Problem Solving

by Mr. Fitzgerald

Problem Solving is easy if you follow these steps

Understandthe

problem

Step 1 – Understand the problem• Read the problem carefully.• Find the important information.• Write down the numbers.• Identify what the problem wants

you to solve.

Step 1 - Understand the ProblemRead the problem carefully.

• Luis earned 14 Accelerated Reading points the first week of November. At the end of the following week he had a total of 31 points. How many points did he earn the second week?

Step 1 - Understand the ProblemFind the important information.

• Luis earned 14 Accelerated Reading points the first week of November. At the end of the following week he had a total of 31 points. How many points did he earn the second week?

Step 1 - Understand the ProblemWrite down the numbers.

• Luis earned 14 Accelerated Reading points the first week of November. At the end of the following week he had a total of 31 points. How many points did he earn the second week?Total = 31 1st week =14

Step 1 - Understand the ProblemIdentify what the problem wants

you to solve.• Luis earned 14 Accelerated

Reading points the first week of November. At the end of the following week he had a total of 31 points. How many points did he earn the second week?Total = 31 1st week =14

2nd week = ?

Step 2 - Decide how you’re going to solve the problem

Choose a method

Use a graph Use formulasWrite an equation Make a listFind a pattern Work backwardsUse reasoning Draw a pictureMake a table Act it out

Step 2 - Decide how you’re going to solve the problem

Write your equation

Since I know both weeks total 31 I write14 + s = 31

Total = 31 1st week =142nd week = ?

Step 3 - Solve the problem

3 1 – 1 4

Total = 31 1st week =142nd week = ?

2

1

71

Problem Solving is easy if you follow these steps

LookBack &Check

Step 4 - Look Back & CheckSubstitute your new number

• Luis earned 14 Accelerated Reading points the first week of November. At the end of the following week he had a total of 31 points. How many points did he earn the second week?

Total = 31 1st week =142nd week = 17

Write an equation to solve this problem.

• Jaylynn had $84.75 in her savings account. She made a deposit. Her new balance was $107.03. How much was her deposit?

$84.75 + d = $107.03Inverse operation

$107.03 – $84.75 = d

Write an equation to solve this problem.

• Anthony has twice as many pokemon cards as Joshua. If Anthony has 124 cards, how many does Joshua have?

2d = 124inverse operation d = 124/2

Write an equation to solve this problem.

• Vicki baked 90 cookies . If there are 15 cookies in each batch. How many batches did she bake?

15b = 90inverse operation b = 90/15

Write an equation to solve this problem.

• Navneet has 3 times as many CD’s as Arlene. If Navneet has 36 CD’s, how many does Arlene have?

3c = 36inverse operation c = 36/3

Write an equation to solve this problem.

• A square has a perimeter of 48 inches. What is the length of each side of the square.

4s = 48

inverse operation s = 48/4

Write an equation to solve this problem.

• One year the city ambulance responded to emergencies on 293 days. How many days were there no emergencies?

293 + d = 365

inverse operation d = 365 - 293

Step 1 - Understand the ProblemRead the problem carefully.

• A Girl Scout troop went on a hike. First they walked 1 mile east, then 2 miles south, then 3 miles west, and 1 mile north, then 2 miles east. How far is the troop from their starting point?

Step 1 - Understand the ProblemFind the important information.

• A Girl Scout troop went on a hike. First they walked 1 mile east, then 2 miles south, then 3 miles west, and 1 mile north, then 2 miles east. How far is the troop from theirstarting point?

Step 1 - Understand the ProblemWrite down the key information.

1 mile east,

2 miles south,

3 miles west,

1 mile north,

2 miles east

Step 1 - Understand the ProblemIdentify what the problem wants

you to solve.

•A Girl Scout troop went on a hike. First they walked 1 mile east, then 2 miles south, then 3 miles west, and 1 mile north, then 2 miles east. How far is the troop from their starting point?

Step 2 - Decide how you’re going to solve the problem

Choose a method

Use a graph Use formulasWrite an equation Make a listFind a pattern Work backwardsUse reasoning Draw a diagramMake a table Act it out

Step 2 - Decide how you’re going to solve the problem

Make your diagram

NE

SWstart

1 mile

finish

Step 4 - Look Back & CheckDid you solve what the problem

asked you to solve?

NE

SW

start

1 milefinish

1 mile east, 2 miles south, 3 miles west, 1 mile north, 2 miles east

How far is the troop from their starting point?

one mile

Draw a diagram to solve this problem.

• A picture frame with a photo is 15 inches wide and 12 inches high. A mat around the photo is 1 ½ inches wide on all sides. What are the dimensions of the photo?

1512

1 ½

1 ½1 ½

1 ½

15”12”

1 ½

1 ½1 ½

1 ½

Step 1 – Add the two mat edges together.

1 ½1 ½+

2/22

Step 2 – Convert the 2/2 into 1 and add this to the whole number 2.

15”12”

1 ½

1 ½1 ½

1 ½

1 ½1 ½+

1

3

Step 2 – Convert the 2/2 into 1 and add this to the whole number 2.

15”12”

1 ½

1 ½1 ½

1 ½

15 3-12

Step 3 – To get the width of the photo subtract the 3 from 15.

15”12”

1 ½

1 ½1 ½

1 ½

12 3-9

Step 4 – To get the height of the photo subtract the 3 from 12.

12”9”

1 ½

1 ½1 ½

1 ½12 3+15

Step 5 – Your photo size is 12 x 9 inches. To check your work, add 2 times the matwidth to each of your new measurements.

9 3+12

Draw a diagram to solve this problem.• The Zunigas, Estoleros, Leys, Penas

and Rices all live on the same road in a row. The Estoleros live in the middle house. The Penas live in the first house. The Leys live between the Estoleros and the Zunigas. Who lives in the second house?

EP ZLR