1

OO b s e r v eb s e r v e ,, T T a k ea k e N N o t eo t e , a n d W, a n d W o n d e ro n d e r ?? Name//Date EXAMPLE: Pablo, Marcia, and LeRon went shopping. Each person bought the same number of CDs. Pablo also bought three books. LeRon bought some shirts, and he had twice as many shirts as CDs. Marcia didnʼt get anything else. If Marcia had 2 CDs, who bought the most things? a. What is the problem about? b. Who are the people in the problem? c. What two things did LeRon buy? d. How many shirts did Pablo buy? e. Write a question of your own: PRACTICE: 1. Pamela is training on her schoolʼs track team to run the marathon. On the first day, she will run one lap. On the second day, she will run four laps. On the third day, she will run seven laps. On the fourth day, she will run ten laps. Pamela stops training on the day after she runs at least 40 laps? a. What is the problem about? b. How many laps will Pamela run on the second day? c. What is the least number of laps she must run before she stops? d. On the third day, how many laps will Pamela add to her training? e. Write a question of your own: Answer to your question:

2

2. Allison, Tamika, Juan, and Erik each had an oak tree in their front yard. Allisonʼs tree was twice as tall as Tamikaʼs tree. Tamikaʼs tree was six feet shorter than Juanʼs tree. Juanʼs tree was three feet taller than Erikʼs tree. Erikʼs tree was 23 feet tall. How tall was Allison's tree? a. What is the problem about? b. How many oak trees did each person have? c. How tall was Erikʼs tree? d. Was Allisonʼs tree taller or shorter than Tamikaʼs tree? e. Write a question of your own: Answer to your question: 3. Calvin must choose three colors of paint for his art project. He can choose from the following colors: blue, pink, white, green, and black. Assuming that Calvin picks three different colors, how many ways can he choose the paint for his paint project? a. What is the problem about? b. What are the colors Calvin can choose from? c. How many colors must Calvin choose? d. List one way that Calvin could choose his colors. e. Write a question of your own: Answer to your question:

3

4. Aunt Cleo has four nephews, Arnold, Roscoe, Daniel, and Sam. Whenever she forgets her glasses, she cannot recognize their faces and she must remember what each boy wears on his head. Neither Arnold nor Roscoe wears a baseball cap. Daniel always wears headphones. Arnold hates ski caps and would never wear one. Samʼs younger brother wears a helmet all of the time. What does each boy wear on his head? a. What is the problem about? b. What are the four things the nephews wear on their heads? c. Which thing does Daniel wear? d. Is Daniel Samʼs younger brother? e. Write a question of your own: Answer to your question: 5. A beaver collected sticks for his dam. During the seven days it took him to build the dam, he collected 154 sticks. Each day he collected 5 sticks more than the day before. How many sticks did the beaver find on the first day? a. What is the problem about? b. How long did it take to build the dam? c. How many sticks did the beaver find all together? d. If the beaver found 4 sticks on the first day, how many did he find on the second day? e. Write a question of your own: Answer to your question:

4

S e a r c h f o r N e e d e d I n f o r m a t i o nS e a r c h f o r N e e d e d I n f o r m a t i o n Name//Date Most of the problems below were not written very well. Some of them give unnecessary information, and some leave out important information. In each problem, cross out any unnecessary information. If the problem is missing information, write what information was left out. If the problem has just the right amount of information needed to solve it, write “OKAY” and solve the problem. EXAMPLES: A. Tom has eleven cats. Five of them had three kittens. Four of them didnʼt have any. How many kittens did Tomʼs cats have all together? B. Shannon has five dogs. Three of them are Dalmatians. Each dog had four puppies. How many puppies did Shannonʼs dogs have all together? C. Carl has six chickens. Three of them had five chicks. The other three didnʼt have any. How many chicks did Carl's chickens have all together? PRACTICE: 1. Danielle walks her neighborsʼ dogs every day. Each neighbor has three dogs. How many dogs must Danielle walk each day? 2. Carl needs to hire four stunt men for his movie. Three of them will work for two hours. The other will work for five hours. Carl must pay $50 per hour to each stunt man. How much money will Carl have to pay all together? 3. Sheila wanted to tell her friends about her new boyfriend. The only telephone nearby was a pay phone. Sheila had 2 quarters, 7 dimes, 4 nickels, and 12 pennies. How many friends can she call?

