# Four in a Row Algebraic Expression. Suggested expressions: x + y x - y -x + 2y x - y -(x + y) 2x - 3y y + 1 2

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1 Four in a Row 7 x y Algebraic Expression Suggested expressions: x + y x - y -x + 2y x - y -(x + y) 2x - 3y y Page 84 Classroom Strategies Blackline Master III - 1

2 y - xz y(x + z) -x + yz x z - y Finish Start x(y - z) X-Racing x - y x - y - z x y x + y X Y Z x + y + z x(y + z) x - yz xy + z x + yz z - xy z(x - y) -y - xz z(x + y) x - y z y(x - z) Classroom Strategies Blackline Master III - 2 Page 85

3 Finish Start Inequality Race -x<15 x > 15 x > -5 -x < 10 x < -5 x < 15 x < 5 x > 10 x < -15 -x < 10 -x< -5 x< Page 86 Classroom Strategies Blackline Master III - 3

4 Equation Dominoes x = 36 When Joe is 12 years older, he will be 36. How old is he now? x + 12 = 36 If Tom had twice as much money as he has now, he would have \$36. How much does he have now? 2x = 36 When 36 brownies are shared among all club members, each gets x12. How many club members are there? 36 = 12 x Joe is 2 years older than his brother. The sum of their ages is 12. How old is Joe s brother? Two years ago, x + (x + 2) = 12 Joe was 36 years old. How old x - 2 = 36 is he now? After Tom reads 36 pages of his x = 36 magazine, he still 12 has 12 pages to read. x - 36 = 12 How many pages are in the magazine? x + (x + 12) = 36 Joe bought 36 ride tickets. The total cost for tickets is \$9. How many ride tickets were bought at the fair? 36x = 9 When a package of candy is shared among 12 friends, each gets 36 pieces. How many pieces of candy were in the package? Pete s dog weighs 12 pounds more than Joe s dog. The dogs weigh 36 pounds together. How much does Joe s dog weigh? When an athletic team is divided into two groups, each group has 36 people in it. How many people are in the team? Classroom Strategies Blackline Master III - 4 Page 87

5 x = 36 2 Five statues are in a box that weighs one pound. The total weight is 36 pounds. How much does each statue weigh? 5x + 1 = 36 A family of 5 gets a \$4 discount on their dinner bill. The total cost is \$36. What would be the cost for each person with no discount? 5x - 4 = 36 Five envelopes each contain the same amount of money. After \$14 is removed, \$36 is left. How much was in each envelope? 5x - 14 = 36 Joe has some baseball cards, and his brother has 1 / 3 as many as Joe. Together, they have 36. How many cards does Joe have? x + 1 / 3 x = 36 Joe wants to deal a deck of 12 cards equally among the players. Each one gets six cards, how many players are there? 12 = 6 x Joe has some baseball cards, and his brother has 1/3 as many as Joe. Joe has 36 more than his brother. How many does Joe have? x - 1 / 3 x = x = 27 Joe has \$36. The amount he has is \$2 more than half the amount his brother has. How much does his brother have? Moe bought a box of cookies. He had a dozen more at home. When he divides them among six people, each gets 7. How many in a box? 1 / 2 x + 2 = 36 x + 12 = 7 6 There are 36 members at a club meeting. After some leave, there are 27 left. How many members left? Joe has \$36. After he goes to the movies twice, he has \$6 left. How much did it cost to go to the movies each time? 36-2x = 6 Joe has \$36. After he buys 12 tapes, he has \$18 left. How much does each tape cost? 36-12x = 18 Joe has 12 baseball cards. He buys four Packs and then he has a total of 36 cards. How many cards are In each pack? Page 88 Classroom Strategies Blackline Master III - 5

6 Over 40 Score Inequality Score Inequality c a 10 _ > < + b 5 Score Inequality a = 10, b = 20, c = 30 Scoring: Each a, b, or c are worth 2 points. All others are worth 1 point. Score Inequality Classroom Strategies Blackline Master III - 6 Page 89

