3rd Grade Graphing Unit 2010-2011 Charlotte Mecklenburg Schools

The following unit contains lessons, activities, and an assessment. Although the majority of this unit is based upon objective 4.01 (Collect, organize, analyze, and display data (including circle graphs

and tables) to solve problems) warm-ups and assessment items have been included for objectives 4.02 (Determine the number of permutations and combinations of up to three items) and 4.03 (Solve probability problems using permutations and combinations.) Assessment: You will find an assessment included with this unit. Research has shown that delayed assessment (or assessments that test residual learning) are the best indicators of student understanding. Therefore, you may want to postpone giving the assessment until after you have completed several weeks of follow-up activities. In addition, observing students as they work (ongoing assessment) will provide a closer look at what students clearly understand, as well as concepts they are still working on. A key part of ongoing assessment is feedback. Students should receive feedback that will help them develop their understanding.

Objective: 4.01 Collect, organize, analyze, and display data (including circle graphs and tables) to solve problems Students need to learn to…

To read and create circle graphs; You can review tallies, line plots and pictographs from the 1st-2nd grade objectives, but spend minimal time on this. Your main focus in 3rd grade is circle graphs. You do not need to teach bar graphs, line graphs, or stem-and-leaf graphs. All of these are 4th and 5th grade objectives. • The purpose of a circle graph is to compare the parts to the whole. • All graphs have a title that describes the main idea of the graph • Circle graphs are sometimes called pie charts since it they look like a pie that has been cut into various slices. • The sections of the circle graph describe the various objects/people. The larger the section, the more objects/people being described. • That each object/person received the same portion of the circle and that the entire circle describes the whole group. • To recognize sections of a circle graph as half, less/more than half, less/more than a quarter, etc.

The students should be able to describe the graph with comments such as more than half the people like… or half the students ate….or less than a quarter of the group found…etc. The students are not expected to label the sections with percentages. Students should be able to describe the shape of the data. Is most of the data centered in one place? What does it tell you? Is there a trend? What does the information say about the people/items surveyed? Does the information tell you something different if you group the data in a different manner?

Warm-Ups and Assessment items have been provided for the following objectives: 4.02 (Determine the number of permutations and combinations of up to three items) 4.03 (Solve probability problems using permutations and combinations.)

Lesson #1: Toss It Objective: 4.01 Collect, organize, analyze, and display data (including circle graphs and tables) to solve problems

Materials:

Plastic pail, bucket, or box for every 4 or 5 students

6 sheets of recycled 8 ½ X 11 paper wadded up into a ball for each group (alternate ideas could include large cotton balls or packages of 6 small cushioned balls sold in the Dollar Tree)

Masking tape or painter’s tape

Post-it note for each student

Copy of Toss It recording sheet for each group

Timer or stopwatch for each group (optional)

Students will:

Solve problems with tallies, tables, and line plots by collecting, organizing, displaying and analyzing data from the “Toss It” activity

Warm-Up: Justin, Connor and Reid have to sit in the first 3 seats of the row at the movie theater. Connor does not want to sit in the end seat on the aisle. How many different ways can they be seated? List all the different combinations. What is the probability that Connor will not have to sit in the end seat on the aisle? Show your work.

Vocabulary:

line plot

tally marks (tallies)

table

data

survey

Before:

Using approximately 3 feet of masking tape or painter’s tape, mark the starting line on the floor

Using more masking tape mark the finish line at least 6 feet away from the starting line. Place the pail or box on

the finish line If using paper wadded up into a ball, count out 6 sheets of 8 ½ X 11 inch paper for each group

During:

Divide students into groups of 4 or 5.

Assign the following roles to one of each of the students: timekeeper, recorder, shooter, retriever(s). (This activity will be repeated so that each participant takes a turn serving in each role).

Tell students that they will be participating in an activity to collect some data to be graphed.

The shooter will toss the paper balls into the basket or box on the finish line. The object is to see how many

baskets can be made in one minute. The timekeeper will keep track of the minute while the recorder will make a

tally mark each time a basket is made. The retriever(s) will make sure the shooter has a steady supply of balls to

toss during the entire minute. (Instruct students to stay behind the starting line when tossing).

Repeat the activity until each student participates in each role once. If there are 5 students in the group, someone

will be the retriever twice.

After:

After everyone has completed the task have students work together in their group to add up their individual tally

marks and record the totals in the table provided.

