# Teacher Lesson Plans - Common Core State Standards

## Teacher Lesson Plans - Common Core State Standards

**Teacher Lesson Plans Common Core State Standards Fourth Edition Volume 1 Daily Lessons for Classroom Instruction MTB4_G3_TG_Vol1_FM_FINAL.indd 1 7/29/13 10:38 PM**

v TLP • Grade 3 Volume 1: Table of Contents Unit 1: Sampling and Classifying Lesson 1: First Names . 1 Lesson 2: Number Line Target . 12 Lesson 3: Kind of Bean . 18 Lesson 4: Who Is Right . 28 Lesson 5: Using Picture Graphs . 33 Unit 2: Strategies Lesson 1: Addition Strategies . 39 Lesson 2: Strategies for Making Tens . 47 Lesson 3: Spinning Sums . 55 Lesson 4: Magic Squares . 66 Lesson 5: Subtraction Facts Strategies .

77 Lesson 6: Spinning Differences . 84 Lesson 7: Workshop: Reasoning from Known Facts . 90 Lesson 8: Assessing the Subtraction Facts . 98 Unit 3: Exploring Multiplication Lesson 1: T-Shirt Factory Problems . 105 Lesson 2: In Twos, Threes, and More . 112 Lesson 3: Multiplication Stories . 121 Lesson 4: Making Teams . 128 Lesson 5: Multiples on the Calendar . 135 Lesson 6: Workshop: Multiplication and Division Stories . 145 MTB4_G3_TG_Vol1_FM_FINAL.indd 5 7/29/13 10:38 PM

vi TLP • Grade 3 Unit 4: Place Value Concepts Lesson 1: Tens and Ones . 151 Lesson 2: Hundreds, Tens, and Ones . 158 Lesson 3: Thousands, Hundreds, Tens, and Ones . 168 Lesson 4: Comparing and Writing Numbers . 182 Lesson 5: Base-Ten Hoppers . 189 Lesson 6: Workshop: Place Value . 196 Lesson 7: Number Sense with Dollars and Cents . 204 Unit 5: Area of Different Shapes Lesson 1: Time to the Nearest Five Minutes . 210 Lesson 2: Measuring Area . 227 Lesson 3: Boo the Blob . 233 Lesson 4: Which Picks Up More . 240 Lesson 5: The Haunted House . 256 Lesson 6: Joe the Goldfish . 262 Lesson 7: Using Number Sense at the Book Sale .

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vii TLP • Grade 3 Unit 6: Adding Larger Numbers Lesson 1: 500 Hats . 276 Lesson 2: The Coat of Many Bits . 285 Lesson 3: Close Enough . 294 Lesson 4: Addition Review . 305 Lesson 5: Addition with Larger Numbers . 320 Lesson 6: Workshop: Addition . 338 Unit 7: Subtracting Larger Numbers Lesson 1: Time Again . 347 Lesson 2: Field Trip . 354 Lesson 3: Subtracting with Base-Ten Pieces . 360 Lesson 4: Paper-and-Pencil Subtraction . 367 Lesson 5: Workshop: Subtraction . 378 Lesson 6: Leonardo the Traveler . 388 Lesson 7: Addition and Subtraction: Practice and Estimation . 401 Lesson 8: Class Party .

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**viii TLP • Grade 3 Volume 2: Table of Contents Unit 8: Multiplication Patterns Lesson 1: Lizardland Problems . 420 Lesson 2: Constant Hoppers . 429 Lesson 3: Handy Facts . 436 Lesson 4: Multiplication and Rectangles . 447 Lesson 5: Completing the Table . 461 Lesson 6: Division in Lizardland . 476 Lesson 7: Stencilrama . 484 Lesson 8: Multiplication Number Sentences . 502 Lesson 9: Multiples of Tens and Hundreds . 521 Lesson 10: Workshop: Strategies for Multiplication Facts . 527 Lesson 11: Midyear Test Review . 537 Unit 9: Parts and Wholes Lesson 1: Kid Fractions . 543 Lesson 2: Circle Pieces: Red, Pink, Yellow, Blue . **

