1. Fill in the table to show all possible scores. Some cells have been filled in for you. Numbers on First Dice
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1 Dice Game show all possible outcomes in a table calculate probabilities In a dice game, two dice are thrown. The two numbers shown on the dice are then added to get the score. 1. Fill in the table to show all possible scores. Some cells have been filled in for you. Numbers on First Dice Numbers on Second Dice Anne needs a score that is odd and greater than 6. What is the probability that Anne will get her score? Explain how you figured it out. Sue needs a score of 8 or more. What is the probability that Sue will get her score? Explain how you figured it out. Who is more likely to get the score she needs, Anne or Sue? 7 Page 1 Dice Game Test 7: Form A
2 Ducklings fill in a frequency chart work with median and mean The local nature club is carrying out a survey of the number of ducklings in each family of ducks in the lake. Here are the results of their survey: 4, 7, 6, 5, 8, 7, 5, 4, 10, 4, 9, 6, 5, 4, 4, 5, 9, 8, 4 1. Write the results of the survey in the table. The first box has been completed for you. Number of ducklings in a family Number of families Find the median number of ducklings in a family. ducklings Show your work. Copyright 2005 by Mathematics Assessment Page 6 Ducklings Test 7 Resource Service. All rights reserved.
3 Activity Day Work with probabilities Dolots School is planning an activity day. Each student has a blank card. Each student randomly chooses a number from 1 through 5. Then writes this number on their card What is the probability that Avery writes the number 4 on his card? 2. All the students who write a prime number on their card will travel by school bus for their activity day. What is the probability that Chas will travel by school bus for his activity day? Explain clearly how you decided. 3. There are 30 students in the class. How many students do you expect to travel on the school bus for their activity day? Show how you figured it out. 4. Do you think it is possible that 15 of the 30 students in the class will write the number 1 on their card? Explain clearly how you made your decision. Copyright 2010 by Mathematics Assessment Page 3 Activity Day Resource Service. All rights reserved. 8
4 Black and White show your understanding of fractions and probability There are 4 black balls and 7 white balls in a bag. Jasper picks a ball without looking. He says, The probability of getting a black ball is 4 7 Jasper is wrong! 1. What is the probability of getting a black ball? Explain why Jasper is wrong. 2. The fractions 4 7, 7 4, 7 11, 4 11 are answers to the questions below. Put each fraction in a correct place. a. What is the probability of getting a white ball? b. What is the probability of not getting a black ball? c. What is the fraction of black balls in the bag? d. What is the number of black balls as a fraction of the number of white balls? e. What is the number of white balls as a fraction of the number of black balls? 7 Copyright 2008 by Mathematics Assessment Page 2 Sixth Grade - Black and White Resource Service. All rights reserved.
5 Tetra complete scores in a table of results work out probabilities from a table of possible scores Anna and Bill play the game Tetra. In this game two four-sided dice numbered 1 to 4 are tossed. The numbers on the base of each dice are then multiplied together to get a score. When the score is even Anna gets a point. When the score is odd Bill gets a point. 1. Complete this table of score results Number on base of red dice red X blue Number on base of blue dice 2. Explain why the probability of getting a score of 4 is. 3. Find the probability that Anna gets a point. Explain your work Copyright 2006 by Mathematics Assessment Page 7 Tetra Test 6 Resource Service. All rights reserved.
6 Winning Spinners work with probability Bill is playing a game of chance at the School Fair. He must spin each of these two spinners. If the sum of the numbers is an even number, he wins a prize Spinner A Spinner B 1. Fill in the empty boxes in the addition chart below to show the possible totals. Spinner A Direction: Spinner B 9 13 Sum of A & B in each box What is the probability of Bill winning a prize? 3. Using two new spinners, rearrange the same eight numbers to increase Bill s chances of winning. What is the probability of Bill winning using his new spinners? Show how you figured it out. 10 Copyright 2005 by Mathematics Assessment Page 4 Winning Spinners Test 6 Resource Service. All rights reserved.
