Summer Calendar for 8th Grade Students taking Integrated Math I WEEK 1 Monday Suppose a provider of a local telephone service offers to charge only $15 per month plus $0.15 per call. What will the monthly bill be if 45 calls are made? Show all work (no calculator). Tuesday What equation shows how to calculate the monthly bill, y, as a function of the number of calls made, x? Wednesday The vendors at a baseball stadium are paid $20 per game and 10% of the value of the food and drinks they sell. Explain how the rule 𝑃 = 20 + 0.1𝑑 shows how the vendor pay depends on the dollar value of food sold by that vendor. Thursday Determine the game pay for a vendor who sells $350 worth of food and drinks. Show all work (no calculator). Friday How much food and drink must a vendor sell to earn a game pay of $75? Show all work (no calculator). WEEK 2 Monday On the first three tests in a grading period Hazel has scores of 85, 90 and 75. What is the lowest possible score Hazel can get on the fourth and final unit assessment in order to have a mean of at least 85 for the grading period? Define the variable and write an inequality to model and solve the problem. Show all work (no calculator). Tuesday What will be her median score be for the grading period if she gets the lowest possible score found above? Show all work (no calculator). What will her range of scores be for the grading period if she gets the lowest possible score above? Show all work (no calculator). Wednesday Find the range, mean and median of the following set of numbers: 6.72, 5.803, 3.5, 7, and 8.07 Show all work (no calculator). Thursday International Falls, Minnesota is often the coldest spot in the lower 48 states during the winter season. During one week in January, the low temperatures in Fahrenheit were: −5°, −15°, −20°, −35°, −4°, 6°, 𝑎𝑛𝑑 10° What was the mean and median low temperature for that week? Show all work (no calculator). What was the range of low temperatures for that week? Show all work (no calculator). Friday On the first five assessments of a grading period, a student has a mean of 6 on a scale of 0 to 10. Find the student’s new mean assessment score if, on the next 10-­‐point assessment, the student earned: a. A score of 10 b. A score of 6 c. A score of 4 WEEK 3 Monday Tuesday Show all work (no calculator). Graph 𝑦 = 2𝑥 − 3. Graph 𝑦 = −5 and 𝑥 = 2. What is the point of intersection? Wednesday Graph 𝑦 = − ! 𝑥 + 1. !
Thursday Write the equation of the line that passes through the points (2, 5) and (4, –3). Show all work (no calculator). Friday Find the x and y intercepts of the linear equation: 4𝑥 − 3𝑦 = −12. What is the slope of the line? WEEK 4 Monday Solve each inequality. Graph the solution. Show all work (no calculator). a. −12 + 11𝑚 ≤ 54 b. 7(𝑥 + 8) < 3(𝑥 + 12) Tuesday Andrea’s parents have rented a suite at a Charlotte Bobcats basketball game for her birthday party. The suite costs $180 to rent. In addition, they must buy $12 tickets to the game for each person. Write and solve equations or inequalities to answer the following questions. How much will it cost for 8 people to be at the party? Show all work (no calculator). Wednesday If Andrea’s parents paid $240, how many people were at the party? Show all work (no calculator). Thursday How many people can be at the party if the cost must be less than $320? Show all work (no calculator). (!!!)
Friday Solve the inequality ≥ −4. Graph the solution. Show all work (no calculator). !!!
Write each expression in a simplified form using exponents. a. 𝑥 ! 𝑥 ! 𝑦 ! 𝑦 b. 𝑥 ! 𝑦 ! 𝑥𝑦 ! c. 3𝑥 ! ! Tuesday In 1989, the supertanker Exxon Valdez spilled 9,415,000 gallons of oil into the Prince William Sound in Alaska. Daily oil consumption in the United States in 1989 was about 706,000,000 gallons. How many spills the size of the Exxon Valdez would it take to equal one day’s consumption? Solve using scientific notation. Wednesday The state of North Carolina covers about 54,000 square miles. The Indian Ocean covers about 28,000,000 square miles. Write each number in scientific notation. How many North Carolinas would it take it to cover the Indian Ocean? Solve using scientific notation. Thursday Find values for x and y that will make these equations true statements. a. 3! 4! ×3! 4 = 3! 4! x = __________ y = _________ b. 5! ! = 5!" x = __________ c. 𝑟 ! 𝑠 ! 𝑟 ! 𝑠 = 𝑟 ! 