551 Lesson 3: Circle Pieces: Red, Pink, Orange, Aqua . 565 Lesson 4: Folding Fractions . 576 Lesson 5: Circles, Fraction Strips, and Number Lines . 589 Lesson 6: Comparing Fractions . 597 Lesson 7: Workshop: Fractions . 609 MTB4_G3_TG_Vol1_FM_FINAL.indd 8 7/29/13 10:38 PM

ix TLP • Grade 3 Unit 10: Exploring Multiplication and Division Lesson 1: Lemonade Stand . 625 Lesson 2: Operations on a Number Line . 635 Lesson 3: Birthday Party . 641 Lesson 4: Money Jar . 647 Lesson 5: Mr. Green’s Giant Gumball Jamboree . 654 Lesson 6: Walking Around Shapes . 665 Lesson 7: Katie’s Job . 680 Unit 11: Analyzing Shapes Lesson 1: Just Passing Time . 692 Lesson 2: Tangrams . 697 Lesson 3: Tangram Puzzles . 706 Lesson 4: Building with Triangles . 714 Lesson 5: Sorting Shapes . 725 Lesson 6: 3-D Shapes . 736 Lesson 7: Skeletons of 3-D Shapes . 744 Lesson 8: 3-D to 2-D . 752 Lesson 9: Sorting 3-D Shapes .

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x TLP • Grade 3 Unit 12: Measurement and Patterns Lesson 1: Using Coordinates . 777 Lesson 2: Using Maps . 785 Lesson 3: Making Predictions from Best-Fit Lines . 794 Lesson 4: Measuring Mass . 803 Lesson 5: Mass vs. Number . 816 Lesson 6: More Patterns in Data . 827 Unit 13: Multiplication, Division, and Volume Lesson 1: Break-Apart Products with Larger Numbers . 837 Lesson 2: More Multiplication Stories . 848 Lesson 3: Multiplication Models and Strategies . 860 Lesson 4: Solving Problems with Multiplication and Division . 871 Lesson 5: Earning Money . 880 Lesson 6: Elixir of Youth . 891 Lesson 7: Measuring Volume of Containers .

903 Lesson 8: Fill It Up . 914 Lesson 9: Measuring Volume of Solid Objects . 926 Lesson 10: End-of-Year Test . 935 MTB4_G3_TG_Vol1_FM_FINAL.indd 10 7/29/13 10:38 PM

1 UNIT 1 Lesson 1 3.MD.B Represent and interpret data. (3.MD.B.3) MP1. Make sense of problems and persevere in solving them. MP2. Reason quantitatively. MP4. Model with mathematics. MP5. Use appropriate tools strategically. This teacher-guided lab is an exploration of the lengths of students’ first names. The class collects and organizes data in a table and graph so students can make predictions and generalizations about a population; specifically, the length of first names. Content in this Lesson • Identifying variables of an investigation. • Collecting, organizing, and graphing data. • Reading a table or bar graph to find information about a data set [E3].

**• Making predictions and generalizations about a population from a sample using data tables and graphs [E4].**

Assessment in this Lesson Assessment Expectation Assessed Lisa’s Class Graph with Feedback Box Teacher Guide – digital E3. Read a table or scaled graph to find information about a data set. E4. Make predictions and generalizations about a population from a sample using data tables and graphs. Vocabulary in this Lesson • data table • frequency • horizontal axis • most common number • prediction • variable • vertical axis Estimated Class Sessions: 3 First Names First Names TLP • Grade 3 • Unit 1 • Lesson 1 MTB4_G3_TG_U01_FINAL.indd 1 7/29/13 2:00 PM

2 Materials List Materials for Students Daily Practice and Problems Lesson Homework Assessment Student Books Student Guide • First Names Pages 2–6 Student Activity Book • First Names Data Table and Graph Page 3 • Family Names Data Table Page 5 • Family Names Graph Page 7 • Careless Professor Peabody Page 9 Teacher Resources Teacher Guide – digital • DPP Items A–F • Clock • Lisa’s Class Graph 1 each per student Supplies for Students • self-adhesive note Materials for the Teacher • Display of First Names Data Table and Graph page (Student Activity Book) Page 3 • Display of Clock Master (Teacher Guide) • chart paper • Unit 1 Assessment Record Materials Preparation Create a Class Data Table.