5

4. Darnell is going to Aliciaʼs birthday party. He wants to buy her several presents. A box of chocolates costs $3.25. Alicia likes long stemmed roses. A long stemmed rose costs $2.00. A stuffed teddy bear costs $5.16. Darnell gets his allowance every Thursday. He has $10.00 that he can spend on Alicia. How many presents can he buy for her? 5. Every hour the gas in Mr. McVickerʼs car leaks 1/4 gallon of gas. At 7:00 p.m. Mr. McVicker noticed that the tank had 6 gallons in it. If nobody uses the car, at what time will the gas tank be empty? 6. Secret agent B7 has three different hats, four different wrist radios, and several cars. Each time she goes out on an assignment she uses one hat, one wrist radio, and one car. If she never uses any hat, wrist radio, or car twice in one month, how many assignments can she go on each month? 7. The rock group Meltdown wants to make a video of their new single, “Let it Breathe”. They need 20 back-up dancers and a chorus with 30 singers. Each back-up dancer needs a special outfit that will cost $30 each. The chorus singers will each provide their own outfit free of charge. What will it cost to outfit the back-up dancers? 8. Pizzazz Pizza sells pizza at $1.75 a slice. A large pizza has twelve slices. How much money does it take to buy an entire large pizza? 9. Club Live is going to show the movie, “Bring ʻEm Back Baby”. The total running time of the movie is 131 minutes. There are only 120 minutes in which to show the movie, and the 120 minutes must also include 10 commercial breaks. How many minutes must be cut from the original movie so that it will fit into the time slot?

6

T r a n s l a t i n g E n g l i s h t o M a t hT r a n s l a t i n g E n g l i s h t o M a t h Name//Date PRACTICE: This year all the kids in Gooberville got lots of candy when they went out trick-or-treating. For each problem, list any needed information, write an equation, and solve to answer each question. 1. Tom got seven more Snicker bars than Nick. Nick got eight Snicker bars. How many Snicker bars did Tom get? 2. April got twenty Heath bars. Eliza got six fewer Heath bars than April. How many Heath bars did Eliza get? 3. Derek got twice as many Nestle Crunch bars as Kelly. Derek got sixteen Nestle Crunch bars. How many Nestle Crunch bars did Derek get? 4. The number of Deannaʼs jaw breakers plus the number of Carlʼs jaw breakers was twenty. Deanna got nine jaw breakers. How many did Carl get? 5. The number of Hershey bars that Dave got minus the number that Tina got was ten. Dave got thirty Hershey bars. How many did Tina get? 6. Rhea got half as many gumdrops as Penny. Penny got twenty gumdrops. How many did Rhea get? 7. The number of Twix that George got was equal to the number of Twix that Nina got. George got twenty-one Twix. How many did Nina get? 8. The number of Baby Ruths that Roy got was nine less than the number of Baby Ruths that Winona got. Winona got eleven Baby Ruths. How many did Roy get? 9. Sherman got three times as many taffy sticks as Mika. Sherman got twenty-four taffy sticks. How many did Mika get? 10. The number of popcorn balls that Justin got times the number of popcorn balls Frank got was forty-two. Justin got seven popcorn balls. How many did Frank get?