Have each student record his/her name and total number of baskets made in one minute on a post-it note.*

Have each group create a pictograph using the data collected. Remind students that the graph needs a title,

labels and a key (to decide on the number of successful shots each picture represents).

Have groups share their graphs and discuss the results.

*Teachers- Please save the post-its with the recorded number of baskets made by each individual. You will need these for a future activity.

Homework:

Brainstorm a list of topics that could be used to survey others in order to collect, display and analyze data on a

graph

Extension: Challenge students to find examples of graphs in newspapers and/or magazines to share with the class.

Lesson #2: Toss It Objective: 4.01 Collect, organize, analyze, and display data (including circle graphs and tables) to solve problems

Materials:

Data from yesterday’s lesson

Large sheet of paper to create a class line plot

Post-it note for each student

Students will:

Solve problems with tallies, tables, and line plots by collecting, organizing, displaying and analyzing data from the “Toss It” activity

Warm-Up: Tyler forgets the combination to the lock on his bike. He knows the three numbers are 5, 1 and 4, but he can’t remember the order to open the lock.

List all the possible numbers he can try.

How do you know you recorded all of the possibilities?

What is the probability that the 5 will be the middle number?

How do you know?

Vocabulary:

line plot

tally marks (tallies)

data

survey

table

Before:

Review the activity from yesterday including a discussion of why tally marks and a table were used to record the

data collected. Include a discussion as to why a pictograph was a good representation for the number of baskets

made.

Make sure each student has his/her post-it note with the total number of baskets made from yesterday.

Pass out another post-it note to each student and instruct them to make a large X in the middle of it.

Tell the students that they will create another type of graph in which to compare all of the data collected

during yesterday’s lesson.

During:

As a class brainstorm a list of other types of graphs that students are familiar with.

Ask what other type of graph would be suitable for displaying the data that was collected during yesterday’s lesson

(a line plot).

Display a large sheet of paper or use the board to create a class line plot.

Discuss and decide on what numbers need to be labeled on the graph.

Give the graph a title.

Have students place their post-its on the line plot above the correct number of baskets scored.

After:

After the class line plot has been created, discuss the results.

Challenge students to create questions that can be answered using the information on the graph.

Although the terms will not be tested, discuss the most frequent number of shots made (known as the mode) and

any numbers that are alone at either end of the graph (the outliers).

Ask students what factors might influence the number of successful shots for students (experience, length of arms,

fatigue, etc.).

Ask the students to estimate their number of shots if the pail or box is moved either closer or further away from the

present finish line.

Ask students what factors might influence the number of successful shots for students (experience, length of arms,

fatigue, etc.).

Allow students time to poll their classmates to find out how many brothers and sisters they have in order to create

a line plot for homework.

Brainstorm ways to collect this information so they are sure to get a response from each classmate.

(a possible chart is included with the homework).

*Teachers- Please remember to save the post-its with the recorded number of baskets made by each individual student. You will need these for a future activity

Homework:

Have students complete the attached homework page.

After finding out how many siblings each student has, have students create an individual line plot to represent the

data.

Ask, “If another 3rd

grader came to our classroom, how many brothers and sisters do you think they might have?”

Explain your answer

Toss IT Recording Sheet

Name of Shooter Baskets Made (record using tally marks)

Total Number of Baskets

1.

2.

3.

4.

5.

Lesson #2 – Homework Name:

Student Name Total number of brothers and sisters

Student Name Total number of brothers and sisters

Create a line plot to represent the data above.

If another 3rd grader came into our classroom, how many brothers and sisters do you think they might have? Explain your answer.

Lesson #3 – Building A Human Circle Graph

Circle graphs, also known as pie charts, are the best type of graph for showing the relative proportions of different categories to each other and to the whole. Circle graphs are used when exact quantities are less important than the relative sizes of the parts.

Objective: 4.01 Collect, organize, analyze, and display data (including circle graphs and tables) to solve problems

Materials: ** YOU will need an area large enough so that all of your students can stand and

sit in a circle.

Yarn- a variety of colors

Students will: Collect, organize, display and analyze data

Create a human circle graph

Compare data displayed in a circle graph and a line plot

Warm-Up:

Grayson needs to pack for his vacation. He has three pairs of pants; black, blue and green. He has two shirts; white and yellow. List all the possible combinations that he could make from the clothes he is packing. How many different outfits does he have? What is the probability that he will be wearing blue? Show your work.