Create a table on chart paper to collect student data. See Figures 2 and 3. Create a Class Graph. Prepare to make a large class graph on chart paper. See Figure 4. Professor Peabody’s Broken Clock. Use the Clock Master to make Professor Peabody’s broken clock for DPP item E. Cut out and attach only the hour hand with a brad. TLP • Grade 3 • Unit 1 • Lesson 1 First Names UNIT 1 MTB4_G3_TG_U01_FINAL.indd 2 7/29/13 2:00 PM

3 First Names TLP • Grade 3 • Unit 1 • Lesson 1 Teacher Planning Notes Teacher Planning Notes MTB4_G3_TG_U01_FINAL.indd 3 7/29/13 2:00 PM

4 TLP • Grade 3 • Unit 1 • Lesson 1 Developing the Lesson Developing the Lesson Introduce the First Names Investigation. The First Names pages in the Student Guide provide the setting for this investigation: finding the most common numbers of letters in students’ names in order to write a letter to a computer game company. TIMS Tip! This investigation can also be introduced by reading the book Tikki Tikki Tembo by Arlene Mosel, the story of a Chinese boy who has a very long name that causes several misadventures.

To start the discussion, ask: X What data would help us decide how many letters the game company should allow children to type when they enter their first names? (the number of letters in students’ first names) The answers to the following discussion questions are based on the table on the First Names page in the Student Guide. X Number of Letters in First Name will be one of the variables of the investigation. Who has the largest number of letters in their name in the class? (Christopher) X Who has the smallest number of letters, the shortest name? (The shortest name in the class has 4 letters.

Five students have 4 letters in their name: Dana, Seth, Katy, Ivan, and Eric.) X What number of letters do you think is most common? (seven) Why? (There are more students in the class (10) that have 7 letters in their names than any other number of letters.) X What might influence the length of a name? (Possible response: The length of a name might be different if you are using nicknames instead of names given at birth.) Your students will probably give a variety of responses to the last question. It should become obvious that a definition of “length of name” must be agreed upon. While a study of first and last names is feasible, it is more straightforward to focus on the number of letters in a first name.

Define the Variables. Have the class discuss and choose a definition of the variable Number of Letters in First Name. It is important that the definition be explicit enough to handle all the names in the class, including two-part first names such as Mary Pat. Students should realize that agreeing on a definition is like agreeing on rules for a game. The rules themselves are less important than everyone agreeing on the same rules. The class may decide to allow nicknames or they may agree to use only the names given at birth as data. Either rule is valid as long as it is used consistently. Lesson 1 2 SG • Grade 3 • Unit 1 • Lesson 1 First Names Elizabeth and Miguel like to play computer games.

**One day, they were playing Math-o-Rama. They tried to type their first names, but the game let them type only five letters.**

What number of letters should players be able to type for their names? Elizabeth and Miguel asked their classmates to help them find out. Students wrote their first names on small slips of paper. Then they wrote the number of letters in their names. They put the information in a data table. Here is the data that Elizabeth and Miguel recorded. First Names Letters in First Name Student Guide — Page 2 3 First Names SG • Grade 3 • Unit 1 • Lesson 1 Elizabeth and Miguel made a graph of their data. Elizabeth #L = 9 Seth #L = 4 Dana #L = 4 Katy #L = 4 Ivan #L = 4 Eric #L = 4 Eric #L = 4 Eric #L = 4 Eric #L = 4 L Number of Letters in First Name Frequency of Letters in First Name S Number of Students “Can you see a pattern?” asked Miguel.

“Yes,” said Elizabeth. “No one has a first name with one, two, or three letters.” “That is right!” said Miguel. “And only two kids have more than seven letters in their first name.” You will carry out an investigation called First Names. You will collect data with your class and graph it. First, you will find the number of letters in your classmates’ first names. Then, you will look for patterns in the data. Later, you will use the information to write a letter to a game company about the number of letters that a computer game should allow for a player’s name.

What first names will your class use? Some children in your class might use shortened names, like “Bob” for “Robert.” Others might have two-part names, like “Mary Pat.” Some children might even use nicknames, like “Digger.” Discuss and decide with your class what you mean by “first name.” Student Guide — Page 3 MTB4_G3_TG_U01_FINAL.indd 4 7/29/13 2:00 PM

5 TLP • Grade 3 • Unit 1 • Lesson 1 You must also establish a notation for the variable Number of Letters in First Name. Here again, agreeing is more important than what is agreed upon. We use L to stand for Number of Letters in First Name.

The class can either follow our notation or make up their own. Collect the Data. The next step is to gather the data. To do this, students write their first names on self-adhesive notes, count the letters, and show L by writing “L 5 ” below their names as shown in Figure 1.

