1.5 problem solving plan part 1Presentation Transcript
20 trees ANSWER Lesson 1.5, For use with pages 28-33 1. Mr. Lu is planting trees around the perimeter of a rectangular park. The park measures 72 feet by 48feet. The trees need to be spaced 12feet apart. A tree is to be planted in each corner. How many trees are needed?
Use a Problem Solving Plan Section 1.5 P. 28 - 34
Students will learn to use a problem solving plan to solve problems Read and Understand Make a plan Solve the problem Look Back
Students will learn to use a problem solving plan to solve problems Key Concepts P. 30 For Your Notebook Formulas C = 5/9(F – 32) I = PRT (Interest = principal x rate x time) D = r t distance = rate x times d/t = r d/r = t P = I – E
Students will learn to use a problem solving plan to solve problems I = Prt (Interest = principal x rate x time) What is the interest on $3000 invested for 3 years in an account that earns simple interest at a rate of 4% per year? $360 of interest
You run in a city where the short blocks on north-south streets are 0.1mile long. The long blocks on east-west streets are 0.15mile long. You will run 2 long blocks east, a number of short blocks south, 2long blocks west, then back to your starting point. You want to run 2miles. How many short blocks should you run? EXAMPLE 1 Read a problem and make a plan Running Students will learn to use a problem solving plan to solve problems
EXAMPLE 1 Read a problem and make a plan SOLUTION STEP 1 Read and Understand What do you know ? You know the length of each size block, the number of long blocks you will run, and the total distance you want to run. You can conclude that you must run an even number of short blocks because you run the same number of short blocks in each direction.
Read a problem and make a plan EXAMPLE 1 What do you want to find out? You want to find out the number of short blocks you should run so that, along with the 4 long blocks, you run 2 miles. STEP2 Make a Plan Use what you know to write a verbal modelthat represents what you want to find out. Then write an equation and solve it, as in Example2.
Totaldistance(miles) Length oflong block(miles/block) Numbershort blocks(block) Numberlong blocks(block) Length ofshort blocks(miles/block) • + • = 0.1 s + 0.15 4 = 2 EXAMPLE 2 Solve a problem and look back Solve the problem in Example 1 by carrying out the plan. Then check your answer. SOLUTION STEP 3 Solve the Problem Write a verbal model. Then write an equation.Let sbe the number of short blocks you run. The equation is0.1s + 0.6 = 2.One way to solve theequation is to use the strategy guess, check, and revise.
2.6 = 2 EXAMPLE 2 Solve a problem and look back Guessan even number that is easily multiplied by0.1.Try20.Checkwhether20is a solution. 0.1s + 0.6 = 2 Write equation. 0.1(20) + 0.6 = 2 Substitute 20 for s. Simplify; 20 does not check. Revise.Because2.6 > 2, try an even number less than20.Try 14. Checkwhether14is a solution.
2 = 2 ANSWER To run2miles, you should run14short blocksalong with the4 long blocks you run. EXAMPLE 2 Solve a problem and look back 0.1s + 0.6 = 2 Write equation. 0.1(14) + 0.6 = 2 Substitute 14 for s. Simplify.
EXAMPLE 2 Solve a problem and look back STEP 4 Look Back Check your answer by making a table.You run0.6mile on long blocks. Each two short blocks add0.2mile. The total distance is2miles when you run4long blocksand14short blocks. The answer in Step3 iscorrect.
Test Practice Students will learn to use a problem solving plan to solve problems SOLUTION Use the formula for the area of arectangle, A= lw,withl = 18inchesandw = 11inches.
ANSWER The correct answer is B. A B C D EXAMPLE 3 Standardized Test Practice A = lw Write area formula. = 18(11) Substitute 18 for land 11 for w. = 198 Simplify. The area is 198square inches, so the total cost is$.25(198) = $49.50.
Assignment: P. 31 (#1-12) - write out Answer the questions by READING the DIRECTIONS Students will learn to use a problem solving plan to solve problems