Vocabulary: Circle graph

Line plot

data

Before: Show the “Other Class” circle graph. Explain to students that another class collected data on how many times they could toss a paper ball in a basket. Ask, “What do you notice about the graph? What does it tell us about their data?” Allow students time to talk about what they see.

During: Ask students to look at the line plot they made yesterday and discuss, “how is our line plot like the Other Class circle graph? How is it different?” Have students get their data from yesterday (post-in note with the number of baskets made) and get in a circle. They should stand next to students with the same response (you might want to start the circle with the smallest number and guide students to continue). Have students pass a ball of yarn around to create the outline of the circle.

Note to teacher about dividing your circle: One way to do this is: Prepare the center point of the circle by using a plastic container such as an ice cream tub. Cut a slit in the lid of the tub. Put a ball of colored yarn in the tub for each item you will be graphing. Pull the yarn through the slit in the tub.)

Ask students- how might we divide the sections of our circle graph? Using string, divide your human circle graph into parts. Have students suggest a variety of ways to divide the graph. They may suggest dividing each group of numbers (9s, 10s, 11s, etc.) into sections, or they may suggest grouping a range of numbers into sections (0-10, 11-20 etc.). Try several of their suggestions and talk about which makes the most sense. Once you have experimented a bit, have students set the yarn on the floor and take a step back. Ask students to sit down and record the graph they just created as a class. As students finish, have them turn and talk to their neighbor about the following question: “How does our graph compare to the Other Class graph?”

Exploring Graphs: During this portion of the lesson, students will spend time looking at graphs and responding to the following:

1. What is this graph about? 2. What question might this graph answer? 3. Who might want to know this information?

After: Call students back and discuss the graphs they just explored. Explain to students that circle graphs are most useful when comparing categories to each other and to the whole. Ask students, “what is being compared in the first graph?” etc. Homework: Reading a pictograph

Lesson #3 Warm-Up

Grayson needs to pack for his vacation. He has three pairs of pants; black, blue and green. He has two shirts; white and yellow. List all the possible combinations that he could make from the clothes he is packing. How many different outfits does he have? What is the probability that he will be wearing blue? Show your work.

Lesson #3 – Building A Human Circle Graph Graph to use during the “BEFORE” section of the lesson

Number of Baskets we made – “Other Class” This graph shows data from another class after they completed the „tossing trash‟ activity.

20-30 baskets

10-20 baskets

more than 30 baskets

Lesson #3 Exploring Circle Graphs

How the Nicholson’s Spend their Money

Food Rent Clothing Savings Miscellaneous

1. What is this graph about? 2. What question might this graph answer?

3. Who might want to know this information?

1. What is this graph about? 2. What question might this graph answer?

3. Who might want to know this information?

Which Countries make the most Computers?

1. What is this graph about?

2. 2. What question might this graph answer?

3. Who might want to know this information?

Adidas

Other

Nike

Reebok

New Balance

Sneaky Shoe Store Sales 2010

United States

Europe

Japan

Other

Homework Lesson #3 Name:

Morgan made a pictograph to show how he spent his time each day.

At School

Play video games

Watch TV

Do chores and homework

Sleeping

1. How much time does Morgan spend sleeping each day? _______________________________________ 2. Morgan watches TV and plays video games at home. Is this longer or shorter than the time he spends at

school? ____________________________________________________________________________

How much longer or shorter? ____________________________________________________________ 3. Morgan’s sister looked at his graph. She said, “That’s not right Morgan, you spend more than 1 ½ hours

playing video games!” Morgan argued, “I did my graph right, you just didn’t read it carefully.” Who is correct, Morgan, or his sister? Explain your answer.

___________________________________________________________________________________

____________________________________________________________________________________ 4. How would the graph change if Morgan would have said each clock = 1 hour?

___________________________________________________________________________________

How Many Jackets do You Own? x

x

x

x x

x x x

x x x

x x x

0 1 2 3

1. How many students own fewer than 2 jackets? _____________________________________ 2. How many students own 1 or more jackets? ________________________________________

Key: = 2 hours

For a math lesson, Mr. Bass

asked his students how many jackets each student owns.

He made the following line plot of the information.

