Unit Five Answer Keys

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1 Probability & Data Analysis Unit Five Unit Five Answer Keys Session Blacklines A. A., Unit Five Pre-Assessment a b range = mode = median = c Graphs may vary slightly. xample: Number of Students Letters in Students First Names 7 Number of Letters in First Name d Questions will vary. xample: How many students in Mr. Potter s class have first names that are letters long? e Questions will vary. xample: How many students in Mr. Potter s class have last names that are letters long? a Strategies will vary. xample: b = boxes = boxes a Strategies and explanations will vary. xample: b Fantasy takes up of the circle. With 0 students, 0 = students. impossible unlikely as likely as unlikely likely certain d c a b e a as likely as unlikely b xplanations will vary. xample: Half the tiles in the bag are green, so she has a chance of getting green when she pulls one out of the bag. a impossible b Any number from 0 to is acceptable, as long as the student can explain his or her choice in part c by referring to the number of tile in the bag and, possibly, the element of uncertainty. c xplanations will vary depending on the number selected in part b. xample: Since half of the marbles in the bag were green, then probably about half of the ones he picked were green, so he would get green ones. Session Connection, pages, Bar & Circle Graphs a students b Responses will vary. xample: a 7 I saw that the hip-hop part was of the circle, and 00 =. b Responses will vary. xample: a Maybe lots of them live in apartments that don t allow pets. Maybe the kids who have or more pets have big houses or yards. b Questions will vary. xample: a. How many kids voted in this election?. How many votes did kids A, B, and C get altogether?. How many fewer votes did C get than D? b Responses will vary. xample: I added up the number of kids and it s 0. 0 kids said they liked popcorn, and 0 is of 0. Bridges in Mathematics, Grade 7

2 Unit Five Probability & Data Analysis Session Connection, pages, Presidents Names a,,,,,,,,,,, 7, 7, 7,,, 0 b range =, mode =, median = a,,,,,,,,,,, 7, 7, 7, 7,, b range =, mode =, median = a., Strategies and degree of precision will vary. xample: = =.7.7 is about equal to.. b., Strategies and degree of precision will vary. xample: = =.. is about equal to.. Letters in First Names of U.S. Presidents Graph itle Session Bridges Student Book, page, dd Coin Game Probabilities Player Player Player Player Player Player H H H H H H H H H H utcome All Heads Heads and ail Head and ails All ails Probability, xplanations will vary. xample: here are rows where someone gets a point out of total rows., xplanations will vary. xample: If you get heads or tails, no one gets a point. But there are things that can happen, so the probability is that no one will get a point. H H presidents Connection, pages 0 and, Briana s Routes of 7 Number nineteenth century presidents Number of letters in name twentieth century presidents Responses will vary, but students will most likely state that there is not evidence to say that one group of presidents had longer or shorter names than the other. Responses will vary. xample: here were more differences in the names of the older presidents. here were two with -letter names and one with a 0-letter name. But overall they re pretty much the same. Mostly, the names are about letters long for both groups. 7 Bridges in Mathematics, Grade

3 Probability & Data Analysis Unit Five Session 9 Bridges Student Book, page, How Many Routes to ach Intersection? Briana s Road Responses will vary. xample: Road Road 0 Road st Ave. nd Ave. 0 rd Ave. 0 th Ave Responses will vary. xamples: It s all s in the top row and on the left side. he numbers go,,, and on nd row from the top. You can add some of the numbers to get others, like = 0 in the bottom right-hand corner. Session 0 Bridges Student Book, pages and, Pascal s riangle & Coins 70 n of the diagonals, the numbers go in order:,,,,,. he numbers are symmetrical. If you cut the triangle in half down the middle, you can see the same numbers on both halves. xcept for the s along the edges, you can figure out what every number is by adding the two numbers in the row right above it. I circled an example with + = 70. Flipping Coin Heads ails How many different ways? Flipping Coins Both Heads Head/ ail Both ails How many different ways? 0 0 Flipping Coins All Heads Heads/ ail Head/ ails All ails How many different ways? bservations will vary. xample: hey all are the same as the numbers in the rows of the triangle but if you re thinking about flipping coin, you have to look at the second row and if you re thinking about flipping coins, you have to look at the third row. Flipping Coins All Heads Heads/ ail Heads/ ails Head/ ails All ails How many different ways? Bridges in Mathematics, Grade 7

