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

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 Problem Read the problem carefully. Manny can stamp 345 envelopes in 15 minutes. How many envelopes can he stamp in 1 hour?

Step 1 - Understand the Problem Find the important information. Manny can stamp 345 envelopes in 15 minutes. How many envelopes can he stamp in 1 hour?

Step 1 - Understand the Problem Write down the numbers. Manny can stamp 345 envelopes in 15 minutes. How many envelopes can he stamp in 1 hour?

Step 1 - Understand the Problem Identify 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 method Use a graphUse formulas Write an equationMake a list Find a patternWork backwards Use reasoningDraw a picture Make a tableAct it out

Step 2 - Decide how you’re going to solve the problem Use Reasoning What number times 15 = 60? Use that number to multiply by 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 What number times 15 = 60? Use that number to multiply by x 4= He will stamp 1380 envelopes in one hour.

Problem Solving is easy if you follow these steps Look Back & Check

Step 4 - Look Back & Check Reread 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?

Example 1 Aimee can read 24 pages in 40 minutes. How many pages per hour can Aimee read? Find a relationship between numerators and denominators. 60/40 = 1.5 Use that information to find the # of pages 24 x 1.5 Aimee can read 36 pages In one hour.

Example 2. A truck driver travels 495 miles in 9 hours. What is the driver’s speed in miles per hour? This is a unit rate! The operation we use to solve it is…. The drivers speed is 55 mph.

Example 3 A 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? = = == 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 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 Rates and Unit Rates Review Problem Solving Interactive HW: Rates and Unit Rates Problem Solving Practice