JASON L = 5 SETH L = 4 MELISSA L = 7 JORDAN L = 6 Figure 1: Sample notes showing a first name and the number of letters method An efficient way to collect this data is to draw a data table on chart paper and have students arrange their self-adhesive notes on it. See Figure 2. Seth L = 4 Jamie L = 5 Peter L = 5 Jason L = 5 Jason L = 5 Colin L = 5 Aesis L = 5 Brian L = 5 Joseph L = 6 Andrew L = 6 Jordan L = 6 Merley L = 6 Darius L = 6 Zachary L = 7 Dana L = 4 Katy L = 4 Ivan L = 4 Eric L = 4 Number of Letters in First Name Names of Students 1 2 3 4 5 6 7 8 9 10 11 Amanda L = 6 Miguel L = 6 Samuel L = 6 Kristin L = 7 Anthony L = 7 Melissa L = 7 Kenneth L = 7 Kathryn L = 7 Jeffrey L = 7 Melissa L = 7 Nicolas L = 7 Natasha L = 7 Elizabeth L = 9 Christopher L = 11 L Figure 2: A sample data table 4 SG • Grade 3 • Unit 1 • Lesson 1 First Names Collect Write your first name and the number of letters in your name on a slip of paper like those below.

**Discuss with your class what the variable L stands for. Put the class data in a table like the one below. Letters in First Name Discuss with your class how you might make the table easier to read. Then copy the class data onto the data table on the First Names Data Table and Graph page in the Student Activity Book.**

Graph Discuss with your class how to make a class graph of your data. Which variable will you graph on the horizontal axis ? Which variable will you graph on the vertical axis ( )? Use the data table to make a bar graph on the First Names Data Table and Graph page. Student Guide — Page 4 TIMS Tip! Since both variables are numerical (Number of Letters and Number of Students), it is best to avoid using N to stand for either variable. Content Note A variable in an experiment is an attribute or quantity that changes or varies. Every experiment has at least two main variables. In this lab, the two main variables are the Number of Letters in First Name and the Number of Students.

A second definition for the term is a symbol that can stand for a variable. In the Lesson Guide, we have chosen to use L to stand for Number of Letters in First Name and S for Number of Students. In this lesson, it is important to model the correct use of the term variable during class discussions while accepting students’ language in discussions.

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6 TLP • Grade 3 • Unit 1 • Lesson 1 Organize the Data. Once you have the raw data, use the following prompt to begin a discussion: X What do you notice about our data table? What patterns do you see? (Students may notice that no one has a first name with only one letter, that many people have first names that have five or six letters, or that there are few very long or very short names.) After a general discussion, pose specific questions that can be answered directly from the raw data. In your questions, try to use “number of letters” to familiarize students with variable terminology: X Who has the longest name? What is the number of letters in that name?

X Who has the shortest name? What is the number of letters in that name? X Does anyone have a first name with eight letters? X How many students have first names with six letters? five letters? X What number of letters is most common in first names? X Do more than half the students have names with either six or seven letters? Adding a third column to the table with the total number of names in each row will clarify the data. See Figure 3. Review the titles of the first two columns and the information contained in them. Ask: X What information will we put in the third column? (The number of students with each number of letters.) X What title should we give it? Why? (Number of Students works best.

Titling the column “Students” insufficiently describes how the information in that column differs from that in the second column.) X Would N for Number of Students be a good choice to represent this variable? Why or why not? (N might seem logical because it is the first letter of the word number, but this would be confusing because N could also refer to “Number of Letters in First Name.”) When the data table is complete, ask students to work with a partner to answer the following questions using the added information: X If you add all the numbers in the last column, what should they total? What does that number represent? (The sum should equal the number of students in the class.

**Finding the sum and comparing it to the class size is one way to check to see if the data gathering is accurate.) X Do more than half the students have names with either five or six letters? (This is a multistep problem that can be solved different ways. Possible response: First I would add the number of students with either 5 or 6 letters, and then I would add the number of students for all the other number of letters. I can then compare my two answers to see if the number of students with 5 or 6 letters is more than half.) TIMS Tip!**

