Lesson: Word Problems with Four Operations Lesson Topic: Represent addition word problems with variables

Transcription

1 Lesson: Word Problems with Four Operations Lesson Topic: Represent addition word problems with variables Question 1: If Shawn picked 200 ripe mangoes off of one tree and 150 off of another, how many mangoes did Shawn pick? m = m = = m m = = m Question 2: Louise and Grace are going to combine their money to buy a new movie that costs $10. If Louise has $5, how much money does Grace need to add so they can buy their movie? = m m 5 = 10 5 m = m = m = 5 Question 3: If 4 kids are jumping on the trampoline and 8 kids total can jump, how many more kids can join in on the fun? k 8 = 4 k 4 = 8

2 4 + 8 = k 8 + k = k = 8 Question 4: Order the 5 steps we will use to write equations and solve word problems. Check your answer. Set up an equation. Solve the equation. Write what you want to know. List what you know. Question 5: If 3 kids are jumping on the trampoline and 6 kids total can jump, how many more kids can join in on the fun? k 6 = = k = k 6 + k = 3 k 3 = 6 Question 6: If 650 people go to the circus and the circus tent seats 1,000, how many more people could go to the circus? p 650 = 1,000 1,000 + p = ,000 = p 1, = p

3 650 p = 1,000 Question 7: On a beautiful day, 10 people are going to jump into the lake. If 5 people have already jumped in, how many more are going to jump in? p 5 = p = p = 5 p 10 = = p Question 8: If one class collected 65 cans for the food drive and another class collected 176 cans, how many cans did the two classes collect for the drive? c + 65 = c = = c = c c 176 = 65 Question 9: If there are 30 kids who are playing with a parachute, and 45 kids in total can play in the parachute, how many more kids can join? 45 + k = 30 k 45 = 30

4 = k k 30 = k = 30 Question 10: Even though it is really cold, 7 people are going to jump into the lake. If 3 people have already jumped in, how many more are going to jump in? p 7 = = p 7 3 = p 7 + p = 3 p 3 = 7

5 Lesson Topic: Represent two-step word problems with variable equations Question 1: A train has 3 passenger cars and each car holds 30 passengers. If one of the cars has 25 empty seats, and the rest of the cars are full, how many passengers are on the train? Which of the following sets of equations correctly represents this situation? Total number of seats: 3 30 = 90 Number of passengers: = p Total number of seats: 3 30 = 90 Number of passengers: = p Total number of seats: 30 3 = 10 Number of passengers: = p Total number of seats: 3 30 = 90 Number of passengers: = p Question 2: Kirk runs 4 miles a day. His goal is to run 20 miles in total. After 3 days, how many more miles does Kirk have left to run in order to meet his goal? Which of the following sets of equations correctly represents this situation? Number of miles already run: m 4 = 12 Number of miles left to run: = 8

6 Number of miles already run: 4 3 = 12 Number of miles left to run: = m Number of miles already run: 4 3 = m Number of miles left to run: m 12 = 8 Number of miles already run: 12 3 = 4 Number of miles left to run: 20 4 = m Question 3: Ellen has $82 saved. If she will save her allowance for the next 6 weeks, and she gets $12 per week for her allowance, how much money will she have after the 6 weeks? Which of the following sets of equations correctly represents this situation? Money saved over 6 weeks: 6 12 = 72 Total money saved: = m Money saved over 6 weeks: 12 6 = 2 Total money saved: = m Money saved over 6 weeks: 12 6 = 6 Total money saved: = m Money saved over 6 weeks: 6 m = 62 Total money saved: = 142

7 Question 4: Which information is given in the problem? Check all that are true. How much will Jonathan and Carrie spend? Each piece of fruit costs $2. They want to buy two pieces of fruit for each classmate. There are 24 people in the class. Each piece of fruit costs $1. Question 5: Tami is building a wooden deck. The deck needs 25 pieces of wood and each piece of wood needs 4 screws. If Tami already has 20 screws, how many more screws does she need to buy? Which of the following sets of equations correctly represents this situation? Total number of screws: 4 25 = 100 Screws needed: = s Total number of screws: 4 25 = 100 Screws needed: = s

8 Total number of screws: 4 25 = 100 Screws needed: = s Total number of screws: 4 25 = 100 Screws needed: = s Question 6: Andy is building a fence. The fence has 4 equal length sides of 10 feet each. If 1 foot of fence costs $2, how much money will Andy spend building the fence? Which of the following sets of equations correctly represents this situation? Total length of fence: 4 10 = 40 Total cost of the fence: 40 2 = m Total length of fence: 4 10 = 40 Total cost of the fence: 40 2 = m Total length of fence: 4 10 = 40 Total cost of the fence: 40 2 = m Total length of fence: 4 10 = 40 Total cost of the fence: 40 m = 2 Question 7: Elisa has 3 buckets of raspberries and she wants to share them all with her 5 friends. If there are 30 raspberries in each bucket, how many raspberries will each of her friends get if the raspberries are divided evenly between her friends?

