Slide 1 / 142 Slide 2 / 142 Table of Contents Strategies & Plans for Problem Solving Rate Problems Solving Percent Problems Word Problems Find a Pattern Estimation Problems Fraction Problems Pre-Algebra LCM / GCF Problems Combination Problems Proportion Problems Geometry Problems Order of Operation Problems Integer Operations Problems Slide 3 / 142 Slide 4 / 142 Problem Solving Strategies Most problems can be solved by incorporating one or more strategies. Strategies & Plans for Work backwards Problem Solving Make a table, chart or diagram Solve a simpler or similar problem Guess and check Look for a pattern Return to Eliminate possibilities Table of Draw a picture Contents Slide 5 / 142 Slide 6 / 142 Plan for Solving a Plan for Solving a Word Problem Word Problem Plan: Read the problem several times. What do you know? Check: Reread the problem. What do you need to find? Did you answer the question? Eliminate any unnecessary information. Did you state your answer clearly with the appropriate units? Set Up: Define a variable. Is your answer consistent with the Making a chart or drawing a picture may be helpful. information given in the problem? Write an open sentence. Solve the open sentence.
Slide 7 / 142 Slide 8 / 142 Tim ran on the elliptical for 1.6 hours at a speed of 11.4 miles per hour. How many miles did she ride the bicycle? Tim ran for 1.6 hours. Rate What do you know? His speed was 11.4 miles per hour. Problems What is the question to be answered? Return to How many miles did he ride the bicycle? Table of Contents Slide 9 / 142 Slide 10 / 142 Tim ran on the elliptical for 1.6 hours at a speed of A grocery store checker can total the purchases for 3 11.4 miles per hour. How many miles did she ride the customers in 10 minutes. At this rate, how many bicycle? customers can the checker serve in one hour? What does this remind you of? What do you know? Distance = Rate Time Checker can serve 3 customers in 10 minutes. Solve the problem and check here What is the question to be answered? How many customers can be served for the answer. 18.24 miles in an hour? Slide 11 / 142 Slide 12 / 142 A grocery store checker can total the purchases for 3 1 You run at a speed of 8.5 minutes per mile. How long does customers in 10 minutes. At this rate, how many it take to run 7 miles? customers can the checker serve in one hour? What does this remind you of? Distance = Rate Time Solve the problem and check here 18 customers for the answer.
Slide 13 / 142 Slide 14 / 142 2 You run at a speed of 8.5 minutes per mile. How many 3 If you are driving at 45 miles per hour, how far can you go in miles per hour do you run? 3.5 hours? Slide 15 / 142 Slide 16 / 142 4 If you are driving at 65 miles per hour, about how long does 5 You can fill 8 bags of sand every 3 minutes. How long does it take to travel 309 miles? it take to fill 20 bags? Slide 17 / 142 Slide 18 / 142 In a restaurant, it is customary to leave a 15% tip. A. How much money should you leave as a tip if the bill for your party comes to Percent $82.97? Problems The total bill is $82.97. The tip should What do you know? be 15% of that total. Return to How much is the tip? Table of What is the question to be answered? Contents Note: For the purposes of instruction, "pin" this page while working through Parts A and B of this question.
Slide 19 / 142 Slide 20 / 142 In a restaurant, it is customary to leave a B. If there are 6 or more people in your party, 15% tip. the restaurant requires you to leave an 18% tip. What would be the difference in the tip A. How much money should you leave as amount if there were 6 people rather than 4 a tip if the bill for your party comes to people in your party? $82.97? The total bill is $82.97. The tip should be Find 15% of $82.97. What do you know? What will you do to find the solution? 18% of that total. What is the difference between a 15% $12.45 Solve the problem and check here What is the question to be answered? and an 18% tip? for the answer. Slide 21 / 142 Slide 22 / 142 As a sales rep, you earn 15% commission on your B. If there are 6 or more people in your party, monthly sales. If your total sales last month was $2,750 the restaurant requires you to leave an 18% how much do you earn? tip. What would be the difference in the tip amount if there were 6 people rather than 4 Solution Do? people in your party? Find 18% of $82.97 and subtract $12.45. What will you do to find the solution? $2.48 Solve the problem and check here for the answer. Slide 23 / 142 Slide 24 / 142 When waiting tables, you can expect to earn 18% of the 6 How much tip should you leave a waitress for a $130 bill? bill as a tip. The total bills for one night is $960. How Her service was good so you want to leave 18%. much can you expect to earn if you need to tip out the other workers at 5%? Solution Do?