7

11. The number of boxes of Goobers that Helen got minus the number of boxes of Goobers that Raquel got was six. Raquel got seven boxes of Goobers. How many did Helen get? 12. Larry got half as many candy apples as Juan. Larry got six candy apples. How many did Juan get? 13. Ray got eight more lollipops than Jeff. Ray got ten lollipops. How many did Jeff get? 14. Connie got twice as many licorice sticks as Chelsea. Chelsea got twelve licorice sticks. How many licorice sticks did Connie get? 15. Shane got thirty Milky Way bars. Shane got five fewer Milky Way bars than Terrance. How many Milky Way bars did Terrance get?

8

P r o v e I t ! P r o v e I t ! S h o w y o u r w o r kS h o w y o u r w o r k Name//Date “Showing your work” means including arithmetic, pictures, or words that explain the methods and reasoning you used to arrive at an answer. For each problem below, identify your answer and document how it was solved. Donʼt forget to circle your answer! EXAMPLE: Jeremy was given a case of cookies to sell. There were 20 boxes of cookies in the case. He sold 8 of them on Monday, 6 on Tuesday, and 2 on Wednesday. How many boxes did he have left to sell? 1. A. 4 Not good! B. 20-16 = 4 Close, but not good C. 20 Good! D. He sold 16 all together (8 on - 8 Monday, 6 on Tuesday, 2 on 12 Wednesday). So He had 4 - 6 left (4 and 16 is the original 20). 6 - 2 Good! 4 PRACTICE: 1. The PR Protein Bar Company has decided to start a new promotion. Anybody who turns in four wrappers from PR Protein Bars can get a free PR Protein Bar. Payton has enough money to buy sixteen Berry PR Protein Bars. How many free PR Protein Bars can he get?

9

2. Years ago Chris set the worlds record for hitting the tennis ball against a wall. She hit the ball against the wall 60 times in 59.8 seconds, with the clock starting when the ball first hit the wall. Billie Jean was determined to break this record. She was timed the same way that Chris was, and in her effort, was able to hit the wall 60 times at a rate of 1 hit per second. Did Billie Jean break the record, or is Chris still the champion? 3. A. Slippery Snail has fallen down a well ten feet deep. Poor thing is anxious to get out of the well as quickly as possible. Every day, he is able to crawl three feet up the wall of the well. But during the evening, while sleeping, he slides down two feet. At this rate, how many days will the Slippery Snail be trapped in the well? 4. Gervis just heard the gossip about the latest scandal. He wants to make sure his fifteen friends learn the gossip as quickly as possible. All the gossiping must take place by telephone, and every telephone conversation lasts 1 hour. What is the shortest amount of time for all of his friends to learn about the scandal? 5. A farmer needs to get a bucket of corn, a prize hen, and a fox to the county fair. In order to get to the fair, he has to cross a river. The boat on the river can support only his weight and the weight of one other object (corn, hen, or fox). He cannot leave the hen and the corn alone because the hen will eat the corn. He cannot leave the fox alone with the hen because the fox will eat the hen. How can the farmer get himself,the corn, the hen, and the fox across the river? 6. An old poem reads: As I was going to Saint Ives, I met a man with seven wives. Each wife had seven kids. Each kid had seven cats. Each cat had seven kittens. Kittens, cats, kids, wives, how many were going to Saint Ives? Assuming that all the wives, kids, cats, and kittens were with the man, what is the answer to the poetʼs question?

10

F i n d i n g , DF i n d i n g , D e f i n i n g a n d U s i n g P a t t e r n se f i n i n g a n d U s i n g P a t t e r n s Name//Date List the next term and define the pattern. Discuss the examples below together, then try to work the rest of the problems on your own. Be sure to define each pattern. EXAMPLES: A. From each sequence below, what is the next thing going to be? a. 2, 4, 8, 16, 32, ? b. 3, 7, 11, 15, 19, ? c. 1, 1, 2, 3, 5, 8, 13, 21, ? d. A, D, G, J, M, ? e. J, F, M, A, M, J, J, A, ? f. , , , , ?

g. , , , , ? h. 81, 27, 9, 3, 1, ? B. When Jessica joined the circus, she could juggle four balls. At the end of the first week, she could juggle five balls. After the second week, she could juggle seven balls. After the third week, she could juggle ten balls. If Jessica continues to improve at the same rate, which week will she be able to juggle 82 balls? C. Marco is a water polo player who swims laps every day to stay in shape. On Monday, he swam 5 laps. On Tuesday, he swam 11 laps. On Wednesday he swam 8 laps. On Thursday, he swam 14 laps. On Friday, 11 laps. How many laps will he swim on Saturday?

