PRACTICE PROBLEMS FOR MATH CELEBRATION

Transcription

1 PRACTICE PROBLEMS FOR MATH CELEBRATION Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 1

2 Suggested Sources for More Problems 1. Creative Problem solver Gr. 1-8, Wright Group Catalogue. 2. Problem Bank at the end of each Nelson 3-6 Chapter. 3. Problems in Math to the Max books. 4. Grade 5, 6 7 & 8 problems in Elementary Math Conference on First Class Desktop Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 2

3 1. SERVING THE CHEESE How did Chef Mardy cut this cheese into eight congruent (identical) pieces with ONLY three straight cuts? Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 3

4 SOLUTION - SERVING THE CHEESE Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 4

5 2. JOLLY JUGGLERS The Jolly Jugglers have a game. They toss balls back and forth till the number each has is exactly the same. Now Ty, Steve, and Matt each have five. But what they had to start you must derive. They came on stage and juggled along. Ty tossed 2 balls to Steve. Then Matt popped one back to Ty. Soon Steve hurled one to Matt. Each ended the act with 5 balls. How many balls did each juggle when the act began. Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 5

6 SOLUTION - JOLLY JUGGLERS TY STEVE MATT Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 6

7 3. HOT DOGS AND HAMBURGERS At a school picnic you can have either a hamburger or a hot dog. You may have the following toppings: ketchup, mustard, pickles, and cheese. You may have all, some, or none of the toppings. How many different types of sandwiches can you make? Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 7

8 SOLUTION - HOT DOGS AND HAMBURGERS Hamburger KMPC KMP KM K NONE KMC KP M KPC KC P MPC MP C MC PC 16 different sandwiches x 2 (hot dog)= 32 Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 8

9 4. TEMPERATURE TALLY This past November, Ms. Curley's class kept track of the temperature every day for one week. They made a chart to post the outdoor temperatures for each day of the school week at 9:00 AM and at noon. On Monday, the temperature was 6 degrees Centigrade at noon. It had been 10 degrees colder that morning at 9:00 AM Thursday's 9:00 AM temperature was 8 degrees warmer than the temperature for the same time on Monday. On Wednesday and Thursday, the temperature rose 6 degrees from nine o'clock until noon. Tuesday morning at 9:00 AM the temperature was 10 degrees warmer than Monday at the same time. At noon on Tuesday, it was exactly at the freezing mark. Wednesday noon was 3 degrees colder than Thursday noon. The first reading on Friday was 5 degrees colder than the day before at the same time. It warmed up 5 degrees each hour until noon. What was the temperature each day at 9:00 AM and at noon? Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 9

10 SOLUTION - TEMPERATURE TALLY Day Temperature at 9:00 am Temperature at noon Monday - 4 o C 6 o C Tuesday 6 o C 0 o C Wednesday 1 o C 7 o C Thursday 4 o C 10 o C Friday - 1 o C 14 o C Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 10

11 5. THREE GAME SERIES The Rangers and the Waves summer basketball teams played 3 games against each other this season. The Rangers scored a total of 105 points and the Waves scored 102 points for the 3 games together. The Rangers won the first game by 9 points with a score of 31. In the second game the Waves doubled their first game score and beat the Rangers by 8 points. What was each team's score for each of the 3 games? Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 11

12 SOLUTION - THREE GAME SERIES Team 1 st Game 2 nd Game 3 rd Game Total Rangers Waves Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 12

13 6. MAKE YOUR OWN SUBTRACTION Here are 6 numbers: 0, 2, 3, 5, 8, 9. Use them to fill in this subtraction so you get the largest answer possible without putting 0 in the hundreds place! Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 13

14 SOLUTION - MAKE YOUR OWN SUBTRACTION The greatest answer is = 782 Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 14

15 7. HECTIC HALLWAY The Webster School has a long hallway that runs from the school office to the gym. Beginning with room 101, closest to the office, all the odd-numbered rooms are on the left, facing the playing field. The even-numbered rooms are on the right, and their windows face out toward the big hill. The rooms are numbered 101, 102, 103, and continue that way without any numbers missing up to room 114. Suzy and Clifton are delivering packages and messages to six rooms. They gave the first package to the teacher in room 101. Then they walked toward the gym, passing two classrooms on the left until they got to the next destination. Then they walked straight across the hall and delivered a message to Mrs. Smith. Their fourth stop was back past 1 classroom on this side on the way to the office. For the next delivery, they walked toward the gym again, passing 3 more classrooms on their right, to another classroom on the hill side of the building. The last message was delivered directly across the hall. Which room number got the last message? Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 15

16 SOLUTION - HECTIC HALLWAY The last stop was room 111. They delivered messages to the rooms in this order: 101, 107, 108, 104, 112, and 111. Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 16

17 8. THE LAST WAFFLE The twins insist on having congruent shapes of waffles to eat. How can Mom cut the waffle to get two identical pieces? Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 17