Slide 25 / 142 Slide 26 / 142 7 What is the tax on a $285 purchase? Tax is 7%. 8 How much will you earn in commission if you sell $2,400 worth of merchandise and your commission is 12%? Slide 27 / 142 Slide 28 / 142 9 You did not pay your bill on time. There is a 24% finance 10 As a waiter, how much can you expect to earn if the total charge. If the original bill was $5,250 what is the new for the night's bills is $950? Standard 18% tipping amount due? applies. Slide 29 / 142 Slide 30 / 142 What are the next three numbers in the pattern: 2, 3 1/4, 4.5, 5 3/4, __, __, __ ? Find a Pattern Return to Table of Answers: 7, 8 1/4 or 8.25, 9.5 or 9 1/2 Contents
Slide 31 / 142 Slide 32 / 142 Audrey, Bjorn, and Clara each began to write a number pattern for a class assignment. Their patterns are Part A. Complete Audrey's pattern by writing shown in the table below. four more numbers in the table. Explain the rule for her pattern. Audrey's Bjorn's Pattern Clara's Pattern Pattern 1 x 2 = 2 2 2 2 2 What do you know? 2 x 2 = 4 or 2 + 2 4 4 4 3 x 2 = 6 4 + 2 6 8 16 What are the next four numbers in the What is the question to be answered? pattern? Note: For the purposes of instruction, "pin" this page while working through Parts A, B, and C of this question. Slide 33 / 142 Slide 34 / 142 Part A. Complete Audrey's pattern by writing Part B. Complete Bjorn's pattern by writing four more numbers in the table. Explain the three more numbers in the table. Explain the rule for her pattern. rule for his pattern. Continue the pattern four more times. What will you do to find the solution? 2 1 = 2 2 What do you know? 2 2 = 4 or 2 x 2 3 = 8 4 x 2 2 8 Solve the problem and check here 10 for the answer. 12 What are the next three numbers in the 14 What is the question to be answered? pattern? x 2 or +2 each step Explain the rule for the pattern. Slide 35 / 142 Slide 36 / 142 Part B. Complete Bjorn's pattern by writing Part C. Complete Clara's pattern by writing three more numbers in the table. Explain the two more numbers in the table. Explain the rule for his pattern. rule for her pattern. Source: Learnia Continue the pattern three more times. What will you do to find the solution? 2 2 = 4 What do you know? 2 4 2 = 16 16 Solve the problem and check here 32 for the answer. 64 What are the next two numbers in the pattern? What is the question to be answered? 2 x or 2x2=4 Explain the rule for the pattern. 4x4=16
Slide 37 / 142 Slide 38 / 142 Part C. Complete Clara's pattern by writing Some cows and chickens live on a farm. two more numbers in the table. Explain the The total number of their legs is 48 and the rule for her pattern. total number of heads is 17. How many cows live on the farm? What will you do to find the solution? Continue the pattern two more times. 256 Solve the problem and check here 65,536 for the answer. Answer: 7 cows. 2x2 = 4 4x4 = 16 Explain the rule for the pattern. 16x16 = 256 Slide 39 / 142 Slide 40 / 142 11 Find the next number in the sequence. The Fibonacci Sequence is a repeating pattern found in nature. Study the sequence and find the next two terms. 0, 1, 1, 2, 3, 5, 8, 13, 21, 33, 54, ___, ___ Answer: Next term is sum of two previous terms. 87, 141 Slide 41 / 142 Slide 42 / 142
Slide 43 / 142 Slide 44 / 142 Slide 45 / 142 Slide 46 / 142 There are 32 members in the Quilting Club. Each member decorated a fabric square that measured 7 inches on each side. The members then sewed the fabric squares together to make a quilt. John estimated that the area of the finished Estimation quilt is about 1500 square inches. Problems Return to Table of Note: For the purposes of instruction, "pin" this page while Contents working through Parts A, B, and C of this question. Slide 47 / 142 Slide 48 / 142 Part A. What is the area of each fabric square? Part A. What is the area of each fabric square? Show your work or explain how you got your Show your work or explain how you got your answer. answer. Use the formula What do you know? Each fabric square measured 7 inches on a side. What will you do to find the solution? A = s s or A = s 2 Solve the problem and check here What is the question to be answered? 49 in 2 What is the area of each fabric square? for the answer.
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