11

PRACTICE 1. The ancient Greeks studied oblong numbers that were made up by arranging pebbles into rectangles. For every oblong number, one side had one more row in it than the other. The first oblong number is 2 (a 1 by 2 rectangle): The second oblong number is 6 (a rectangle that is 2 by 3): The third oblong number is 12 (a rectangle that is 3 by 4): What is the greatest oblong number that is less than or equal to 100? 2. The Protech Computer Company sold 1 computer in January, 3 in February, 7 in March, and 15 in April. If sales continue to increase at this rate, how many computers will they sell during the first twelve months? 3. Aaron and Ishmael both delivered pizzas. They made a bet that each of them would deliver 100 pizzas in one week before the other. During the first week, Aaron delivered 3 pizzas. The second week he delivered 6. The third week he delivered 12. And the fourth week he delivered 24. Ishmael, on the other hand, delivered 52 pizzas the first week. During the second week he delivered 59. The third week he delivered 66, and his fourth week, 73. If they both continue to increase at the same rate, who will win the bet? 4. At an archeological excavation, Professor Peach discovered sketches of the headdresses worn by Egyptian pharaohs. Natkeem the Firstʼs headdress looked like this: Natkeem the Secondʼs headdress looked like this: Natkeem the Thirdʼs headdress looked like this: If the head dresses expand in this pattern, what will Natkeem the Sixthʼs headdress look like?

12

5. When Helen decided to become a poet, she decided to keep all of her poems in a special notebook. After the first week she had three poems in the notebook. After the second week she had four. After the third week she had six. After the fourth week she had nine. If Helenʼs book only has room for 100 poems, during which week will she run out of room? 6. The rock group “Flee•Fly•Flow” may soon have to end their career as musicians. Their first album sold 128 thousand albums. Their second sold 64 thousand. Their third sold 32 thousand, and their fourth only sold 16 thousand. If their popularity continues to decline at this rate, how many copies of their ninth album will sell?

13

L o g i c a n d D e d u c t i v e R e a s o n i n gL o g i c a n d D e d u c t i v e R e a s o n i n g Name//Date EXAMPLE: A. Skreeps are alien creatures found on the planet Zandar. There are only four kinds of Skreeps (see picture below). Alpha Skreeps are not striped. Beta Skreeps have fangs. Delta Skreeps are not the smallest kind of Skreep. Gamma Skreeps never have an even number of antennas. Can you match the four kinds of Skreeps to their picture below? A B C D PRACTICE: 1. Albert, Ben, and Charles live next door to each other. They have different jobs, namely, chemist, radio announcer, and doctor. Find each gentlemanʼs occupation from the clues given below. Ben lives in the middle apartment. When Charles goes on vacation, the radio announcer feeds his dog. The chemist pounds on Albertʼs wall when his music is too loud. 2. Three teams in the soccer league played each other at home and away. Find the win-loss record for the six games from the clues given below. The Aʼs never defeated the Bees. The Ceezes never lost a home game. The Ceezes lost 2 games.

