Math Practice Problems to Teach Strategies for Sixth Grade

6S-9f) Strategy: Guess, check and revise Answer: X=9; Y=2; Z=1

One day Ben' teacher put a very unusual math problem on the board. It looked like this: XX + YY = ZYZ (XX refers to a two digit number with the ten's digit equal to the unit's digit). His teacher asked the class to find the values for X, Y, and Z in the problem. She told the class that if a letter was used more than once. It had the same value each time it was used. What are the values for X, Y, and Z?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-9e) Strategy: Guess, check and revise Answer: 26

I'm thinking of a number. Twice the number minus 18 equals 34. What is the number?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-9d) Strategy: Guess, check and revise Answer: 10

I'm thinking of a number. Three times the number plus 23 equals 53. What is the number?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-9c) Strategy: Guess, check and revise Answer: 6

I'm thinking of a number. Multiply the number by itself and then by itself again and you will get 216. What is the number?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-9b) Strategy: Guess, check and revise Answer: Jane Jones, Emily Robinson, Sherrie Smith, & Kathy Brown

Eight children divided 30 books. Jane took 1 book, Emily 2, Sherrie 2, and Kathy 4. Bob Smith took as many as his sister. Ken Brown took twice as many as his sister, Jim Jones took 3 times as many as his sister, and Tom Robinson 4 times as many as his sister. What is the last name of each of the 4 girls?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-9a) Strategy: Guess, check and revise Answer: 16 problems were correct

At a math contest 20 problems were given. Each correct answer earned 5 points, and 2 points were deducted for each incorrect answer. Lenore answered all the problems, receiving a score of 72. How many correct answers did she have?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-8d) Strategy: Draw a picture Answer: Farmer Joe would at 20.48 a dozen compared to Farmer John at $1.20

There are 2 chicken farmers who are constantly trying to outsell each other with their eggs. Farmer John planned to sell the first egg for 10 cents, the second for 20 cents, the third for 30 cents, and so on. Farmer Joe decided to sell his first egg for 1 cent, the second for 2 cents, the third for 4 cents, the fourth for 8 cents and so on, doubling the cost of each additional egg. Which farmer will earn more money selling one dozen eggs?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-8c) Strategy: Draw a picture Answer: Ten is the greatest number of tents that could have been set up.

A group of 30 Scouts set up their tents for the campout. In each tent there were exactly the same number of scouts. Later another group of 20 scouts arrived. They did not set up any tents, but instead divided themselves into equal size groups so that they could share the tents already set up. If there were an equal number of Scouts in each tent, what was the greatest number of tents that could have been set up.  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-8b) Strategy: Draw a picture Answer: Jennifer took 15 seconds between each pair of flags. Six groups of 15 equals 90 seconds.

At the State Cross-Country Meet there is a circular track with 6 flags spaced around at an equal distance apart. At the race yesterday, the 3 fastest runners lined up at the finish line facing the first flag, and started to race all the way around the track Jennifer took 30 seconds to get to flag number 2. How long did it take her to get all the way around the track if she kept up the same pace?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-8a) Strategy: Draw a picture Answer: First: Lightning; Second: Speedy; Sid Third: Secretariat; Fourth: Citation; Fifth: Seattle Slew

Five famous horses raced yesterday at the track. Citation finished 1 length ahead of Seattle Slew. Speedy Sid finished ahead of Citation but behind Lightning. Secretariat finished 4 lengths ahead of Seattle Slew and 1 length behind Speedy Sid. What was the finish place of each horse?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-7e) Strategy: Act out the problem or use objects Answer: 7

Mr. Murray challenged his class with this puzzle. He placed 3 pieces of paper on the table. On the sheet on the far left he stacked up 3 circular disks, each one smaller than the one below it. His challenge was to move the 3 disks, one at a time, to the paper on the far right. Oh yes! He had one rule: a larger disk could never be stacked on top of a smaller disk. What is the least number of moves needed to accomplish this task?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-7d) Strategy: Act out the problem or use objects Answer: 4 boys and 3 girls

There is a family in which each boy has as many sisters as brothers. But each of the girls has twice as many brothers as sisters. How many girls and boys are in the family?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-7c) Strategy: Act out the problem or use objects Answer: They could get 20 prizes

There are 4 boys and 5 girls standing outside of the new music shop. The sign in the window offers a prize to every couple (1 boy and 1 girl) that enters the store. How many prizes can the 9 people get?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-7b) Strategy: Act out the problem or use objects Answer: The number cards would read: 2,3,1,2,1,3

