One fifth of them like pizza,one half like spaghetti, one fifth like cheeseburgers,one tenth like tacos. How many students like each

type of food?

05

10152025

30354045

50

P S C T

NumberofStudents

SIMPLIFYMake the numbers simpler to solve

the problem.

The backyard is 2,400cm long and 1,700cm wide.

How many metres of fencing is needed to surround the backyard?

10cm = 1dm10dm = 1m100cm = 1 m P = (L x 2) + (W x 2)

2,400cm = 24m1,700cm = 17mP = (24 x 2) + (17 x 2) = 82 metres of fencing

USE LOGICUse prior knowledge to solve

problems.A number is composite, and amultiple of 6. The first digit isprime, but not 2. The number isless than 50 but greater than 20. What is the number?

1. Composite numbers have factors other than one and themselves.

2. Prime numbers have only one and themselves as factors.

3. Multiples of 6 >20, < 50: 24, 30, 36, 42, 48

BRAINSTORMCreate a new way to look at a

problem.

How do 6 ¼ and 9 ¾ make 4 x 4?

$6.25 + $9.75 = $16.00

4 x 4 = 16

OTHER PROBLEM SOLVING STRATEGIES

• Using a Formula• Arithmetic Computations – using

‘clue’ words to operation• Make a Model