14

3. Lillian, Leo, Dorene, and Braden visited four different museum exhibits. Dorene asked Braden to come see the Peruvian Paintings with her, but Braden did not want to visit an exhibit that started with the letter “P”. Lillian didnʼt want to see an exhibit that had the letter “Y” in it (something about yellow yogurt was at the root of her distaste for the letter “Y” that she never completely explained). Leo wanted to see the Irish Tapestry, the Japanese Armor, and the Persian Pottery, but only had time to see one of them. Who saw each exhibit? 4. The 6 grade students at Magnolia Intermediate School were performing the Twelve Days of Christmas. Taylor, Cassandra, and Sierra each brought their flock of turtledoves to school. All of the kids had an even number of turtledoves and nobody had more than seven. Taylor had more turtledoves than Cassandra, but fewer than Sierra. How many turtledoves did each boy have? 5. Five yachts held a race across the Yachts Sea. The S.S. Small Straight finished behind the S.S. Chance. The S.S. Fours came in third. The S.S. Large Straight did not finish second or fourth. The S.S. Full House was ahead of the S.S. Chance, but behind the S.S. Large Straight. Who won the yacht race? 6. Hilary, Alex, Bill and Tanya all decided to see a Saturday matinee. There were only four movies playing at the local theaters. Slugfest, How Romantic, That Canadian Connection, and Kid, I Blew Up the Honey. Tanya and Alex both decided to see the same movie. No boy wanted to see That Canadian Connection. Only one person saw a movie that started with the same letter as their first name. The movie Bill saw had less than four words in the title. There was only one movie that nobody went to. Who went to see which movie? 7. Daphne, Daren, Eva, Ernest, Pam, and Patrick all wanted to play volleyball. They will split into two teams of three each. Both teams had two people with the same first initial. Whenever Pam served the ball, Daren always returned it. Evaʼs team had two boys on it. What were the two teams?

15

8. The Sanderson sisters are a weird lot. Midge always lies, Melody always tells the truth, and Maxine tells the truth only when sheʼs in a good mood. One day they all lined up from tallest to shortest. “The middle sister is Melody,” said the tallest. “Iʼm Maxine,” the middle said. “The middle sister is Midge,” the shortest said. Is Maxine in a good mood? 9. Find the cost of the chunk of chocolate: $1.00 $ ? 10. A rancher was asked how many horses he owned. He said, “They ran down the road just now, and I saw one horse in front of two horses, one horse behind two horses, and a horse between two horses.” How many horses did the rancher have? 11. A can with 40 mints in it weighed 135 grams. The same can with 20 mints weighed 75 grams. What is the weight of the can? 12. The Red Robins played the Blue Jays in a baseball game. The score was tied 2 -2 at the end of the sixth inning. The Blue Jays scored twice as many runs as the Red Robins in the seventh inning. After the seventh inning, the Red Robins did not score, but the Blue Jays scored another run. The total number of runs scored by both teams was eight. What was the final score?

16

D r a w a D i a g r a mD r a w a D i a g r a m Name//Date EXAMPLE: 1. The six knights of the Hexagonal Table sat around a six sided table. Sir Deltus sat to the immediate left of Sir Bellows. Sir Edgar sat to the immediate left of Sir Flog. Sir Carl sat directly across the table from Sir Deltus. What two knights did Sir Allen sit in between? PRACTICE: 1. Ray has to decorate his backyard for his birthday party. There are eight trees arranged in a circle. Ray has decided that each tree must be connected to all other seven trees with a streamer. How many streamers will Ray need? 2. Jeopardy has invited 27 people to play their teen tournament. During each round, contestants are put into groups of three. Every group plays the game at the same time. Only the person with the highest score from each group gets to go on to the next round. If the tournament continues until there is only one champion left, how many games will have to be played? How many games will the winner have played? 3. During the last race at the Belldish Race Track, Happy Hobo finished two yards ahead of Dianaʼs Pride. Sky Rocket finished 8 yards ahead of Light Bulb. Light Bulb finished three yards behind Happy Hobo. Tootie Fruity finished six yards ahead of Dianaʼs Pride. Who won the race and how far behind the leader were each of the other horses?