There are two 1's, two 2's, and two 3's. There is one digit between the two l's, there are two digits between the two 2's, and there are three digits between the two 3's. Holding number cards, can you duplicate this sequence of numbers?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-7a) Strategy: Act out the problem or use objects Answer: 28 handshakes

All the members of an exclusive country club are very polite. Whenever they meet each other, they always shake hands, address each other by their full names, and inquire about the health of the club member, his wife, and children. At a recent meeting, 8 members of the club were present. If each member shook hands with every other member once, and only once, how many handshakes would have taken place?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-5e) Strategy: Make a table, chart, or organized list Answer: In this case, the best buy is to purchase three 5-pound boxes and one 3-pound box, a total of 18 pounds at $24.24, to get the 17 pounds he needs.

Gardener Lee wants to put fresh grass seed down on his front lawn. Grass seed is available in three-pound boxes and in five-pound boxes. A three-pound box costs $4.50, and a five-pound box costs $5.58. Gardener Lee needs 17 pounds of the grass seed. How many of each size box should he purchase to get the best buy?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-5d) Strategy: Make a table, chart, or organized list Answer: Mary - Chris: 1 - 48; 2 - 24; 3 - 16; 4 - 12; 6 - 8; 8 - 6; 12 - 4; 16 - 3; 24 - 2; 48 - 1

Mary and Chris were playing a factors game. Mary would name a factor of 48 and Chris would give the other factor. Make a table to show the different ways Mary and Chris could play the 48 game.  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-5c) Strategy: Make a table, chart, or organized list Answer: make a grid with 1-6 along the top row and 1-6 along the left side filling in all products row by row: 1,2,3,4,5,6; 2,4,6,8,10,12; 3,6,9,12,15,18; 4,8,12,16,20,24; 5,10,15,20,25,30; 6,12,18,24,30,36

Tweedle Dee and Tweedle Dum were playing a dice game. They needed to know all the possible products they could get by rolling two dice. What products are possible?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-5b) Strategy: Make a table, chart, or organized list Answer: Tables-Stools-Legs: 8-0-32; 7-1-31; 6-2-30; 5-3-29; 4-4-28; 3-5-27; 2-6-26; 1-7-25; 0-8-24

Mr. Banks works in a shop that produces 4-legged desks and 3-legged stools. Nine customers ordered 8 items each. Each order was different. How many legs are needed for each of the customers?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-5a) Strategy: Make a table, chart, or organized list Answer: BGY; BYG; GBY; GYB; YBG; YGB

Lavar has three markers- one blue, one green, and one yellow. If he arranges them in a row, show the different arrangements he could make.  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-4c) Strategy: Look for a pattern Answer: a) wagon - things that have wheels; b) shoes - words that end in s or things you wear; c) rooster - words that end in r; d) 1700 - add 500; e) 26 - five times the term number plus one

For each of the following, tell in your own words what the pattern rule is. Then write the next term in the sequence. a) Bicycle, car, airplane, roller-skates, __ Pattern rule: b) shirts, ties, socks, jackets, __ Pattern rule: c) river, paper, mother, strainer, __ Pattern rule: d) 200, 700, 1200, __ Pattern rule: e)6,11,16,21, __ Pattern rule:  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-4b) Strategy: Look for a pattern

In how many segments do "n" points divide a line segment?  Explain in detail how you found your answer using words, numbers, and/or pictures.

Answer

6S-4a) Strategy: Look for a pattern Answer: 10 line segments; 15 line segments; 5 line segments

Two points can be connected with 1 line segment. Three points (put them around a circle) can be connected with 3 line segments. Four points can be connected with 6 line segments. How many segments connect five points. Predict, then check, the number of line segments that will connect six points. Predict, then check. the number of line segments that will connect ten points.  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-3e) Strategy: Use logical reasoning Answer: From first to last: #4, #5, #7, #1, #2 and #3, and #6

The main event at the auto races had seven entries. In what order did the cars finish? a) The driver of car #1 was the only one wearing green. b) Car #6 blew a tire and finished last. c) Car #2 and car #3 crossed the finish line together. d) Car #4 beat car #7 by two lengths. e) Only one car finished ahead of car #5. f) The winning car had an even number. g) The driver of car #2 saw green on the driver of the car ahead of him. h) Car #7 finished two lengths ahead of car #1.  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-3d) Strategy: Use logical reasoning Answer: Your busiest day is Friday