Lesson #4: Creating Circle Graphs to Answer a Question Objective: 4.01 Collect, organize, analyze, and display data (including circle graphs and tables) to solve problems

Materials: One small bag of candy for each group of 4 students (Skittles, M&M plain, M&M peanut,

jelly beans,

Rulers- to draw lines on their circle graphs

Copies of Allergic to Red Food Coloring Activity Sheet

Students will: Collect, organize and display data in a circle graph

Compare circle graphs to solve a problem

Warm-Up: Display the favorite foods graph. Ask students, “what does the information on this graph tell you?” About how many students like pizza? (Students may try to respond with a number, if so ask, “how do you know?”). What if I told you this was data from Mr. /Ms. ________‟s class and he/she has 25 students. Then would you be able to tell? Allow students a few minutes to determine about how many students like pizza and about how many like hamburgers.

Vocabulary: Circle graph

Data

compare

Before: During this lesson, small groups of students will create circle graphs from a set of data. Students will learn more from this graphing activity if it is tied to something that they care about. The remainder of this lesson is written using an “allergic to red food coloring” scenario.

Tell students you just found out that your daughter/son/niece/etc. is allergic to red (or another color) food coloring. You were supposed to buy snacks for his/her party, and need to know which type of candy has fewer red pieces than the others.

Organize students into 4-5 groups and explain the task to students. “Your job is to find out if the candy your group has would be a good choice. Each of you will create your own graph” You may want to limit the time students spend coloring so they focus their work on collecting and organizing the data.

Give each group a different set of data: skittles, jelly beans, M&Ms, etc. Tell students to create a circle graph that represents their candy.

During: Allow students time to create a circle graph of candy colors. Although students are working with a small group, each student should create his/her own graph. Circulate and note how students are deciding to divide their graphs. If they are struggling with dividing the circle, ask, “how this is like what we did yesterday?” (Students might put their candies in a circle). As you observe students working, make a note of examples you want to bring to the class during discussion. (The discussion should focus on the ways in which students determined how to divide their circle graphs. Note: Have extra copies of circles- students will make mistakes at first. This is an important process for them to go through. If they are allowed to experiment and make mistakes, students will more fully understand how to create and read circle graphs. Keep in mind that the purpose of this is to create a representation of the data. Students do NOT need to divide the total number of candies and find exact percentages. Instead, they should use what they know about fractions (i.e. “I put a line down the middle and made this section yellow because I had 13 yellow candies and there were 25 total candies in our bag. “13 is about half of 25 so I colored half of the graph to show this”.

As students finish creating their graphs, ask them to answer the “Would our group‟s candy be a good choice? Why or why not?” question near the bottom of the activity page. Do not have them answer the last question as it will be used tomorrow. If some students finish their graphs early, you may want to challenge them to graph their data in another way.

After: Bring the students together for a discussion. This should focus on having students share how they decided to divide their circles. Did anyone figure out how many red were in each type?

Homework: Graphing playground activities activity

Lesson #4/5: Allergic to red food coloring!

Type of candy:

Name:

Create a circle graph that displays the candy in your bag. Use color to represent candy colors, but do NOT label the number of candies in each portion.

(Title for your graph)

How many candies did you have in all?

Would our group‟s candy be a good choice? Why or why not?

Look at all of the graphs displayed in the room. Which candy would be the best choice? Why? Write a letter to your teacher that explains which candy she should choose and why she should choose it.

Homework Lesson #4 Name:

A 3rd grade class collected data to find out the most popular activity on their playground. Their data is shown below:

Student Favorite Sport Student Favorite Sport Jacob Kickball Natasha Kickball

Tyler Swings Ty’rese Tag

Shaundra Tag Amaya Kickball

Brandon Kickball Antoine Kickball

Kayla Tag Jin Tag

Jose’ Kickball Absolan Tag

Lucia Swings Marco Kickball

Madison Tag La-Trice Swings

Taylor Kickball Omari Kickball

Ignacio Kickball Cindy Kickball

Organize the data into a table: Then create a Circle Graph:

1. If you surveyed your class, how would the data look different?

2. Do more or less than half of the students like kickball? Explain how you found your answer.

Lesson #5: Using Circle Graphs to Answer a Question Objective: 4.01 Collect, organize, analyze, and display data (including circle graphs and tables) to solve problems

Materials: One small bag of candy for each group of 4 students (Skittles, M&M plain, M&M peanut,

jelly beans,

Rulers- to draw lines on their circle graphs

Copies of Allergic to Red Food Coloring Activity Sheet

Students will:

Collect, organize and display data in a circle graph Compare circle graphs to solve a problem

Communicate through written language

Warm-Up: Addison wants to serve pizza for her birthday party. She wants one type of meat and one type of vegetable on each pizza. The meat choices are pepperoni, sausage and ham. The vegetable choices are peppers and mushrooms. List all the possible pizzas she can make. How many different pizzas can be made? What is the probability that a pizza will have mushrooms on it? Show your work.