Save the class graph for use in Unit 3 Lesson 1 T-Shirt Factory Problems. Students solve problems that involve the number of letters in their names. Seth L = 4 Jamie L = 5 Peter L = 5 Jason L = 5 Jason L = 5 Colin L = 5 Aesis L = 5 Brian L = 5 Joseph L = 6 Andrew L = 6 Jordan L = 6 Merley L = 6 Darius L = 6 Zachary L = 7 Dana L = 4 Katy L = 4 Ivan L = 4 Eric L = 4 Names of Students 1 2 3 4 5 6 7 Amanda L = 6 Miguel L = 6 Samuel L = 6 Kristin L = 7 Anthony L = 7 Melissa L = 7 Kenneth L = 7 Kathryn L = 7 Jeffrey L = 7 Melissa L = 7 Nicolas L = 7 Natasha L = 7 Number of Students 7 8 10 5 Number of Letters in First Name L S Figure 3: A portion of a modified data table MTB4_G3_TG_U01_FINAL.indd 6 7/29/13 2:00 PM

7 TLP • Grade 3 • Unit 1 • Lesson 1 Graph the Data. Now that there are two variables, Number of Letters in First Name (L) and Number of Students (S), a graph can be made. The class makes one poster-size graph, and each student makes a graph using the First Names Data Table and Graph page in the Student Activity Book. Ask students to record the Number of Students (S) in the table. Introduce the graph by drawing attention to the elements of a graph, such as the vertical and horizontal axes and the labels for these axes using a display of the First Names Data Table and Graph page.

One way to make a class graph is simply to move the self-adhesive notes onto a labeled graph on a piece of chart paper.

Place the self- adhesive notes on the vertical grid lines rather than in the spaces between them so there will be less confusion later when students make point graphs. Figure 4 shows a graph of the data presented in Figures 2 and 3. Help students read the graph by asking: X Which numbers show the number of letters in the names—those on the horizontal axis or those on the vertical axis? (horizontal axis) X What do the numbers on the vertical axis show? (Number of Students) Seth #L = 4 Jordan #L = 6 Dana #L = 4 Katy #L = 4 Ivan #L = 4 Eric #L = 4 Eric #L = 4 Eric #L = 4 Eric #L = 4 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 Dana L = 4 Eric L = 4 Ivan L = 4 Katy L = 4 Seth L = 4 Zachary L = 7 Kristin L = 7 Anthony L = 7 Melissa L = 7 Kenneth L = 7 Kathryn L = 7 Jeffrey L = 7 Melissa L = 7 Nicolas L = 7 Natasha L = 7 Elizabeth L = 9 L Number of Letters in First Name Frequency of Letters in First Name S Number of Students Joseph L = 6 Andrew L = 6 Merley L = 6 Amanda L = 6 Miguel L = 6 Jordan L = 6 Darius L = 6 Jason L = 5 Colin L = 5 Brian L = 5 Samuel L = 6 Peter L = 5 Jason L = 5 Aesis L = 5 Jamie L = 5 Christopher L = 11 Figure 4: Graphing the data on a bar graph 3 Copyright © Kendall Hunt Publishing Company Name Date First Names SAB • Grade 3 • Unit 1 • Lesson 1 First Names Data Table and Graph Complete the table.

Use the table to make a bar graph. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 Frequency of Letters in First Name Frequency of Letters in First Name S Number of Students Student Activity Book — Page 3 MTB4_G3_TG_U01_FINAL.indd 7 7/29/13 2:00 PM

8 TLP • Grade 3 • Unit 1 • Lesson 1 Explore the Data. At this point, you have two representations of the same data: a data table and a graph. Questions 1–5 of the Explore section in the Student Guide can be answered by reading either the data table or graph. Encouraging multiple solutions lets every student access the problem in different ways and using different representations. Point out that solutions by different methods should agree. If a graph shows that ten people have names with seven letters and a data table shows that there are only nine such names, something is wrong. Ask groups to show how they used each tool to answer Questions 1–5.

**Assign Questions 6–13 in the Student Guide. These questions ask students to extend their interpretation of the data and to make predictions. Ask small groups of students to prepare to share their solutions to one or more problems with the whole class. Question 6 asks students to compare the graph and the data table. The graph and the data table contain the same information in different forms. Both show the number of students who have a given number of letters in their first names. The data table shows the Number of Letters in First Name in the first column and the Number of Students with those numbers of letters in the second column. **

The graph shows the Number of Letters in First Name on the horizontal axis and the Number of Students on the vertical axis. The height of each bar shows the number of students for a given number of letters. Here are some sample student responses to this question taken from Content Note Interpreting data in tables and graphs. Students often have problems distinguishing between variables in an investigation, especially when both of the main variables are numerical. Discussing the Explore questions will help students learn to interpret the graph and data table correctly. Students need to understand when they are talking about Number of Letters and when they are talking about Number of Students.