17

4. Dennis and Flora were discussing their strategies for tic-tac-toe. Dennis said, ”Everyone knows that you can put five xʼs on a tic-tac-toe board and still not have three in a row. But can you do it with six xʼs?” Flora thought about it for a while and decided that it was possible. What was her solution? 5. There are only four stops on the Reading Railroad, one at each end and two somewhere in between. They are all in a straight line. The Chestertown stop is four miles from the Downtown stop. The Warehouse stop is three miles from the downtown stop. The Warehouse stop is eight miles from the Terminus, which is at the end of the railroad. If the whole railroad is only nine miles long, what is the order of the four stops? 6. A group of archaeologists is stranded in the desert with a 6-day walk back to the nearest town. Each person in the group can carry a 4-day supply of food and water. The archaeologists decide to send a party to get help, but each person in the party must have enough food and water to reach civilization or make it back to the stranded group alive. How many people must start out in order for at least one person to reach civilization and get help?

18

C r e a t e a nC r e a t e a n O r g a n i z e d L i s t O r g a n i z e d L i s t Name//Date EXAMPLES: A. There are several different types of fish in Patchover Pond. Each fish eats at least one type of algae and no two fish eat the same combination of algae. There are four types of algae: red, blue, yellow, and green. Whatʼs the largest number of fish that could be in Patchover Pond?

Fifteen possible types of fish g (green) b (blue) r (red) y (yellow) g-b b-r r-y g-y b-y g-r g-b-y b-r-y g-b-r g-y-r g-b-y-r B. Three students at Hamilton Middle School ran for class president. Their names were Oscar, Toni, and Gwen. Three other students, Shaun, Ellen, and Myles, ran for vice-president. How many different ways could a student vote for a president/vice president combination? 9 possible combinations Oscar-Shaun Toni-Shaun Gwen-Shaun Oscar-Ellen Toni-Ellen Gwen-Ellen Oscar-Myles Toni-Myles Gwen-Myles

19

PRACTICE: 1. Mrs. Kennedy, Mr. Nat, Mrs. Hollister, Mrs. Baker, Mrs. Ertola, and Mrs. Phelps all teach sixth grade. The principal needs to arrange time for the teachers to have conferences with each other. Each conference consists of only two teachers, and each teacher needs to be able to meet with all of the other teachers. How many conferences will the principal need to arrange? 2. At the Perivale Pizza Parlor there are four pizza toppings: pepperoni, sausage, mushroom, and olives. When you order a pizza, you have to get at least two different toppings. You can get more if you want, but you must always have at least two. How many different kinds of pizza could you order? 3. The Adler family has five children: John, Yvonne, Ron, Dawn, and Fawn. They want to take pictures of the children and they want each photo to have exactly three kids in them. If they never have the same trio of kids in two different photos, how many pictures could they take? 4. In the country of Malawala there are five kinds of coins. They are worth 11 cents, 7 cents, 5 cents, 3 cents, and 1 cent. Jamal had 15 cents worth of Malawalan coins, as did his friend Daniel. Jamal had three coins and Daniel had five. How many different combinations of coins could Jamal have? How many different combinations of coins could Daniel have? 5. There are three aerobics classes that take place in the local gym during January: jazzercise, cardio-funk, and advanced aerobics. The jazzercise class meets every third day starting January 3. The cardio-funk class meets every fourth day starting January 2. The advanced aerobics class meets every fifth day starting January 4. On how many days in January are there two classes on the same day? (January has 31 days) 6. African Adventure has six guides: Michael Thompson, Michael Anderson, Betty Anderson, Robert Keenan, Norman Underwood, and Norman Keenan. In order to conduct a safari, three guides must be selected. To avoid confusion, African Adventure has decided to never let two guides with either the same first name or the same last name work together. How many possible ways can three guides be selected?