7 Inequality Match Bill wants to buy a concert ticket to see the group Bomber. He only has \$16 which is not enough. B = cost of Bomber ticket. Mark s package weighs 1 pound, but Brett s package is heavier. B = weight of Brett s package in ounces. When the bus leaves school, it travels 16 miles to Tom s stop. Brad gets off the bus at the next stop. B = the distance from Brad s stop to the school. Bell buys a shirt for \$16. Tax is added to the total. B = amount Bell pays. Bob has a model rocket that is 16 inches tall. His model of the booster rocket is shorter. B = height of the booster model in inches Joe is 16 years old, but he has a younger brother, Biff. B = Biff s age. Carl worked 16 hours at the car wash. His friend Bud didn t have to work as long. B = number of hours Bud worked at the car wash The tallest tree in Don s yard is an oak which is 16 feet tall. There is also a balsam tree in the yard. B = height of the balsam tree in feet Mark wants to buy five magazines, but he only has \$16 which is not enough. B = price of one magazine Page 90 Classroom Strategies Blackline Master III - 7

8 Inequality Match When Tom tries to mail five identical books to his cousin Joe, he finds that the package weighs more than one pound. B = weight of one book in ounces Donna has five sections of brick border to put along her flower garden. The five sections are not enough to cover the 16 feet she needs. B = length of one section of border Earl wants to make a banner 16 feet long. If he glues five poster boards end to end, the banner still won t be long enough. B = length of one piece of poster board Bill has enough gas to drive 16 miles, but he runs out of gas before he can make five round trips from home to school. B = round trip distance from Bill s home to school In Brenda s state, the minimum driving age is 16. If Brenda were five times as old as she is now, she still would not be old enough to drive. B = Brenda s age now. A bush in Bob s yard was 5 feet tall last year. This year it is over 16 feet tall. B = amount the bush grew in the last year (in feet) Marcie has \$16. With this, she can buy four bottles of shampoo, but she doesn t have enough to buy five bottles. B = cost of one bottle of shampoo Betty is babysitting to earn money. If she works for 5 hours, she still won t have the \$16 she wants for a shirt. B = Betty s hourly wage for babysitting. Frank has \$16. He does not have enough to buy a movie ticket for \$5 plus refreshments. B = price of refreshments Classroom Strategies Blackline Master III -8 Page 91

9 Inequality Match When George packs his baseball which weighs 5 ounces and his bat, the total package weighs more than 1 pound. B = weight of the bat in ounces Jack is 5 feet tall. When he stands on a ladder, he still can t reach to a height of 16 feet. B = height of the ladder in feet. Bert has a container of soft drink. After he pours out a 5- ounce cup, he still has more than a pint left in the container. B = amount of soft drink originally in the container (in ounces) Harry lives 16 miles from the state line. He drives 5 miles to the gas station and from there to a park over the state line. B = distance from the gas station to the park In Bonnie s state, the minimum driving age is 16. If Bonnie were five years older, she still would not be old enough to drive. B = Bonnie s age now. Students are planning a field trip. After five of them change their minds about going, there are still too many to fit in a 16-passenger mini-bus. B = number of students originally planning to go Ina can buy a \$5 book plus a CD, and the total including tax is \$16. B = cost of the CD Betty has \$5. She does a babysitting job, but she still doesn t have enough to pay for a \$16 CD that she wants. B = Betty s earnings from babysitting The price of a pair of jeans is reduced by \$5. Bob has \$16, but that still is not enough to pay for the jeans. B = price of jeans before the discount Page 92 Classroom Strategies Blackline Master III - 9