The following sample dialog of a class discussing Questions 1–4 is based on the data in Figures 3 and 4. Student responses are adapted from a video of a classroom discussion.

Teacher: How many letters are in the longest name? Maya: There are 11. Teacher: Eleven what? Maya: 11 letters. Teacher: How do you know? Where did you look to find that answer? Maya: I looked at the numbers at the bottom of the graph and went across and saw that the last one that went up to a line was 11. Teacher: What do the numbers that go along the bottom of the graph tell you? [Maya looks confused.] Are they the Number of Letters or Number of Students? Jackie: Number of Letters in our names. Teacher: How many letters are in the shortest name? Where can you look to find the answer?

Jacob: Four letters.

I looked at the numbers at the bottom of the graph. Teacher: How did you know it was the shortest? Jacob: Because you look on the graph or the table. Nobody has one, two, or three letters in their names. Then five people have four letters. Teacher: What is the most common number of letters in our names? What is the most common name length? Linda: The number seven. Teacher: Seven what? Linda: Seven letters. Teacher: How do you know? Linda: Because I picked seven and went across and because I looked and seven was the tallest bar.

Teacher: How many students have seven letters in their names? How do you know? Where do you look to find out? Come and show us. Linda: Ten students. You look at the data table and look for the most number of students, and you see it’s ten, and you go over here, and you see that it is seven letters. Teacher: How many students have names with six letters in their names? How do you know? Keenya: You look at the graph where it says Letters and go to where the 6 bar stops, then go up to see the number is 8. Teacher: Where do you go to see the number 8? What does it tell you? Keenya: You go to the left where it says Number of Students.

**5 First Names SG • Grade 3 • Unit 1 • Lesson 1 Explore Use your data to answer the following questions about the first names in your class. 1. How many letters are in the longest name? 2. How many letters are in the shortest name? 3. What is the most common number of letters? 4. How many students have names with four letters? 5. How many students have names with five letters? Discuss Discuss Discuss the following questions with your group. Be prepared to discuss your answers with the class. 6. Compare the graph and the data table. How are they alike? How are they different?**

7. What is the shape of the graph? Why does it have this shape? 8.

Which bars are the same height? Why? 9. Why aren’t there bars above every number on the horizontal axis? What does this mean? Student Guide — Page 5 MTB4_G3_TG_U01_FINAL.indd 8 7/29/13 2:00 PM

9 TLP • Grade 3 • Unit 1 • Lesson 1 a video of students working in groups: Group A “They are alike because they give the same information. They are different because one has rows of numbers and one has bars with numbers and letters.” Group B “They are alike because the graph and the data table have the same data. They have the same stuff in them. They are different because of the different ways of showing the data.” Question 7 asks students to discuss the shape of the graph. While students may describe the shape as stair steps or as a mountain, it is more important to recognize why the bars form that shape.

The bars represent the number of students with very short names on the left and very long names on the right. These names are not as common as names with five, six, or seven letters. The tall bars in the middle represent the length of the most common names. Possible answers for Questions 8–13 are in the answer key. Summarizing the Lesson Summarizing the Lesson To bring the ideas of the lesson together, ask students to review the first two pages in the Student Guide. In a class discussion, ask them to compare Elizabeth and Miguel’s data to your class data. Ask: X What is the most common number of letters in Elizabeth and Miguel’s data? How do you know? (Possible responses: Seven letters because it looks like the most names in the seven row of the data table.

The tallest bar is for seven letters on the bar graph.) X Is it easier to tell how many students have seven letters in their names from Elizabeth and Miguel’s data table or their graph? Why do you think so? (Possible response: The graph is easier because it is easy to pick out the tallest bar and then look where it stops on the left. If the bar reaches ten, then the number is ten.) X What do you think they should do to their data table to make it easier to read? (Possible response: They should add a third column and count the names.) X What should the title of the third column be? (Number of Students) 6 You make predictions every day.

Predictions are statements based on what you know and the patterns you see.

