Grade 7 Practice Problems: Algebra
Examples from Standards Revision and GLEs
7A-30) Answer: 20th place
The Tripoli Triathalon has ended. The contestants, who had trained long for this event, all came hoping to win. But only the best remained in the competition to the end. The judges noticed something very interesting as the contestants crossed the finish line. There was one first-place winner, two second-place winners, and three third-place winners. If that pattern continued, in what place was the 200th person who crossed the finish line? Explain in detail how you found your answer using words, number, and/or pictures.
7A-29) Answer: 3,680
One day an eagle and a hummingbird happened to settle not far from each other on the same tree branch. The eagle had been soaring around on the air currents, and the hummingbird had been exploring new territory for sweet nectars. The birds struck up a conversation. The hummingbird said, "You have big, powerful wings that carry you very high, and they beat so seldom. I admire the grace and ease of your flight." The eagle responded, "That is true. It does not take many beats for me to travel. I have large wings, and I do enjoy soaring. But you possess an ability that I do not have. You are able to fly in reverse, even though your wings must beat many times. How many times per minute do your wings beat?" The hummingbird replied, "You are wise, so I will give you the information to find the answer. Two-fifths the number of beats, plus 368, equals one-half the number of beats my wings make in a minute." The wise eagle thought for a few moments before saying the number. What number did the eagle tell the hummingbird? Explain in detail how you found your answer using words, number, and/or pictures.
7A-28) Answer: 6 jorgs
The Intergalactic Inventors Convention is meeting next week. Representatives from Mars, Jupiter, Saturn, and Venus will bring their newest inventions to sell. There is one small problem: each planet has its own money system and the price for the inventions will be in the currency of the inventor's planet. If only there were some way to figure out how many Jupiter jorgs equaled what number of Saturn skeeps! Luckily, Mr. Orz, the convention organizer, has developed the following chart: 5 Mars pims = 6 Jupiter jorgs; 2 Venus firps = 7 Saturn skeeps; 8 Venus firps = 4 Mars pims What number of Jupiter jorgs would be equivalent to the fewest Saturn skeeps? Explain in detail how you found your answer using words, number, and/or pictures.
7A-27) Answer: Jasmine: 1st week - 11; 2nd week - 27; 3rd week - 13; 4th week - 45; total - 96. Jasper: 1st week - 22; 2nd week - 9; 3rd week - 26; 4th week - 9; total - 66
Jasmine and Jasper share a paper route. Their route manager is having a new subscription contest. The carrier who gets the most new subscriptions will win a trip to Disneyland, so Jasper and Jasmine have been competing to see who can get the most. The contest lasts four weeks. During the first week, Jasmine got half as many new subscriptions as Jasper, but during the second week she got three times as many as he did. During the third week Jasmine got half as many subscriptions as Jasper did during the same week. This is the last week of the contest, and Jasmine has signed up five times as many new subscriptions as her brother has this week. In total, Jasmine has 30 more than Jasper has, and together they have 162 new subscriptions. How many new subscriptions did each of them get each week of the contest? Explain in detail how you found your answer using words, number, and/or pictures.
7A-26) Answer: 7 minutes bus = 16 minutes bike
Four friends are traveling by different forms of transportation. They are trying to compare their travel times, so that they can get together during their vacation. Elena is traveling by horse, Carlotta is traveling by bus, Gina is traveling by train, and Joan is traveling by bicycle. So far the girls have figured out that 20 minutes on horseback is equal to 14 minutes by bus, 12 minutes by train is equal to 32 minutes by bicycle, and 18 minutes by train is equal to 30 minutes on horseback. What is the shortest amount of time that a bus and a bicycle would take to travel the same distance? Explain in detail how you found your answer using words, number, and/or pictures.