10 Inequality Match In Brad s state, the minimum driving age is 16. Brad s older brother was driving over five years ago. B = Brad s brother s age Bob loaned \$5 to his brother. Now Bob doesn t have enough money to buy a model that costs \$16. B = amount of money Bob had before the loan Bill leaves his home and drives for 5 miles. He is now less than 16 miles from his cousin s house. B = distance from Bill s house to his cousin Bernie is swimming in a pool. When he dives 5 feet below the surface, he is less than 16 feet from the bottom. B = depth of the pool A class is planning to go on a field trip. When the students are separated into five equal groups, each group still has over 16 students. B = total number of students Belanna is making candy to ship to her friend. Her brother removes 5 ounces of the candy, and now there is less than a pound to ship. B = original weight of the candy The cost of a birthday present is being shared by five friends. Each one has to pay over \$16. B = cost of the birthday present Five students are helping their teacher carry some papers. When each student has an equal amount to carry, each still has over a pound. B = weight (in ounces) of all the papers. Five friends are painting a fence. Each one has to paint over 16 square feet. B = total area of the fence Classroom Strategies Blackline Master III - 10 Page 93

11 Inequality Match The average age of five friends is less than 16 years. B = sum of their ages Five students conduct a survey of all teenagers on their block. They each question the same number of people, but each questions fewer than 16 people. B = total people surveyed on the block A group of 16 students contribute the same amount to make a total that is over \$5. B = amount each student paid A package contains five equal boxes. Each box weighs less than a pound. B = weight of the package in ounces Bob pays the same amount for 16 candy bars. The total is over \$5. B = price of one candy bar A rectangle has a length of 16 inches. The area is over 5 square inches. B = width of the rectangle in inches A group of five friends go to a restaurant and share the bill equally. Each one pays less than \$16. B = total amount of the restaurant bill A turtle travels at a constant rate for 16 hours. He travels over 5 miles. B = turtle s rate of speed in miles per hour A rectangle has a length of 16 inches. The area is less than 5 square inches. B = width of the rectangle Page 94 Classroom Strategies Blackline Master III - 11

12 Inequality Match Billy pays the same amount for each of 16 phone calls. The total cost of the calls is less than \$5. B = price paid per call Sixteen copies of the same magazine are in a stack. The stack is less than 5 inches tall. B = thickness of one magazine A radio station plays 16 ads of equal length, The total time required for all the ads is less than 5 minutes. B = time for one ad B - 5 < 16 16B < 5 16B > 5 Classroom Strategies Blackline Master III - 12 Page 95

13 Inequality Match 5B > 16 B < 16 B > 16 B + 5 < 16 B + 5 > 16 5B < 16 B > 16 5 B < 16 5 B - 5 > 16 Page 96 Classroom Strategies Blackline Master III - 13

14 Pythagorean Spiral Pattern The spiral shown below is created by constructing right triangles one on the other. The smallest triangle has sides of 1 and 1. Each succeeding triangle uses the hypotenuse of the last one drawn as a leg of the new one. The second leg of each triangle always has a length of 1. The lengths of the first two triangles are shown. Find the other lengths and complete the chart. Predict the length of the hypotenuse of the 99th right triangle in the design Leg A Leg B Hypotenuse 1st Triangle nd Triangle rd Triangle 4th Triangle 5th Triangle 6th Triangle What is the hypotenuse of the 99th triangle? Classroom Strategies Blackline Master III - 14 Page 97

15 Cooperative Problem Solving with Patterns Problem A A porpoise is swimming and jumping in a motion that produces a pattern Sometimes he is above sea level and sometimes he is under the sea. The numbers show how high or deep he is as compared to sea level. Problem A At 1:00 pm, the porpoise is 9 feet above the ocean surface. At 1:02 pm, he is only 6 feet above sea level. Find the height of the porpoise at 1:10 pm. Problem A At 1:01 pm, the porpoise is 1 foot under water. But at 1:04 he is 3 feet above the water. Find the height of the porpoise at 1:10 pm. Problem A At 1:03 pm, the porpoise is 4 feet under water. And at 1:05 he is 7 feet under water. Find the height of the porpoise at 1:10pm.. Problem B John s calculator is broken. Every time he hits the enter key, the calculator does the same operation to the answer in the screen. What number was on the screen after the enter key was hit three times? Problem B The number on the screen of the calculator before it was discovered to be broken was a -5. After the enter key is hit twice, the number on the screen is -20. What number was on the screen after the enter key was hit three times? Problem B After the enter key was hit five times, the number on the screen is 160. What number was on the screen after the enter key was hit three times? Page 98 Classroom Strategies Blackline Master III - 15