18 SOLUTION THE LAST WAFFLE Hint Use tiles Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 18

19 9. FLOWER POWER Rose, Iris and Daisy are each wearing a flower. The girl wearing the rose said, The flowers match our names but none of us is wearing a flower that matches our own name. Wow, said Iris, You re right! Who is wearing what flower? Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 19

20 SOLUTION - FLOWER POWER Flower Girls Rose Daisy Iris Rose X X Daisy X X Iris X X Rose is wearing an iris Daisy is wearing a rose Iris is wearing a daisy Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 20

21 10. FOLLOWING ALONG 1, 1, 2, 6, 24, 120, 720, 5040, 40320,, Determine the next two numbers in the above list of whole number values. Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 21

22 SOLUTION - FOLLOWING ALONG 1, 1, 2, 6, 24, 120, 720, 5040, 40320, , x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11 Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 22

23 11. FIBONACCI NUMBERS Fibonacci numbers are 1, 1, 2, 3, 5, 8,,, If one is the first Fibonacci number, what is the 20 th Fibonnacci number? Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 23

24 SOLUTION - FIBONACCI NUMBERS 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765 Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 24

25 12. SNACK PACKS The school cafeteria got two shipments of snack packs. These shipments totaled only 1/3 of the school's total order of snack packs for the week. The first shipment included one snack pack for each of the 21 students in the 3 fourth-grade classrooms, one for each of the students in the 4 fifth-grade classes of 24 students, and one for each student in the 3 sixth-grade classes of 22 students. After each student got one snack pack, there were still 63 snack packs left over from the first shipment. Then the second shipment arrived with 12- dozen snack packs. How many snack packs were ordered in all that week? Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 25

26 SOLUTION - SNACK PACKS The total order was for 1,296 (or 108 dozen) snack packs. Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 26

27 13. SWIM STROKES The Sandy City swim program has 10 more girls than boys enrolled. Each swimmer is learning one swim stroke. Half of the girls are learning the crawl. Three times as many girls are learning the side stroke as are learning the breast stroke. Only three girls are learning the butterfly stroke. There is one more girl learning the breast stroke than the butterfly. How many boys and girls are enrolled in the swim program altogether? Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 27

28 SOLUTION - SWIM STROKES Butterfly Breast Crawl Side Total Stroke Stroke Stroke girls 28 boys 66 swimmers Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 28

29 14. MAGIC TRIANGLE Mrs. Prime, the math teacher, has given Jaspreet a special math problem. He is to arrange the numbers from 1 6 in the triangle so that the sum of each straight line of three circles gives the same result. How many different ways could you place the numbers? Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 29

30 SOLUTION MAGIC TRIANGLE Four unique solutions (excluding rotations and reflections) are illustrated below. Here s how: Figure it this way... the total for each line can t be smaller than 9 because the smallest group containing the 6 has to add up to 9 ( = 9). This gets you started. Switch and swap explorations will amazingly yield an additional 3 answers Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 30

31 15. SYMMETRY Materials: Symmetry 2 Cards 1. Cut out the cards. 2. Deal one card to each group member. 3. One at a time, read your clue to your group. 4. Work together using all the clues to create a solution. 5. Draw the polygon. 6. Show 4 lines of symmetry. Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 31

32 Use Pattern Blocks. Make a polygon having four lines of symmetry. The Polygon has eight sides. Use one square block, four tan rhombus blocks, and four triangle blocks. Use nine blocks in all to make the polygon. Name the polygon, record the group s solution, and draw the lines of symmetry. Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 32

33 SOLUTION - SYMMETRY Octagon Octagon Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 33

34 16. GUESS THE WEIGHT One event at a math celebration asked participants to guess the weight of three objects: a tetrahedron, a sphere, and a cube. Participants are given three clues, and different combinations of the items are placed on scales. What is the weight of each of the three items? How do you know? 23 kg 22 kg 28 kg Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 34

35 SOLUTION: GUESS THE WEIGHT I. = 12 = 7 = 4 Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 35

36 17. NO REPEATS I promised to help out at the library every day after school. Going the same way can get boring so I d like to try a different 6-block route each day. How many days can I go from school to the library, in only 6 blocks, without repeating a route and using only right angle turns? * You must only use the perimeter of the squares, not cutting through a square. Library School Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 36

37 USING DIAGRAMS - No repeats Library Library Library Library School School School School Library Library Library Library School School School School Library Library Library Library School School School School Library Library Library Library School School School School Library Library Library Library School School School School Library Library Library Library School School School School Library Library Library Library School School School School Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 37

38 SOLUTION NO REPEATS No repeats correct solution all 20 different routes. Library Library Library Library School School School School Library Library Library Library School School School School Library Library Library Library School School School School Library Library Library Library School School School School Library Library Library Library School School School School Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 38

