Warm Up! Evaluate these expressions if m = 7, n = 9, and Q = 10: Q + m = 3Q – 4m = (m + 2) ÷ n =

Use a Problem Solving Plan Chapter 1, Lesson 6

Vocabulary Verbal Model – describes a real world situation using words as labels and using math symbols to relate the words.

Problem Solving Plan Read and Understand Make a Plan Solve the Problem Read the problem carefully. Identify the question and any important information Make a Plan Decide on a problem solving strategy Solve the Problem Use the problem solving strategy to answer the question Look Back Check that your answer is reasonable

Problem Solving Strategies! Strategy When to use How to use Draw a diagram Draw a diagram when any problem involves relationships you can represent visually Draw a diagram that shows the given information. Label any unknowns in your diagram Look for a pattern Look for a pattern when a problem involves a series of numbers that you need to analyze Look for a pattern in any given information. Apply and extend the pattern to help you solve the problem Guess, Check, revise Guess, check, and revise when you need a place to start Make a reasonable guess. Check to see if your guess solves the problem. If it does not, revise your guess and check again Make a list or table Make a list or table when you need to record, generate, or organize information. Generate a list, accounting for all possibilities. Look for relationships. Work backwards Work backwards when a problem gives you an end result and you need to find beginning conditions Work backwards from the given information until you solve the problem.

Example 1 During a kayak trip, you kayak for 2 hours, break for lunch, kayak for 3 hours, have a short break, and kayak for 2 more hours. During the first part of your trip, you travel 4 miles. You travel the same rate for the second part of the trip. During the last part of the trip, you travel twice as fast. How many miles did you travel on the kayak trip?

Step 1: Read and Understand What do we know?? We can organize the given information on a diagram: 2 hours 3 hours 2 hours start end lunch break Traveled 4 miles Traveled at the same rate Traveled twice as fast What do you need to find out?? You need to find the distance traveled after lunch and the distance traveled after the break in order to find the total distance traveled.

Step 2: Make a Plan Use what you know to write a verbal model for the total distance traveled. Distance traveled after lunch Distance traveled after break Distance traveled before lunch How can you determine the distance traveled after lunch? How can you determine the distance traveled after the break?

Step 3: Solve the Problem You traveled 4 miles in 2 hours before lunch. Find the rate that you traveled before lunch: 4 miles 2 hours = 2 miles per hour This means you traveled 2 miles per hour before lunch and after lunch. You traveled twice as fast during the last part of the trip… 2 • 2 = 4 miles per hour

Continued… 4 6 8 4 + 6 + 8 = You traveled a total of ____ miles. Distance traveled after lunch Distance traveled after break Distance traveled before lunch 4 6 8 4 + 6 + 8 = You traveled a total of ____ miles.

Step 4: Look back Suppose you traveled all 7 hours at a rate of 2 miles per hour. Then you would have traveled 7 • 2 = 14 miles. Because you traveled faster during one part of the trip, you traveled more than 14 miles. So…a distance of 18 miles seems reasonable.

Let’s practice: Writing a Verbal Model One serving of rice weighs 2 ounces. A bag of rice weighs 90 ounces. How many full servings of rice are in the bag? Weight of bag ÷ Weight of 1 serving

Let’s practice: Writing Verbal models One t-shirt costs $10. How much do 15 t-shirts cost? Number of t-shirts • cost of 1 t-shirt

Independent Practice Work quietly at your seat. Raise your hand if you need help 

Study Guide!! (Test on Friday) Test will be on 1.4 – 1.6, with a few questions from 1.1 – 1.3 This is Homework if you do not finish in class!