Problem Solving Skills

WHY???• Mathematical word problems (or story problems)

require you to take real-life situations and find solutions by translating the given information into equations with unknowns. Since very few problems in life are clear cut with simple steps and easily defined numbers, knowing how to set up and solve (word) problems is something beneficial to know. Although you may be anxious when you see a word problem, having a strategy will help you to organize your information and resources so that you can become a good problem solver.

Objectives

• Students will be able to…• Read a word problem and write a statement

defining the problem. • Correctly set up mathematical equations based

on the information provided in the problem.• Apply the Methodology for Solving Word

Problems.

Problem Solving is easy if you follow these steps

POLYO’s Problem Solving

Plan

Problem Solving Plan

• Step 1: Understand the problem• Step 2: Devise a Plan• Step 3: Carry out the plan• Step 4: Look Back and Check your answer

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.• Ask if your answer is going to be a

larger or smaller number compared to what you already know.

Step 1 - Understand the ProblemRead the problem carefully.

• Manny can stamp 345 envelopes in 15 minutes. How many envelopes can he stamp in 1 hour?

Step 1 - Understand the ProblemFind the important information.

• Manny can stamp 345 envelopes in 15 minutes. How many envelopes can he stamp in 1 hour?

Step 1 - Understand the ProblemWrite down the numbers.

• Manny can stamp 345 envelopes in 15 minutes. How many envelopes can he stamp in 1 hour?

345𝑒𝑛𝑣𝑒𝑙𝑜𝑝𝑒𝑠15𝑚𝑖𝑛

?𝑒𝑛𝑣𝑒𝑙𝑜𝑝𝑒𝑠1h𝑜𝑢𝑟

Step 1 - Understand the ProblemIdentify what the problem wants

you to solve.Manny can stamp 345 envelopes in 15 minutes. How many envelopes can he stamp in 1 hour?How many envelopes can he stamp in 1 hour?

Notice hours and minutes are different. How many minutes in one hour?

Problem Solving is easy if you follow these steps

Devise a Plan

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

Choose a methodUse 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

Use Reasoning345𝑒𝑛𝑣𝑒𝑙𝑜𝑝𝑒𝑠

15𝑚𝑖𝑛?𝑒𝑛𝑣𝑒𝑙𝑜𝑝𝑒𝑠

60𝑚𝑖𝑛

What number times 15 = 60?

Use that number to multiply by 345

345 x 4=

THINK>>> 1 hour = 60 min

Set up equivalent ratios to help you find the answer.

Problem Solving is easy if you follow these steps

Carry Out The

Plan

Step 3 - Solve the problem

?𝑒𝑛𝑣𝑒𝑙𝑜𝑝𝑒𝑠60𝑚𝑖𝑛

What number times 15 = 60?

Use that number to multiply by 345

345 x 4=

345𝑒𝑛𝑣𝑒𝑙𝑜𝑝𝑒𝑠15𝑚𝑖𝑛

He will stamp 1380 envelopes in one hour.

Problem Solving is easy if you follow these steps

LookBack &Check

Step 4 - Look Back & CheckReread the problem

Manny can stamp 345 envelopes in 15 minutes. How many envelopes can he stamp in 1 hour?

Does it make sense that Manny can stamp 1380 envelopes if he can do 345 in 15 minutes?

Yes, because 1380

Example 1• Aimee can read 24 pages in 40

minutes. How many pages per hour can Aimee read?24𝑝𝑎𝑔𝑒𝑠

40𝑚𝑖𝑛?𝑝𝑎𝑔𝑒𝑠60𝑚𝑖𝑛

Find a relationship between numerators and denominators.60/40 = 1.5Use that information to find the # of pages

24 x 1.5

Aimee can read 36 pagesIn one hour.

Example 2.A truck driver travels 495 miles in 9 hours. What is the driver’s speed in miles per hour?495𝑚𝑖𝑙𝑒𝑠

9h𝑜𝑢𝑟𝑠?𝑚𝑖𝑙𝑒𝑠1h𝑜𝑢𝑟

This is a unit rate! The operation we use to solve it is….

495

The drivers speed is 55 mph.

Example 3A walker walks by three tree. It takes her 120 seconds to walk from Tree A to Tree B, a total of 120 meters. It takes her 40 seconds to walk from Tree B to Tree C, a distance of 100 meters. What is her average speed?

REMEMBER: Average Speed =

120+100120+40

220160

2216

118= = = = 1

His average speed is 1 and 3/8 miles per second.

Ricardo started working at a company 3.2 years ago. He earns $55,000 per year. How much has Ricardo earned since he started working for the company?

Example 4

$55,0001 𝑦𝑒𝑎𝑟𝑠

?3.2 𝑦𝑒𝑎𝑟𝑠

Find a relationship between numerators and denominators.

1 x 3.2 = 3.2, so 55,000 x 3.2 will give us are answer.

Ricardo has earned $176,000

Practice- Go to this website to complete word problems:

• Rates and Unit Rates Review Problem Solving Interactive

• HW: Rates and Unit Rates Problem Solving Practice