𝑠 ! x = __________ y = _________ Friday Aaron invests $500 in a certain investment portfolio, which is expected to have a growth rate of 8% per year. Make a table showing how much Aaron will have each year if he invests for 5 years. Number 0 1 2 3 4 5 of Years Dollars in Account You may use a calculator. Explain how you got your results. WEEK 5 Monday WEEK 6 Monday Groups of campers were going to an island. On the first day 10 went over and 2 came back. On the second day, 12 went over and 3 came back. If this pattern continues, how many would be on the island at the end of a week? How many would be left? Show or explain your strategy. Tuesday A bat ate 1050 dragon flies on four consecutive nights. Each night she ate 25 more than on the night before. How many did she eat each night? Show or explain your strategy. Wednesday Monday, the Produce manager, Arthur Applegate, stacked the display case with 80 heads of lettuce. By the end of the day, some of the lettuce had been sold. On Tuesday, the manager surveyed the display case and counted the number of heads that were left. He decided to add an equal number of heads. (He doubled the leftovers.) By the end of the day, he had sold the same number of heads as Monday. On Wednesday, the manager decided to triple the number of heads that he had left. He sold the same number that day, too. At the end of this day there were no heads of lettuce left. How many were sold each day? Show or explain your strategy. Thursday Friday Sam needs to rent a car for his upcoming trip. Cheap Wheels charges $20.25 per day plus $.14 a mile. Easy Rider charges $18.25 a day plus $.22 a mile. Sam plans to do a lot of driving on his 3-­‐day trip. Which company should Sam go with? Explain your choice. Does the difference in cost go up or down as mileage increases? Show or explain your strategy. Mr. and Mrs. Corkwood were going to tile their den floor. They had tiled the kitchen floor earlier in the year with ceramic tile. The kitchen was 14ft by 10 feet. The den is 20 ft. by 14 ft. The kitchen tile job cost the Corkwoods $1400 including labor. How will this help them determine the price of the den floor? WEEK 7 Monday The costs for mailing packages of certain weights at a mail delivery service are listed in the table below. Weight (lb.) Cost 0.5 $2.50 1 $5.00 2 $10.00 2.5 $12.50 Write an equation that expresses the cost c in terms of the weight w. !
Using the equation what is the cost of mailing a package that weighs 3 ! pounds. Show all work (no calculator). Tuesday A camper can have a total weight of 7,400 pounds including cargo and passengers. Without water in its water tanks, the camper cargo weighs 7,155 pounds. If water weighs 8.3 pounds per gallon, how many gallons of water can be loaded into the tanks before the camper exceeds its total weight capacity? Define the variable. Write and solve an inequality. Wednesday Stacy works at a greenhouse during the summer. She has to wrap mum plants with colored foil. There are 130 rows with 40 mums in each row. Each mum must be wrapped in one sheet of foil before it can leave the greenhouse. Colored foil comes in boxes of 250 sheets and costs $34.25 per package. What is the total cost to wrap all the mums? Show your work. Thursday Mark, Dave, Steve, and Matt had a race. Steve was faster than Mark but slower than Matt. Dave took the least time of all. Match the times with the runners. Times: 18.6 seconds; 17.5 seconds; 18.2 seconds; 17.9 seconds. Friday Umbrellas rent for $3 a day. The Jacksons will be at the shore for 2 weeks. Should they buy an umbrella for $34.95 or rent one every day? Show your work (no calculator). WEEK 8 Monday !
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Solve ! 𝑥 − 5 = ! 𝑥 + 10. Show your process (no calculator). Tuesday Solve 4𝑚 + 6 = 8𝑚 − 2. Show your process (no calculator). Wednesday Solve 2𝑥 − 3 − 3 𝑥 + 4 = 14. Show your process (no calculator). Thursday Solve −9𝑥 − 18 ≤ 54. Show your process (no calculator). !
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Friday Solve ! 𝑥 + ! 𝑥 − 12 < 52. Show your process (no calculator). WEEK 9 Sir Dwayne is in charge of dragon designs at the King's Toy Factory. He hopes that his new designs will please the king. "Your Highness," he says. "I have the plans for the toy dragons. If it pleases you, every 6th dragon shall have glowing eyes, every 4th dragon shall breathe fire, every 3rd dragon shall billow clouds of smoke through its nostrils, and every 8th dragon shall have a tail with spikes on it. I shall make 100 dragons." The king asks, "Sir Dwayne, how many dragons shall have more than one of these characteristics?" Sir Dwayne doesn't have the answer. Can you help him answer the king before he is thrown into the dungeon? Show or explain your process. Tuesday Shawn bought a car for $5400. He sold it to Rachael for 5/6 the price he paid for it. Rachael sold it to Ray for 1/5 less than she paid for it. Ray sold it to Rick for 3/4 what he paid. What did Rick pay for the car? Show or explain your process. Wednesday Jody, Amy, and Tim are building a model out of Legos. The top level is a 1 by 2 rectangle. The level directly underneath is a 2 by 3 rectangle. The level underneath is a 3 by 4 rectangle. How many Legos will they need if their building is to be 12 levels high? Make a chart to show your work. Thursday Every day when Lisa returns from school she puts her change from buying lunch into a jar on her dresser. This weekend she decided to count her savings. She found that she had 72 coins—all nickels and dimes. The total amount was $4.95. How many coins of each kind did she have? Show or explain your process. Friday Vladmir builds 3 legged stools and 4 legged tables. Last month he used 72 legs to build 3 more stools than tables. How many stools and how many tables did he build?