39 18. WORLD S GREATEST PRIMATE PUZZLE It s lunchtime at the local zoo, and down at the primate pavilion the cry is for bananas. Every day 100 bananas are divided up among 100 animals. Each gorilla gets three bananas; each chimpanzee gets two. The lemurs, being the smallest, get a half a banana each. Using these facts to work with, can you figure out how many gorillas, chimpanzees and lemurs there are? Note: All animals eat There will be no leftovers Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 39

40 SOLUTION - WORLD S GREATEST PRIMATE PUZZLE Gorilla ANSWER = (5) 5 x 3 = 15 Chimpanzee ANSWER = (25) 25 x 2 = 50 Lemur ANSWER = (70) 70 x.5 = animals 100 bananas Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 40

41 19. ANGLES AND POLYGONS Special Instructions: Cut into cards Each member of group reads their clue to the group Solution on back of problem Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 41

42 Use nine Pattern Blocks that are the same. Make a larger copy of one of the blocks. The Polygon has two acute angles. The polygon has two obtuse angles. All sides of the polygon are the same length. Name the polygon and record the group s solution. Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 42

43 SOLUTION ANGLES AND POLYGONS Rhombus made using 9 blue or tan blocks. Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 43

44 20. MAGIC SQUARE Mrs. Holderman, the math teacher, has given Johnny a special math problem. He must place the remaining numbers on the wall chart so that the sum of each row and column, as well as both diagonals, is the same. Mrs. H. has already spotted Johnny three numbers. How should he position the rest of the numbers to solve the problem? Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 44

45 SOLUTION - MAGIC SQUARE The two solutions (which are diagonal reflections of each other) are shown below. Here s how: Mrs. Holderman s three hint numbers add up to 15, so all columns and diagonals must add up to 15. Neither the 9 nor the 7 can go into a row with the 8, since they would force the row totals to be more than 15. When they are placed in either of the two remaining positions, the rest of the solution consists of filling in the blanks. Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 45

46 21. FOOTBALLERS EQUIPMENT: The board shows 3 overlapping circles, like Venn diagrams: 1 for footballers that can sprint, 1 for footballers that can kick and 1 for footballers that can mark. 14 footballers are going to training and the coach has worked out those that can kick, mark and sprint. The coach knows that: 3 can mark and kick but not sprint. 2 can sprint and kick but not mark. 1 can sprint and mark but not kick. 8 can mark 8 can sprint 8 can kick Your problem is to demonstrate how all this can be shown on the board and still only use the 14 footballers. Draw your answer. Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 46

47 FOOTBALLERS Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 47

48 SOLUTION: FOOTBALLERS Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 48

49 22. STUCK A frog is stuck down a hole that is 610 cm. deep. Its back legs are broken and it cannot jump! It climbs 100 cm. in a day, and as it rests at night it slips back 40 cm. How many days will it take the frog to get out of the hole? Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 49

50 SOLUTION STUCK Only 10 days Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 50

51 23. THE RUSTY RUDDER The Rusty Rudder is having a sunken ship treasure sale. They have red, green, and blue bags filled with surprise treasures! Ken and Katrina each take home 3 bags, and Ken s bags are equal in weight to Katrina s. Ken has 2 red bags and 1 green bag, and Katrina has 1 red bag and 2 blue bags. Together all the bags weigh 24 kg. The bags that are the same colour have the same weight. Bags that are a different colour have different weights. If you use whole numbers, what could the weight of each colour bag be? R R G R B B Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 51

52 SOLUTION THE RUSTY RUDDER For whole numbers: red 2, green 8, and blue 5 Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 52

53 24. CROSSING THE RIVER A farmer wants to cross a flooded river in a small boat with his goat, his dog and his cabbages. The problem is he can only take ONE thing with him at a time. But if he leaves the goat with the cabbages they will be eaten, and if the dog is left alone with the goat it will eat the goat. Can you get the farmer, his goat, dog and cabbages safely across the river? It cannot be done by tying up the dog or the goat. Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 53

54 SOLUTION - CROSSING THE RIVER Take the goat first, go back for the dog. Bring back the goat, take the cabbages. Go back for the goat. Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 54

55 NOTES FOR USING ATTRIBUTE BLOCKS There are four different attributes to observe in the blocks: 1. SHAPE 2. SIZE 3. COLOUR 4. THICKNESS SHAPE triangle, circle, hexagon, rectangle or square SIZE small or LARGE COLOUR yellow, blue and red THICKNESS THICK thin Attribute pages: 36, 37 students put blocks in the circles different from each other in the ways indicated on the arrows. 39, 40 for example page 39 has a large, yellow, thick triangle in the top left and a large, yellow, thin circle in the top right. Macintosh HD:private:var:folders:u1:u1-ZUXCHHXmnGg2Q9uIGNE+++TI:TemporaryItems:fcctemp:Practice Problems for Math Celebration.doc 55

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