4 Unit Five Probability & Data Analysis Session 0 (cont.) Bridges Student Book, pages and, Pascal s riangle & Coins (cont.) (challenge) Flipping Coins H H/ H/ H/ H/ How many different ways? 0 0 Connection, pages and, Another Spinner xperiment Students might situate their colored regions in different ways. xample: red red white Responses will vary xample: If you spin the spinner once, you have of a chance of landing on red and of a chance to land on white because of the spinner is red and is white. Responses will vary. xample: I think I ll land on red about times and white about times because one-third of is, and one-third of the spinner is white. wo-thirds of is, and two-thirds of the spinner is red. Responses will vary. Responses will vary. Responses will vary. 7 Responses will vary. Responses will vary xample: ven though the spinner is red and white, that doesn t mean that you re going to land on red exactly of the time and white exactly of the time. In probability, anything can happen, including getting half and half when you should get and. I got closer to and with spins than I did with spins though. Bridges Student Book, page, Pascal s riangle Color-In Challenge Starting with row, the numbers in each row of Pascal s riangle are:,, 0, 0,,,,, 0,,,, 7,,,,, 7,,,,, 70,,,,, 9,,,,,,, 9,, 0,, 0, 0,, 0, 0,, 0,,,,, 0,,, 0,,,,,,, 0, 9, 79, 9, 79, 9, 0,,,,, 7,, 7, 7, 7, 7, 7, 7,, 7,,,, 9,, 00, 00, 00,, 00, 00, 00,, 9,,,, 0,,, 00, 00,,, 00, 00,,, 0,, bservations will vary. xample: If you color in the odd numbers, you get little triangles. 0 he colored triangles go along the outside of the big triangle until the th row, and then there s a bunch of new little triangles starting in the middle. very number in the th and the th row is colored in. I think the same thing will happen with the th row Bridges in Mathematics, Grade

5 Probability & Data Analysis Unit Five Session Bridges Student Book, page 7, Lori & Nicole s Dice Game Numbers will vary based on the results of your class. xplanations will vary. xample: here are possibilities in all. here are different ways to get even and odd, so your chances are out of. here s only way to get evens or odds, so the chances of getting either of those are both out of. a out of or b out of or c out of or Responses will vary depending on the class game results. (challenge) out of or Session Connection, pages 7, Spinner & Dice Probabilities a out of or b 0 out of or 0 a out of or b Spin Spin c he probability is 9 or. Responses will vary. xample: here are nine possible ways to spin the two spinners. In three of the nine ways, the spinners add up to ; and, and, and. a out of or b out of or or c Responses will vary. a out of or b Spinner Dice b he probability is. Responses will vary. xample: here are possible combinations of the spinner and die. nly one combination is a and. Session Bridges Student Book, page &, Secret Sack Problem Responses will vary. xample: here probaby is about red tile, yellow, blue, and green. Red tiles are the fewest in number. he number of yellow and blue tile are about the same. here is more green tile than there is any other color. Responses will vary. xample: Sack A is likely. Sack B is impossible (You need at least red.) Sack C is unlikely (here should be more green than yellow or blue.) Sack D is unlikely (Red should be the fewest not the most.)) 9 red, blue. green red, blue, green Responses will vary. xample: Green 0% /0 Yellow 0% /0 Blue 0% 9/0 If 0% of the bag is green gum, then half of the 0 pieces would be green pieces. If blue gum is /0, then every out of 0 pieces is blue. For 0 pieces, there must be or 9 blue pieces. If 0% of the bag is blue, and green is 0%, that leaves 0% as yellow. 0, or of the 0 pieces is yellow. Bridges in Mathematics, Grade 7

6 Unit Five Probability & Data Analysis Session Connection 7, pages 9 7, allies & Graphs Graphs will vary. xample: Number of Votes lection Results Graph itle A B C D Students Responses will vary. xample: he students who were running for the Student Council and also all the kids in the school would be interested in this graph. a b c, Strategies will vary. xample: = 0 0 =, so the mean number of votes for carrots & celery was. d.7 or, Strategies will vary. xample: = =.7 so the mean number of votes for tomatoes was and. e Responses will vary. xample: r r he people who run the school cafeteria, the people who pack kids lunches, and the kids in these classes would be interested in the results of this survey. Session Connection, pages 7 7, Reading Survey Data 9 because = 9 kids took the survey. Strategies may vary slightly. xample: I added up all the numbers of kids = Answers will vary. xample: I don t think so because only kids took this survey, and that s not very many compared to the number of fifth graders in the United States. a an assembly b Answers will vary. xample: All of the students will be at an assembly. he other choices just give you some students. Session (cont.) Connection, pages 7 7, Reading Survey Data (cont.) a b xplanations will vary. xample: r r0 r First I added up the numbers =. I knew that 9 is half of, so I looked for a graph with a half in it. I knew it had to be the third graph, because only the middle two show a half, and on the other one, the sections are equal, but and aren t equal. 7 Bridges in Mathematics, Grade

Probability. Sometimes we know that an event cannot happen, for example, we cannot fly to the sun. We say the event is impossible

Probability. Sometimes we know that an event cannot happen, for example, we cannot fly to the sun. We say the event is impossible Probability Sometimes we know that an event cannot happen, for example, we cannot fly to the sun. We say the event is impossible Impossible In summer, it doesn t rain much in Cape Town, so on a chosen