9 Which of the following sets of equations correctly represents this situation? Total number of raspberries: 3 30 = 90 Raspberries each friend gets: 90 5 = r Total number of raspberries: = 90 Raspberries each friend gets: 90 5 = r Total number of raspberries: 3 30 = 90 Raspberries each friend gets: 90 3 = r Total number of raspberries: 3 30 = 90 Raspberries each friend gets: 90 5 = r Question 8: What piece of information do we want to know? The amount of money Jonathan and Carrie will spend. The number of people in their class. The cost of each fruit. The number of fruits each classmate gets.

10 How happy their classmates will be after getting the fruit. Question 9: There are a total of 37 third graders and 63 fourth graders who are going on a field trip. If a bus holds 25 students, how many buses are necessary to transport all of the students? Total number of students: = 26 Number of buses needed: = b Total number of students: = 100 Number of buses needed: = b Total number of students: = 26 Number of buses needed: = b Total number of students: = 100 Number of buses needed: = b Question 10: Cynthia likes to water ski on her brother's boat. The boat takes 2 gallons of gas each hour to run. If the price of gas is $5 per gallon, how much money will she spend on gas to ski for 6 hours? Which of the following sets of equations correctly represents this situation? Number of gallons of gas: 2 6 = 12 Total price: = m

11 Number of gallons of gas: 2 6 = m Total price: m 5 = 50 Number of gallons of gas: 2 6 = 12 Total price: 12 5 = m Number of gallons of gas: 2 6 = 12 Total price: 12 5 = m

12 Lesson Topic: Solve two-step word problems with variables Question 1: Steve likes to snowboard. It takes him 120 minutes to climb to the top of the mountain, 5 minutes to get ready to go, and 10 minutes to ride down the mountain. How long does his snowboard trip take? m = minutes Question 2: Which information is given in the problem? Check all that are true. It will be 24 minutes before you get to ride. How many minutes will it be before you can get on the ride? There are 96 people ahead of you in line. One ride takes 3 minutes. There is one 12-person train. Question 3: Kelsy is climbing up a mountain and will then climb down to a ledge on the side of the mountain. The ledge is 425 meters down when measured from the top of the mountain. If Kelsy has climbed a quarter of the way up the mountain and is currently at 125 meters, what will be her height above the ground when she is on the ledge? h = meters

13 Question 4: What piece of information do we want to know? There are 96 people ahead of you in line. The number of minutes before you ride. There is one 12-person train. The ride takes 3 minutes. You are going to ride a big roller coaster. Question 5: A teacher offers her students 2 prizes when they get perfect scores on their spelling quizzes. If one of her students gets a perfect score on 5 of the quizzes and already has 4 prizes, how many prizes in total does this student have? p = prizes Question 6:

14 Which of the following equations represents this problem? 12 8 = = m 96 8 = = m 4 3 = = m = = m = = m Question 7: If there are 6 egg cartons that are filled with eggs and there is an 7th egg carton that has 7 eggs, how many eggs are there in total, if each egg carton holds 12 eggs? e = eggs Question 8: There are 10 fruit trees in a yard and each tree produced 8 pounds of fruit this year. The family that owns the trees already has 150 pounds of fruit, how many pounds of fruit in total does the family have? f = pounds

15 Question 9: Which of the following correctly checks the answer? 3 8 = = = = = = = = = = 24 Question 10: A farmer had a total of 995 horses and cows. After selling some of the horses and cows, he had 510 horses and 390 cows left. How many horses and cows did he sell altogether? a = horses and cows

16 Correct Answers Lesson: Word Problems with Four Operations Lesson Topic: Represent addition word problems with variables Question 1: MC5 Question 2: MC4 Question 3: MC5 Question 4: 1) List what you know. 2) Write what you want to know. 3) Set up an equation. 4) Solve the equation. 5) Check your answer. Question 5: MC2 Question 6: MC4 Question 7: MC2 Question 8: MC4 Question 9: MC5 Question 10: MC3 Lesson Topic: Represent two-step word problems with variable equations Question 1: MC1 Question 2: MC2 Question 3: MC1 Question 4: MC3 MC4 MC5 Question 5: MC4 Question 6: MC3 Question 7: MC4 Question 8: MC1

17 Question 9: MC2 Question 10: MC3 Lesson Topic: Solve two-step word problems with variables Question 1: Time to climb and get ready = 125 Total time of the snowboard trip = m m = 135 minutes Question 2: MC3 MC4 MC5 Question 3: Height of mountain = 500 Height from ground to the ledge = h h = 75 meters Question 4: MC2 Question 5: Prizes from the 5 perfect quizzes 2 5 = 10 Total number of prizes = p p = 14 prizes Question 6: MC4 Question 7: Total number of eggs in the 6 filled egg cartons 6 12 = 72 Total number of eggs = e e = 79 eggs Question 8: Total pounds of fruit produced 10 8 = 80 Total pounds of fruit the family has = f f = 230 pounds Question 9: MC3 Question 10: Number of animals left after sale = 900 Number of animals sold = a a = 95 horses and cows.