16 Cooperative Problem Solving with Patterns Problem C An archaeologist found an ancient clay tablet on which students from long ago were writing a fraction pattern. The first fraction was broken off the tablet. Find the first fraction. Problem C The first fraction visible on the tablet appears To be the second fraction in the pattern. This second fraction is Find the first fraction. Problem C The denominator of the third fraction is not clear, but the numerator is visible. The third fraction looks like 9 and the fourth fraction is Find the first fraction. Problem C The fifth and sixth fractions look like This: and Find the first fraction. Problem D A hiking party wants to climb a path that winds 2700 feet up a mountain path that gets steeper and steeper. They begin at noon, and during the first hour they travel 1800 feet and have 900 feet left to go. At what hour will they be within 10 feet of the top? Problem D At 2:00 pm they have traveled a total distance of 2400 feet, but they still have 300 feet of very steep terrain to cover. At what hour will they be within 10 feet of the top? Problem D From 2:00 till 3:00 they travel another 200 feet, and there are 100 feet to go. If their progress follows this same pattern, at what hour will they be within 10 feet of the top? Problem D Hint: Make a chart with columns for time, distance traveled, and distance remaining. At what hour will they be within 10 feet of the top? Classroom Strategies Blackline Master III - 16 Page 99

17 Cooperative Problem Solving with Patterns Problem E Joe s friends have a band. They want Joe to help them make CD copies of their music to sell to fans. After doing some research on the software he would need and the price for supplies, Joe finds that making ten CDs would cost him \$80. Problem E The friends think they may want more than ten copies, so they ask Joe for some other prices. He tells them that 100 copies would cost him \$350 and 1000 copies would cost him \$3050. Problem E The friends decide to buy 50 copies from Joe. If they sell the CDs for \$8 each, how many copies must they sell to have enough to pay Joe s bill? Problem F Mrs. Avonia has a door to door cosmetics business that she started in January. She has been looking for receipts so she can check on the number of customers she had. She finds that she had four customers in January. Problem F She remembers that she had 26 customers in May; however when she finds her receipts For February, she notices that she had only six customers that month. Problem F She finally finds her receipts for March and April and finds that she had ten customers in March and 16 the month after that. Problem F Aha! cries Mrs. Avonia. I see a pattern here! How many customers should she predict for the months of June and July? Page 100 Classroom Strategies Blackline Master III - 17

18 Cooperative Problem Solving with Patterns Problem G A local baseball stadium is trying to plan for an upcoming exhibition game. Records show that when they had a crowd of 20,000 fans, they sold 16,000 hotdogs. Problem G Last year they had a crowd of 32,000, and they sold 25,600 hotdogs. The lowest turnout they ever had for this event was 15,000 and they sold 12,000 hot dogs that year. Problem G They buy hot dogs in bulk packages of 64. The buns come 48 in a pack. Problem G This year they expect a record turnout of 48,000 fans. How many packages of hot dogs and buns should they buy? Problem H The band is planning a bake sale to raise money for a trip. In years past, the parents signed up to contribute cakes and the band set up the tables and conducted the sale. Problem H The second year of the sale more parents participated. Forty signed up, and they contributed 50 cakes. The first year of the sale, 24 parents signed up and they made a total of 30 cakes to sell. Problem H In the third year, the PTA got involved. Sixty parents signed up and they baked 75 cakes for the sale. Problem H This year the entire community is involved. The number of adults signing up to bake cakes is 160. If the tables can hold 25 cakes each, how many tables should the band set up for the sale? Classroom Strategies Blackline Master III - 18 Page 101

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