20

W o r k i n g B a c k w a r d sW o r k i n g B a c k w a r d s Name//Date EXAMPLE: A. Kim spent half of her money in the theater. After the show she stopped at the supermarket and spent half of what she had left. She now has $2.15 in her pocket. How much money did she have before she went to the theater. Working backwards: a. Remaining amount = $2.15 b. Since $2.15 is 1/2 of what Kim had when she went into the supermarket, multiply $2.15 x 2 = $4.30 c. Since $4.30 is 1/2 of what Kim had when she went into the theater, multiply $4.30 x 2 = $8.60 d. Answer: Kim starts with $8.60 PRACTICE: 1. Raul came home with $3.00 in his pocket. He had given Rene $1.50 on his way home. Pedro gave him $1.00 that he had borrowed last week. How much money did Raul have at the beginning of the day? 2. Donnie, his cat, and his dog got on the scale which showed 111 pounds as their total weight. The dog stepped off and the scale showed 95 pounds. The cat stepped off of the scale and it showed 88 pounds. What was the weight of the dog and the cat? 3. On the last report card, Tasha got twice as many Aʼs as David. David got the same number of Aʼs as Rita and Yvonne added together. Rita had 2 more Aʼs than Yvonne. Yvonne got one A. How many Aʼs did Tasha get?

21

4. During last nights game, Hank scored half as many runs as Karen. Karen scored two more runs than T.J. T.J. scored three fewer runs than Margo. Margo scored five runs. How many runs did all four kids scored all together? 5. On Monday, Clarence put all his allowance into his empty piggy bank. On Tuesday, Clarence put in an extra $1.40. On Wednesday, he spent half of the money in the piggy bank. On Thursday, he spent $3.50, and his piggy bank was then empty. How much was Clarenceʼs allowance? 6. Friday morning the Wilson's sink still had some dishes in it from last night. After breakfast, the number of dishes doubled. After lunch, there were four new dirty dishes. After dinner, the number of dishes tripled. When Rose cleaned the dishes, she washed 60 dishes. How many dishes were left from last night? 7. Quincy, Ralph, Samantha, and Theresa all joined a summer reading program. Quincy read five more books than Ralph. Ralph read half as many books as Samantha. Samantha read three fewer books than Theresa. Theresa read eleven books. How many books did Quincy read? 8. While the Munoz family was out camping, Mr. Munoz decided to build a campfire. He told everyone to collect sticks for kindling. Myra found ten more sticks than Mrs. Munoz. David found three times as many sticks as Mr. Munoz. Mrs. Munoz found the same number of sticks as Mr. Munoz. Mr. Munoz found seven sticks. How many sticks did the family have for the campfire? 9. Raquel needs to go to an important business deal across town at 2:15 p.m. It will take her twenty-three minutes to walk from her office to the bus station. The bus ride will take an hour and fifty-one minutes. It will take eighteen minutes to walk to the building where the meeting is, and another five minutes to ride the elevator to the top floor. If she wants to arrive ten minutes before the meeting starts, what time should she leave?

22

10. Eleanor and the other members of the tour group boarded a local bus. Except for the bus driver, the bus had been empty. At the next stop, nobody got off, but enough people got on to exactly double the number of passengers. At the next stop, 2 passengers got off. At the next stop, half of the passengers got off. At the next stop, 3 passengers got on and one got off. At the next stop, nine passengers got off. Eleanor was going to ask where the next stop was, but she discovered that she was the only passenger on the bus. How many people were in her tour group? 11. Pirate Percy wrote the following instructions to help him remember where he hid the treasure in the house below. “I buried the treasure. Then I walked into the next room. I opened the door that was to the right of me and went into the next room. I opened the door that was to the right of me and went into the next room. I opened the door that was to the right of me and went into the next room. I opened the door that was to the left of me, and that took me outside the house.” In which room is the treasure buried? 12. Alvin the spy uses this set of instructions to scramble all his secret messages. 1. Write the message in backwards order, with no spaces for words. 2. Change all aʼs to eʼs, the eʼs to iʼs, the iʼs to oʼs, the oʼs to uʼs and the uʼs to aʼs. 3. Rewrite every letter, including the vowels, as the next letter in the alphabet (aʼs written as bʼs, bʼs as cʼs, cʼs as dʼs, etc., and zʼs as aʼs). 4. Switch the first and second letters with each other, the third and fourth with each other, etc. (Example: this---> htsi) This is the way Alvinʼs latest message looked: “MJUUJFOTTPCPVNJCUI” What is the actual message?