Vocabulary: Circle graph

data

compare

more than/less than half

about a fourth or quarter

Before: Remind students that the goal for this activity is to determine which candy is the best choice. Explain to students that they will have a chance to walk around and look at a graph from each group (type of candy). As they walk, they will want to think about which candy is the best choice.

Have a sample of each graph posted around the room. Have students do a gallery walk to view all of the graphs.

During: Direct students‟ attention to the question and task at the bottom of the activity page. “Look at all of the graphs displayed in the room. Which candy would be the best choice? Why? Write a letter to your teacher that explains which candy she should choose and why she should choose it.” Give students time to complete this task. As students work, observe how they determine which is the best choice. - Do they look at the total number of candies and estimate how many reds for each graph? - Do they compare the size of the pieces?

After: Bring the students together for a discussion (This is a vital part of the lesson- make sure to leave at least 20 minutes for it). This should focus on having students share how they chose their candy. If a student doesn‟t suggest using the total number of candies to estimate how many in each portion, ask the students something like, “In the jelly bean graph, I see that more than half of the graph was colored in red. Can we figure out about how many red jelly beans were in their bag?” There were 20 Skittles and about half of the graph was colored in red, so that‟s about 10. Then I looked at the jelly beans and saw that there was a bigger part colored in red.

Homework: Draw a large bull’s eye as shown. Tell students that three

darts hit this target. How many different possible scores could the player

have earned? (It does not matter in what order the darts landed). Make an

organized list of the possible totals. See Blackline Master IV - 2.

Homework Lesson #5 Name: Mr. Dart has 3 darts to throw at the target. How many different possible scores could he earn? (It doesn’t matter in what order the darts landed) Use the table below to help you make an organized list of the possible totals (you might not need to use all of the lines on the table).

1st dart 2nd dart 3rd dart TOTAL

1. How many of the possible scores are even? __________________

2. How many of the possible scores are odd? __________________

2

5

9

Lesson #6: Reading and Analyzing Graphs

Objective: 4.01 Collect, organize, analyze, and display data (including circle graphs and tables) to solve problems

Materials: Computers Graphing Station Cards (several copies of each).

Student journals or notebooks to record their work as they move through each station.

Students will: Solve problems about graphs

Warm-Up: Thomas‟ computer game has a three-digit secret code. The code has a 9, 6 and 4 in it. How many possible secret codes could there be with these three digits? What is the probability that the code will end in an even number? Show your work

Vocabulary: Circle graph

Line plot tally marks (tallies)

data

survey

table

Before: Briefly explain the activity at each graphing station.

During: Have partners circulate through the following graphing stations. Station 1: Collect data, make a table and choose a circle graph (online activity). Station 2: Answer questions about pictographs, line plots, and circle graphs Station 3: Create a circle graph from data given. Station 4: Match line plots and statements. As students work, note how they are solving the word problems in Graphing Station 2. Are they struggling with any of the language? Do their word problems match the line plot? Do use the pictograph key? Also observe as students complete the circle graph. Make note of strategies you see students use that would benefit the rest of the class- you will want to use those during the Classroom Discussion.

After: Briefly discuss graphing ideas with your students. The topic of this discussion will depend upon what your students need. Ask students, “What questions do you have about creating and reading circle graphs? Pictographs? Line Plots?

Homework: Students may need to complete work from graphing stations 2 and 3.

Graphing Station 1 Go to the internet. Type in the following address: http://www.bbc.co.uk/education/mathsfile/shockwave/games/datapick.html Choose level 1 (the other levels are for bar graphs and line plots). Click “Start” Repeat the activity and answer the following questions:

1. What was the subject of your pie chart?

2. What data were you gathering as you made the tally marks?

3. Draw a sketch of your pie chart and label each section:

Graphing Station 2

Third graders were asked a question. Here is what the graph looks like: X X X X X X X X X X X X X X X X X 1 2 3 4 5

Mr. Nelson took an inventory of the kinds of books in his classroom. Animals

History

Friendship

Mystery

6. If Mr. Nelson asks parents to donate books, what type of book do you think he will ask for? Why? 7. How many more Animal books does Mr. Nelson have than Friendship books?