7A-25) Answer: Sol - 6 days; Sal - 9 days; Sherry - 48 days; Sondra - 30 days; Sara - 15 days; Sigmund - 36 days
"My goodness, what a lovely family!" exclaimed Bonnie Banana Slug. She was admiring a family portrait in the house of her new neighbor, Susanna Snail. "Yes; I'm very proud of my little ones," replied Mrs. Snail, beaming. "How old are they?" asked Bonnie. "Let's see," sighed Mrs. Snail. "Sara is half as old as Sondra. Sol is 3 days younger than Sal and one sixth as old as Sigmund. Sherry is 12 days older than Sigmund and twice as old as the combined ages of Sal and Sara. And the total of the children's ages is twice my age." Bonnie scolded, "That doesn't tell me very much. How old are YOU?" Mrs. Snail whispered, "72 days." Then she quickly changed the subject by offering her new neighbor a look at the garden. How many days old is each Snail child? Explain in detail how you found your answer using words, number, and/or pictures.
7A-24) Answer: only 1, #120
If you go to the airport early in November and look very closely, you can see hundreds of turkeys cleverly disguised as tourists. They are fleeing the country, to avoid becoming someone's Thanksgiving meal. Most of them head for the islands, until the holidays are over. An airline ticket agent, familiar with this annual event, kept track last year of the disguises used by the clever turkeys. The agent noticed every eighth turkey wearing sunglasses, every sixth one with a blond wig, every twelfth in a Hawaiian shirt, every fifth carrying a camera, and every third was hiding behind a copy of Gobble. How many turkeys, out of the first 200 that the agent noticed, wore sunglasses, a blonde wig, a flowered shirt, carried a camera, and were reading Gobble? Explain in detail how you found your answer using words, number, and/or pictures
7A-23) Answer: 14 rainbows = 15 birds
Maxine, Patti, and Laverne belong to a sticker-trading club, which meets once a month. They collect stickers during the week, and then at the meeting they trade stickers with each other to try to complete their collections. They have agreed that they may trade 16 insect stickers for 5 bird stickers, 2 flower stickers for 1 rainbow sticker, or 7 flower stickers for 12 insect stickers. Maxine wants to trade some of her 20 rainbow stickers for a fair number of Patti's bird stickers. How can they make a fair trade? Explain in detail how you found your answer using words, number, and/or pictures.
7A-22) Answer: 12
Carl's hands trembled as he stood in front of the safe and unfolded the crumpled piece of paper holding the combination that would open the safe. "Rats!" he moaned. The combination was written in the form of a riddle. The last number was described in the following way: Find 2/3 of the final number, add 16, and this number will be equal to two times the mystery number. What was the final number of the combination? Explain in detail how you found your answer using words, number, and/or pictures.
7A-21) Answer: 2628
There is, in some deserts of the world, a cactus that many people believe does not exist at all. Others, who believe it exists, have given it a name: the Night- Blooming, or Starlight, Cactus. It blooms only by the clear, soft light of the stars, and only on cloudless nights. It produces small, white, star-shaped blossoms in five-minute intervals: one blossom in the first five minutes of exposure to starlight, two blossoms in the next five minutes, three blossoms in the third five minutes, and so on until sunrise, when all the blossoms evaporate in the light of the sun. If you had been lucky enough to watch this cactus throughout 6 hours of starlight one evening last summer, how many blossoms would you have seen on the Starlight Cactus? Explain in detail how you found your answer using words, number, and/or pictures.
7A-20) Answer: 20 bikes (40 wheels) and 30 trikes (90 wheels)
A bicycle dealer just put together a shipment of two-wheel bicycles and three-wheel tricycles. He used 50 seats and 130 wheels. How many bikes and how many trikes did he put together? Explain in detail how you found your answer using words, number, and/or pictures.
7A-19) Answer: 64 papers
Brad has agreed to take over his brother's paper route while his brother is out of town. Brad's mother drives while Brad throws the papers. Out of a total route of 320 papers, Brad missed four times the number of front door areas as he hit. How many papers landed at the front door? Explain in detail how you found your answer using words, number, and/or pictures.
7A-18) Answer: $5.25
Carol and Monica are spending the day at the mall. They began with $20 between them. Monica started out with $5 more than Carol, but spent twice as much as Carol. If, at the end of the day, Monica has $2 left, how much did Carol spend? Explain in detail how you found your answer using words, number, and/or pictures.