23

G u e s s a n d C h e c kG u e s s a n d C h e c k Name//Date EXAMPLES: A. Leeʼs age is 4 times Daleʼs. Kilroy is twice Daleʼs. The sum of all three ages is 21. How old is each? Guess Leeʼs age Kilroyʼs age target Daleʼs age Dale x 4 Dale x2 sum 21 10 40 20 70 too high 5 20 10 35 too high 2 8 4 14 too low 3 12 6 21 on target B. Jessie has started saving nickels and dimes. So far she has 42 coins that total $3.35. How many nickels and how many dimes does she have? guess #dimes totals target # nickels value (42-#nickels) value #coins value 42 $3.35 C. Farmer Dell raises chickens and horses. He has 12 of them. That makes a total of 38 legs. How many chickens and how many horses does he have? guess #horses totals target #chickens # legs (12-#chickens) # legs animals # legs 38

24

PRACTICE: Construct your own guess and check chart to solve the problems below. 1. A text book is opened by chance. To what pages is it opened if the product of the facing pages is 3192? 2. You put 12 blocks in three piles. Pile A has 2 more blocks than Pile B. Pile C has 2 fewer blocks than Pile B. How many blocks are in each pile? 3. The sum of three consecutive numbers is 189. What are they? 4. There are 24 television sets in the video store. Some are color T.V. sets and some are black and white sets. There are 14 more color T.V. sets than black and white sets. How many color T.V. sets are there? 5. Zed is one year older than Ted. Ted is one year older than Ed. If you add up their ages you get 54. How old are each of the three brothers? 6. Jeri is two years older than Mary. Mary is three years older than Carrie. All their ages add up to 26. How old is each sister? 7. Tony picks apples 5 days a week. One week he picked 70 apples. Each day he picked two more apples than the day before. How many apples did Tony pick each day? 8. Liza picks pears four days a week. One week she picked 44 pears. Each day, she picked four pears more than the day before. How many pears did Liza pick each day?

25

9. The Four Legged Zoo is a small zoo that has only four kinds of animals. There are twice as many giraffes as there are elephants. There are twice as many camels as there are giraffes. There are twice as many alligators as there are camels. There are 45 animals in the zoo. How many of each animal is there? 10. Danielle was awarded the #1 Salesperson Award at Carolina Cars because she sold 20 cars last month. She sold five kinds of cars: Toyotas, Fords, Buicks, Cadillacs, and Jeeps. The number of Toyotas was two greater than the number of Fords. The number of Fords was three less than the number of Buicks. The number of Buicks was the same as the number of Cadillacs. The number of Cadillacs was half the amount of the number of Jeeps. How many of each car did Danielle sell? 11. Five kids entered the Nevada County Goldfish Eating Contest. Jesse ate as many goldfish as David. Milo ate as many goldfish as Tanisha. Tanisha ate three goldfish less than Jesse. Ralph didnʼt eat any goldfish. During the contest a total of 14 goldfish were eaten. How many goldfish did each person eat? 12. Cecil built a lemonade stand. It was open for five days. Each day he made three dollars less than the day before. All together he made $80. How much did Cecil make each day? 13. Sherrie had six weeks of summer vacation. She started reading books. Each week she read 2 books more than the week before. She read 72 books during the six weeks. How many books did she read each week? 14. Ms. Davis collected pine cones over a 7-day period. Every day she collected one more pine cone than the number she collected the day before. By the end of the seventh day she had 42 pine cones. How many did she collect each day?