Today is going to be your busiest day! You have to meet your friend Sue for lunch at the neighborhood deli, get to the Art Museum, and go to the doctor. In addition, you promised to visit your sick uncle. The deli is closed on Monday, and the art museum is open only on Mondays, Wednesdays, and Fridays. Your doctor has office hours on Thursday, Friday, and Saturday. Your sick uncle can have visitors only on Friday and Saturday. What day is your busiest day?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-3c) Strategy: Use logical reasoning Answer: Jeannie is the Chemist, Wendy is the Announcer, and Sara is the Doctor

Wendy, Jeannie, and Sara live next to each other. They work as a chemist, a radio announcer, and a doctor. Find each woman's occupation from these clues. a) Jeannie lives in the middle apartment. b) When Sara goes away, her cat is fed by the radio announcer. d) The chemist taps on Wendy's wall when her stereo is too loud.  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-3b) Strategy: Use logical reasoning Answer: Keith is the dancer, William the singer, Bruce the writer, and Dave the artist

Keith, William, Bruce, and Dave all practice fine arts. One of the men is an artist, one is a singer, one is a writer, and the other a dancer. Find the interest of each man using the clues. a) Keith and Bruce listened while the singer made his debut. b) Both William and the writer have had their portraits done by the artist. c) The writer, whose biography of Dave is a best-seller, is planning a biography of Keith. d) Keith and Bruce do not know each other.  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-3a) Strategy: Use logical reasoning Answer: Debbie own the parakeet or the goldfish(b); Debbie own the parakeet (c); Marty does not own the cat (b); Marty owns the dog (b) and Debbie own the parakeet (c); Debbie owns the parakeet, Marty own the dog, Leo own the goldfish, and Linda owns the cat

Debbie, Marty, Leo, and Linda own four pets: a dog, a cat, a parakeet, and a goldfish. 1) Debbie's pet does not have four legs. 2) Leo owns the goldfish. 3) Marty went to the pet show with the cat's owner. Select the best answer: What conclusion(s) can you draw from statement 1? Þ (a) Debbie owns the parakeet or the dog. b) Debbie owns the parakeet or the goldfish. (c) Debbie owns the goldfish. What conclusion(s) can you draw from statements 1 and 2? Þ (a) Debbie owns the goldfish. (b) Debbie and Marty came to the pet show in the same car. (c) Debbie owns the parakeet

What conclusion(s) can you draw from statements l and 3? Þ (a) Leo and Linda are brother and sister. (b) Marty does not own the cat (c) Debbie owns the parakeet     What conclusions call you draw from statements 1, 2, and 3? Þ (a) Linda owns the goldfish. (b) Marty owns the dog. (c) Debbie owns the parakeet (d) Debbie owns the cat Tell who owns each pet.  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-2e) Strategy: Work backward Answer: He saw 39 sea animals altogether

Claude kept track of what he saw at Point Defiance Zoo. He saw twice as many sharks as dolphins. The number of whales was 6 less than the number of sharks. There were 5 times as many sea lions as there were whales. He saw 20 sea lions. How many did he see altogether?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-2d) Strategy: Work backward Answer: There are 24 pupils in the class

Half the students in Mrs. Feryn's class are boys. Half the boys have blue eyes. Half the blue-eyed boys have blond hair. There are 3 boys with blue eyes and blond hair in Mrs. Feryn's class. How many students are in that class?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-2c) Strategy: Work backward 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 $I,600. How much was the first question worth?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-2b) Strategy: Work backward Answer: 36

Mr. Carroll sells orchid plants. One day he found that 8 of his plants had died. So he bought the same number of plants as were still living. He then divided all the plants into equal packs and sold them to 7 customers. Each customer bought 4 orchid plants. How many had he started with?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-2a) Strategy: Work backward Answer: 16

Jesse was out playing golf last Thursday. On the first six holes, he lost 4 golf balls. On the next six holes he lost one half of the number of golf balls he had then. On the last six holes, he only lost 2 more golf balls. He finished with 4 golf balls. How many did he start with?  Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-1b) Strategy: Simplify Answer: 36

The nine directors of the Whacky Widget Corporation always open their annual board meetings with a special ceremony in which each director shakes hands with each of the other directors.  How many handshakes take place?   Explain in detail how you found your answer using words, numbers, and/or pictures.

6S-1a) Strategy: Simplify Answer: 108

How many palindromes are there between 0 and 1000?   Explain in detail how you found your answer using words, numbers, and/or pictures.