7A-17) Answer: six at 30 cents; four at 60 cents
Darlene bought some 30 cent and some 60 cent candy bars. Altogether she bought 10 candy bars and paid a total of $4.20. How many candy bars at each price did she buy? Explain in detail how you found your answer using words, number, and/or pictures.
7A-16) Answer: Gunnar-5 cookies; I have-7 cookies
If Gunnar gives me a cookie, I will have twice as many as he. If I give Gunnar a cookie, we will have the same number of cookies. How many cookies do I have? How many cookies does Gunnar have? Explain in detail how you found your answer using words, number, and/or pictures.
7A-15) The perimeter of a rectangle is 72 cm. The length is twice as long as the width. Find the length and width. Explain in detail how you found your answer using words, number, and/or pictures.
7A-14) Answer: $6.30
Jack and Valerie went out for the evening. Jack spent $25.80 and Valerie spent $38.40. How much money should Jack give Valerie for them to have shared the expenses equally? Explain in detail how you found your answer using words, number, and/or pictures.
7A-13) Answer: 33
Janice has a favorite number. If you multiply it by 3, add 1 and divide by 20, you get 5. What is Janice's favorite number? Explain in detail how you found your answer using words, number, and/or pictures.
7A-12) Answer: 73 cards
Michelle has 72 baseball cards. She gave 2-for-1 in five trades, and received 3-for-1 in three trades. How many cards does she now have? Explain in detail how you found your answer using words, number, and/or pictures.
7A-11) Answer: 4 months
Mr. Davis wants to encourage his son Jimmy to save money. Each time Jimmy puts $3 into a savings account (once a month), Mr. Davis doubles the amount of money in the account. Jimmy now has exactly $90 in the account. How many months ago did he start? Explain in detail how you found your answer using words, number, and/or pictures.
7A-10) Answer: 12 bracelets; 6 rings
Nancy sells rings and bracelets at the local crafts fair. She receives $6 for a bracelet and $4 for a ring. She started the day with the same number of bracelets as rings, and, at the end of the day, she found that she had twice as many rings left as bracelets. She had taken in $96 altogether. How many of each did she sell? Explain in detail how you found your answer using words, number, and/or pictures.
7A-9) Answer: $25
On the quiz show "What Do You Know?" each question is worth four times as much as the previous question. The fourth question is worth $1,600. How much was the first question worth? Explain in detail how you found your answer using words, number, and/or pictures.
7A-8) Answer: Rob-10; Archie-25; Lionel-20
Rob, Archie, and Lionel exercise every morning. Rob exercises 15 minutes less than Archie, and Lionel exercises twice as long as Rob. Lionel exercises for 20 minutes. How long does each person exercise? Explain in detail how you found your answer using words, number, and/or pictures.
7A-7) Answer: seventh day
The new movie, Return to Monkey Island, opened on Monday, March 1st. On the first day, 50 people attended the show. On the second day, there were 78 people in attendance. On the third day, 106 people were there. If the pattern continues, what is the first day on which there will be at least 200 people in the audience? Explain in detail how you found your answer using words, number, and/or pictures.
7A-6) Answer: A-120; B-150
There are 270 students in two classes, A and B. Thirty students moved to class B from class A, and then there were twice as many students in class A as in class B. Find the original number of students in each class. Explain in detail how you found your answer using words, number, and/or pictures.
7A-5) Answer: 18 years old
Today Connie is three times as old as Grace. Six years from now, Connie will be twice as old as Grace. How old is Connie today? Explain in detail how you found your answer using words, number, and/or pictures.
7A-4) Answer: 520
Wal-mart is having a contest. They filled a large jar with peanuts and whoever guesses closest to the number of peanuts in the jar wins a $50 gift certificate at Wal-mart. Carolyn made a guess of 655 peanuts, which was 135 off. Carl guessed 480 peanuts, which was only 40 off. How many peanuts are in the jar? Explain in detail how you found your answer using words, number, and/or pictures.
