Problem Solving

Steps and Strategies

The Problem Solving PlanStep 1: Understand the Problem

What are you asked to find? Reword the problem so it makes sense to you.

What information is given? Identify the important facts in the problem.

What information do you need? Not all information is always needed. Sort out the

important facts needed to solve. Is all the information given?

Can you solve the problem with the information given?

Step 2: Make a PlanHave you ever solved a similar problem?What strategy or strategies can you use?

Step 3: SolveFollow your plan – Show the steps in your

solution. Write your answer as a complete sentence.

Step 4: Look BackHave you answered the question?Is your answer reasonable? Is there another strategy you could use? Did you learn anything while solving this

problem that could help you solve similar problems in the future?

In SummaryWhen problem solving:

1. Understand the problem2. Make a Plan (Know the strategies)3. Solve (Show All Work and Write in

Complete Sentences)4. Check your Work

Key WordsWhy is it important to understand key

words when problem solving? They help you decide how to solve the problem - Key words will tell you whether to add, subtract, multiply, or divide.

What key words do you already know? Discuss with your partner and be ready to share with the class.

Let’s Practice Identifying Key Words

Practice: Choose a key word from each operation

(addition, subtraction, multiplication, and division) and create a story problem using your key words.

Example: Key Word: ProductWhat is the product of 3 and 5?

Example: Key word: DifferenceSally and Joe were competing in the 100 meter dash. Sally ran it in 9.5seconds. Joe ran it in 7.5 seconds. What is the difference between their times?

Make sure your name is on your paper.

Switch papers with your partner. Take a few minutes to read through your partners paper. Underline the key words in each story problem. Then decide which operation you would use (+,-, x, or ÷) and write it out next to each problem. You do not have to solve the problem.

Now check with your partner. Do you both agree what the key words and operations are? If not, discuss why.

Be ready to share one of your story problems with the class.

Sometimes There is MoreThan just needing to know key words.

There are lots of different ways to go about solving a problem – Knowing and understanding different strategies will help make problem solving much easier!

What strategies do you already know?

Know the StrategiesDraw a Picture

A bald eagle has built a nest 18 feet below the top of a 105 foot tall oak tree. The eagle sits on a limb 72 feet above the ground. What is the vertical distance between the eagle and its nest?

105 feet

72 feet

18 feet

??? feet

Make an Organized ListA spinner has 4 different colors: red, blue,

yellow, and white. If you spin the spinner 2 times, how many different color combinations could you get?

Red, BlueRed, YellowRed, WhiteRed, Red

Blue, YellowBlue, White, Blue, Blue

(Blue, Red is already used)

Yellow, WhiteYellow, Yellow

(Yellow, Red & Yellow, Blue are already used)

White, White

(White, Red & White, Blue & White, Yellow are already used)

What makes this an organized list?

Guess and CheckShannon used equal numbers of quarters and nickels to buy an embossing template that cost $1.50. How many of each coin did she use?

Hmmm…does this work?

3 Q = $0.753 N = $0.15 $0.90 No

Hmmm…does this work?

5 Q = $1.255 N = $0.25 $1.50 Yes

Make a Table/ChartA subway train left downtown with 121

passengers aboard. At the first stop, 1 person got off. At the second stop, 3 people got off. At the third stop, 5 people got off. At the fourth stop, 7 people got off. If the pattern continues, how many people will get off at the 7th stop?

1st Stop 2nd Stop 3rd Stop 4th Stop 5th Stop

- 1 - 3 - 5 - 7 - 9

121 people

120 people

117 people

112 people 105 people

96 people

How many people will be left after the 7th stop?

Use Logical ReasoningAll elephants are wrinkled. Ajax is an

elephant. A) Ajax is wrinkledB) No conclusion possible

All squares have 4 sides. Susan drew a 4-sided figure. A)Susan drew a squareB) No conclusion possible

Work BackwardsSusan made a deposit of $74 to her bank

account. She then had $192 in the account. How much money was in the account before the deposit?

$192 - $74 = $118

(Deposit means add, but to find out how much she had BEFORE the deposit we need to subtract from the end result)

Act it Out

Make a Model

Find a Pattern

Other Strategies…

Review Problem Solving Process:When problem solving:

1. Understand the problem2. Make a Plan (Know the strategies)3. Solve (Show All Work and Write in Complete

Sentences)4. Check your Work

Now you try….1) Today is the teacher’s birthday. The teacher

said: “If you multiply my age by 3, then subtract 20, the result is 100.” How old is the teacher?

2) The sum of two numbers = 15The difference of the numbers is 3Find the numbers

Work Backwards: 100 + 20 = 120 120 ÷ 3 = 40

Guess and Check: 9 + 6 = 15 9 – 6 = 3 It Works!

3) The telephone operator has told Jed to deposit 60 cents. In how many ways can he do this using nickels, dimes, and quarters?

Organized List: 0Q 12N 0D2 Q 2N 0D 1Q 7N 0D 0Q 10N 1D2Q 0N 1D 1Q 5N 1D 0Q 8N 2D

1Q 3N 2D 0Q 6N 3D1Q 1N 3D 0Q 4N 4D

0Q 2N 5D0Q 0N 6D