1. What do teenagers spend most of their

money on?

2. Do teenagers spend more money on food or

presents? How do you know?

Key

= 10 books

3. What could this line plot be about?

4. Write a word problem that could be

answered using this line plot.

Graphing Station 3 Eighty 5th graders were asked about their favorite Wii game. The table below shows this data.

Game Number of Students Madden NFL 40

Wii Sports Resort 20

NHL 2K 15

Mario Strikers Charged 5

Create a circle graph that represents this data.

Graphing Station 4 Match each line plot with a statement. Record your answers here: Statement A = Graph __________ Statement B = Graph __________ Statement C = Graph __________ Statement D = Graph __________ Which graph and statement was the easiest to match? Why? Which graph and statement was the most difficult to match? Why?

Graphing Station 4 Cards- Cut apart before presenting to students. Graph 1

x x x x x x x x x x x x x x x x x x x x x x x x x

0 1 2 3 4 5 6 7 8 9 10 11

Statement A

The number

of cavities the sixth graders

have

Graph 2

x x x x x x x x x x x x x x x x x x x x x x x x

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73

Statement B

The heights of the sixth graders in

inches

Graph 3

x x x x x x x x x x x x

x x x x x x x x x x x x

46 47 48 49 50 51 52 53 54 55 56 57 58

Statement C

The ages

of the sixth

graders’ mothers

Graph 4

x x x x x x x x x x x x x x x x x x x x x x x

0 1 2 3 4 5 6 7 8

Statement D

The number of people in the sixth graders’

families

3rd Grade Graphing Assessment NAME:

All 100 students at Westwood school voted for their favorite season. The results are shown in the graph below. 1. How many students chose summer as their favorite season?

2. Which question can be answered from the graph? Fish Caught

Sue Bob Bill

a. Why did Bill get fewer fish? b. What kind of fish did Sue catch? c. How many fish did Bob and Bill catch together? d. Who fished the longest?

4. Smithfield collected cans of soup for a food drive. Use the graph to answer the questions below:

3. How many cans did the third grade collect? a. 2 ½ b. 27 c. 24 d. 5 ½ 4. Which grade levels collected at least 12 cans?

How Often Adults Eat a Salad

5. How often are adults most likely to eat a salad? a. Once or twice a day b. Several times a week c. Once a week d. Less than once a month

6. Elvira recorded the number of seeds she found in each apple.

What could Elvira most likely predict about the number of seeds in apples?

a. most apples have 10 seeds b. most apples have more than 6 seeds c. most apples have less than 6 seeds d. most apples have 5 seeds

#7-10. Gabriela made a circle graph to show the colors of the cars in the school parking lot. She counted 53 red cars, 11 black cars, 15 blue cars, and 21 gray.

Car Colors Fill in the circle graph with the correct color to represent her data.

Rajah made this pictograph to show how many points he scored in each basketball game.

Rajah’s Points

Game 1

Game 2

Game 3

Game 4

If Rajah scored 30 points in game 1, 15 points in game 2, and 18 points in game 3… 11. How many points does each basketball on the graph represent?

12. Edmund and his friends had a contest to see who could do the most sit-ups in one minute. The table below shows their data?

Name Number of sit-ups in one minute

Mike 18

Edmund 14

Charlie 17

Celeste 21

Kelsey 11

How many more sit-ups did Celeste do than Edmund?

13. According to the graph below, which activities do students spend the least amount of time doing? 14. If this graph represents a class of 50 students, about how many students spend time doing homework? 15. about how many students spend time playing computer games?

16. Four students kept a chart of how many books they read in one month. Which picture graph shows the same information as the chart? A.

C

17. Mom is making Billy’s lunch. She has

ham, turkey and pepperoni. She has two

kinds of cheese: cheddar and swiss. Billy

likes one meat and one cheese on his

sandwich. List all the different sandwiches

Billy’s Mom can make.

18. Malika has two pairs of pants and three different shirts.

How many different outfits can she wear?

19. Mrs. Briggs is lining her class up for

lunch. The first three names she called out

were Zach, Jose and Tyler. They all want to

be first in line. What is the probability that

Jose will be number one in line?

20. There is a special code for the door to the office. Mr. Dixon

can’t remember the order of the numbers, but he knows the

three numbers are 2, 9 and 8. What is the probability that the

code will end in an odd number?