7A-13) Jane went to the store and bought a bag of potato chips. After eating 6 chips, she gave half of the remainder to her brother, Phil who gave 7 to his dog and ate the rest. Jane ate 5 more chips and gave half of the remainder to her sister, Mary. Jane ate 10 more chips and emptied the bag by giving 2 to her Mom, who is on a diet. How many chips were in the bag originally and who ate the most chips? Explain in detail how you found your answer using words, number, and/or pictures.
7A-2) Limericks contain 5 lines and sonnets contain 14 lines. Linda memorized sonnets and limericks with a total of 112 lines. How many sonnets and how many limericks did Linda memorize? Explain in detail how you found your answer using words, number, and/or pictures.
7A-1) Duke and Donna each have 10 coins. All coins are either dimes or quarters. Duke has 5 quarters. Donna has 60 cents more than Duke. How many quarters does Donna have? Explain in detail how you found your answer using words, number, and/or pictures.
Expectations & Examples of Algebra from the 2008 Math Standards Revision (draft) - Grade 7
Solve two-step linear equations and explain the solution process using models, pictures, or symbols. Write an equation that corresponds to a given problem situation, and describe a problem situation that corresponds to a given equation. Example:
Solve multi-step contextual problems involving rational numbers and justify the solution. Solve problems involving proportional relationships and justify the solution using words, numbers, models, or symbols. Problems could include those that involve rate, percent increase or decrease, discount, markup, profit, interest, tax, or the conversion of money or measurement. Solve problems involving similar figures. Read and create drawings made to scale, construct scale models, and solve problems related to scale.
Create similar figures on a coordinate plane by sketching the image of a figure dilated around a center of dilation at the origin. Describe the impact that a change in scale factor has on the length, area, surface area, and volume of a geometric figure. Example:
Represent proportional relationships using graphs, tables, or equations, and translate among representations. Example:
Identify the rate of change in a proportional relationship and relate it to the slope of the associated line. Determine whether a relationship is proportional or non-proportional and justify why. Example:
— Art noticed that, on average, a person’s maximum heart rate should be 200 beats per minute minus the person’s age. Is the relationship between the maximum heart rate and age proportional or nonproportional? Justify your answer. — Is the relationship described by the rule y = 7 – 3x a proportional relationship? Justify your answer. — Does this graph appear to represent a proportional relationship? Why or why not?
— Does the table below appear to represent a proportional relationship? Why or why not?
Select, convert (within the same system), and use appropriate units of measurement. Examples:
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Examples of Algebraic Sense from the 2006 GLEs – Grade 7
Select a linear relationship that has the same pattern as another linear relationship. Use technology to generate graphic representations of linear relationships. Select, extend, or represent patterns and sequences using tables, graphs, or expressions. Use technology to generate graphic representations of linear and non linear relationships. Describe the relationship between a term in a sequence and its position in the sequence. Identify patterns that are linear relations and provides missing terms in the beginning, middle, and/or end of the pattern. Write a rule to represent a pattern with combinations of two arithmetic operations in the rule. Use an equation or graph to describe a linear relationship. Use technology to determine the rule for a linear pattern or sequence. Create a representation of a linear relationship given a rule and explains what makes it a linear relationship. Express relationships between quantities including integers, and non negative decimals and fractions using =, ≠, <, >, ≤, and ≥. Describe a situation represented by an equation or inequality involving integers and/or non-negative decimals and fractions. Write a simple equation or inequality using rational numbers and integers to represent a given situation. Write an expression, equation, or inequality using variables to represent a given situation. Describe a situation that corresponds to a given expression, equation, or inequality. Describe a situation involving a linear relationship that matches a given graph. Translate among different representations of linear equations, using symbols, graphs, tables, diagrams, or written descriptions. Explain the meaning of a variable in a formula, expression, equation, or inequality. Substitute non negative rational values for variables to evaluate expressions and formulas. Evaluate expressions and formulas using order of operations. Write an expression with a variable that represents a given situation and determine the value of the expression given a value for the variable. Simplify expressions using order of operations and explain the procedure. Solve single variable one step or two step equations and checks the solution. Write and solve a single variable one or two step equation for a given situation. Explain or show the meaning of the solution to an equation. |