7 Pick a Cube work with probabilities Maria has 12 white cubes and 8 black cubes in her bag. She chooses one of the cubes without looking. 1. Draw a circle around the five values in the rectangle below that show the probability that Maria chooses a white cube % 12 60% 32 20% Carmen has 15 red cubes and 5 black cubes in her bag. She chooses one of the cubes without looking. 2. Find the probability that Carmen does not choose a black cube. Explain your answer. 7 Page 6 Pick a Cube Test 6: Form A
8 Tank solve problems about volume A closed tank is 24 inches long, 12 inches high, and 16 inches wide. It is filled with water to a depth of 10 inches. 10 inches 16 inches 24 inches 12 inches 1. What volume of water is in the tank? Show your calculations. 2. How deep will the water be if the tank is turned so that it stands on one end? Explain how you figured it out.? 16 inches 12 inches 7 Page 7 Tank Test 6: Form A
9 Choosing a Cube work with probabilities Carmen has 4 white cubes and 1 black cube in her bag. She asks two friends, Without looking in the bag, what is the probability of picking a black cube? Marco says: It is 1 because there is 1 black cube and 4 white cubes. 4 Gloria says: It is 1 because there is 1 black cube and 5 cubes in all Which of Carmen s friends is correct? Explain why the other friend is wrong. Page 4 Choosing a Cube Test 6: Form A
10 2. Tessa has a different bag of black and white cubes. 3 The probability of picking a black cube from Tessa s bag is 11. What is the probability of picking a white cube from Tessa s bag? 3. How many black cubes and how many white cubes could be in Tessa s bag? black cubes white cubes 4. Paul has a different bag of black and white cubes. Paul has more cubes in his bag than Tessa. The probability of choosing a black cube from Paul s bag is also How many black cubes and how many white cubes could be in Paul s bag? black cubes white cubes 5 Page 5 Choosing a Cube Test 6: Form A
11 M & M S show your understanding of probability. The diagram below shows fifteen M & M s in a candy dish. There are four yellow (Y), two brown (B), seven green (G), and two red (R). R G G Y R Y G B G G Y B Y G G Maria closes her eyes and picks up an M & M. 1. Which color is she most likely to pick up? Explain how you figured it out. 2. Which colors is she equally likely to pick up? Explain your reasons. 3. The probability that Maria will pick up a yellow M & M is 4 15 Write down the probability that Maria will pick up a green M & M. MARS 2000 Page 1 M&M's: Grade 6 Write down the probability that Maria will pick up a brown M & M. Write down the probability that Maria will pick up a red M & M. 4. Explain how you can check that your answers are correct. [8]
12 The Lifespan of an Umbrella use measures of center and understand what each indicates about a data set. Umbrellas don t seem to last long. They blow inside out in the wind and the metal spokes break. Sometimes the material rips and often they just get lost. Megan s family each bought a new umbrella. This table shows how many months each umbrella lasted. Name Megan Carl Mom Dad Granny Grandpa Jill Fred Jo Months What is the median of this set of data? months Show how you figured it out. 2. What is the mode of the life spans of these umbrellas? months Explain how you know. 3. What is the range of the life spans of these umbrellas. months 4. Megan read this statement on an internet site of random facts. The mean lifespan of an umbrella is about 23 months. She said that the mean lifespan of her family s umbrellas was greater than this. Was she correct? Show how you figured this out. Copyright 2009 by Mathematics Assessment Page 1 The Lifespan of an Umbrella Resource Service. All rights reserved 7
13 Katy s Cat Show Survey represent and interpret data Katy wants to find out which breed of cat people like best. She asks 30 people at a cat show which of four breeds they like best. Here is how she records what she finds. S P P P M S P S D P M P S M D D D P P S S D D M P D D D D S Here is the key. S = Siamese P = Persian M = Maine Coon D = Domestic/Non-Breed 1. Help Katy by filling in the tally and find the number of people who like each breed. Breed of Cat Tally Number of Cats Siamese Persian Maine Coon Domestic Total 2. Represent Katy s data as a bar graph using the grid below. Remember to label the axes and select a sensible scale. Copyright 2010 by Mathematics Assessment Page 8 Katy s Cat Show Survey Resource Service. All rights reserved
14 Piles of Oranges describe, extend and make generalizations about a number pattern Here are some piles of oranges that are displayed in Mrs. Changʼs grocery store. pile # 1 pile # 2 pile # 3 pile # 4 number of oranges = = 6 1. Draw pile # 4 of oranges next to pile # 3 in the diagram above. 2. How many oranges are needed for pile # 4 and pile # 5? Write your answers in the table below. Pile # Number of oranges How many oranges does Mrs. Chang need for pile # 6? Show how you figured it out. 4. Mrs. Chang says, I need 44 oranges to make pile # 9. Without drawing a diagram, explain how you know that she is wrong. 5. How many oranges does she need to make pile # 9? 8 Published by CTB/McGraw-Hill LLC. Copyright 2004 Page 4 Piles of Oranges Test 4 by Mathematics Assessment Resource Service. All rights reserved.
15 Bikes and Trikes solve number problems in a real context The cycle shop on Main Street sells bikes (two wheels) and trikes (three wheels). 1. Yesterday, Sarah counted all of the cycles in the shop. There were seven bikes and four trikes in the shop. How many wheels were there on these eleven cycles? Show your calculation. 2. Today, Sarah counted all of the wheels of all of the cycles in the shop. She found that there were 30 wheels in all. There were the same number of bikes as there were trikes. How many bikes were there? How many trikes were there? Show how you figured it out. 8 Copyright 2006 by Mathematics Assessment Page 8 Bikes and Trikes Test 4 Resource Service. All rights reserved.
16 NUMBER STEPS recognize and continue number patterns 1. Look at this series of numbers. Fill in the next four numbers in the series. 3, 7, 11, 15, 19, 23, 27,,,, Hint: The numbers go up by the same amount each time. 2. What patterns can you see? 3. Write down the last digit of each number in the series. 4. What patterns can you see? MARS 1999 Page 3 Grade 3
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A 21.0% B 34.3% C 49.0% D 70.0%
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Name: Class: Date: 6. An event occurs, on average, every 6 out of 17 times during a simulation. The experimental probability of this event is 11
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The tree diagram and list show the possible outcomes for the types of cookies Maya made. Peppermint Caramel Peppermint Caramel Peppermint Caramel
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Copyright 2015 Edmentum - All rights reserved Picture is not drawn to scale.
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3 x 5 is greater than 5. x 8 is greater than 8. 1 x 10 is less than 10 x 7 is less than 7. x 21 is less than 21. x 4 is greater than 4 3 = = =
6 6 5 6 7 8 9 0 6 6 x 8 is greater than 8 5 x 5 is greater than 5 x 0 is less than 0 x 7 is less than 7 7 8 x is less than x is greater than 5 6 = x = x5 x5 7 8 x6 = = x6 8 x x 9 0 . Edward had 0 baseball