**When the temperature is cold and you see big, dark clouds in the sky, you might predict snowy weather. If you have a bag with more red jelly beans than any other color, you might predict that the next bean you pull from the bag will be red. People look at patterns to see what is most likely to happen. Then they make predictions based on that information. 10. Pretend a new student is coming to class. What can you predict about the length of his or her name? Explain your thinking. 11. How would the graph change if you added all the third-grade classes in your school?**

12. Elizabeth and Miguel are discussing Question 11.

Do you agree with Elizabeth or Miguel? Explain your thinking. 13. How would the graph change if everyone in class added two names from their family? Discuss. 14. What number of letters should computer games allow for first names? Write a letter to the TIMS Game Company to let them know. Describe the investigation you did. Include the results that helped you reach your decision. SG • Grade 3 • Unit 1 • Lesson 1 First Names Student Guide — Page 6 MTB4_G3_TG_U01_FINAL.indd 9 7/29/13 2:00 PM

10 TLP • Grade 3 • Unit 1 • Lesson 1 X Look at Miguel and Elizabeth’s graph and our class graph. How are they alike? How are they different? (Answers will vary. However, students should notice where the tall bars and short bars are located on each graph. There will likely be very short bars for the longest and shortest names. The tall bars will likely center around five, six, or seven letters. Students may also compare the most common number of letters for Elizabeth and Miguel’s data (seven) to the most common number of letters in the class data.) Refer students to and discuss Question 14 in the Student Guide.

This question returns to Elizabeth and Miguel’s original question about a computer game, “What number of letters should players be able to type for their names?” Students should consider both the range of the numbers of letters in the names as well as the most common number of letters.

Distribute the Lisa’s Class Graph Assessment Master from the Teacher Guide. Ask students to complete Questions 1–5 using the graph at the top of the first page. Ongoing Assessment Use the Lisa’s Class Graph Assessment Master and the Feedback Box from the Teacher Guide to assess students’ abilities to describe a data set by interpreting a graph [E3] and to make predictions and generalizations about a population using a graph [E4]. Homework and Practice X Assign the Family Names Data Table and Family Names Graph pages in the Student Activity Book after completing the lab in class. There are two parts to the assignment that can be done on successive nights.

Using the Family Names Data Table, each student collects family first names. On the second evening, he or she graphs the data on the Family Names Graph. Students can also write about how their family graphs compare with the class graph.

X Assign the Careless Professor Peabody page in the Student Activity Book. This page provides practice reading a bar graph. X Assign DPP items A–F. Bits A and C involve partitioning numbers and Task B asks students to write a story for a number sentence. DPP Bit E and Task F provide practice with telling time. Math Facts. DPP Task D asks students to analyze an incorrect solution to a subtraction math fact question. 5 Copyright © Kendall Hunt Publishing Company Name Date First Names SAB • Grade 3 • Unit 1 • Lesson 1 Family Names Data Table Homework Dear Family Member: Help your child collect at least ten first names from your immediate or extended family.

**Count the number of letters in each name. Write each family member’s first name in the Names of Family Members column next to the corresponding number of letters in the name. For example, “James” would be written in the row with “5.” Thank you for your cooperation.**

Collect at least ten ﬁrst names from your family. Count the number of letters in each name. Write each name in the corresponding row. 1 2 3 4 5 6 7 8 9 10 11 L Number of Letters in First Name Names of Family Members Student Activity Book — Page 5 7 Copyright © Kendall Hunt Publishing Company Name Date First Names SAB • Grade 3 • Unit 1 • Lesson 1 Family Names Graph Homework Dear Family Member: In class, we collected data on the number of letters in our first names. We displayed this data in a bar graph. Now, your child is using the data from your Family Names Data Table to create a new bar graph.

Ask your child how this graph compares to the graph made in school.

Thank you for your help. Graph the data from your Family Names Data Table. Use the dotted lines to help you draw the bars. 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 L Number of Letters P Number of People Family Names Student Activity Book — Page 7 MTB4_G3_TG_U01_FINAL.indd 10 7/29/13 2:00 PM

11 TLP • Grade 3 • Unit 1 • Lesson 1 Extensions X Explore the number of letters in full names. (This variable must be defined by the group.) The distribution of Number of Letters (L) for full names will be shifted to the right on the graph and will be more spread out than the first names distribution, allowing some interesting comparisons.

X The class might change the definition of name length. For example, they could count the number of syllables or the number of vowels instead of the number of letters.

X The class can collect additional first names from, for example, another third-grade class. They can add these names to those already collected, or they could treat them separately. The following question explores what might happen if geographic location or culture were changed: X The Tikki Tikki Tembo story gives one interpretation of why Chinese names are shorter than names in other cultures. How might the graph be different for a third-grade class in China? Draw the new graph. 9 Copyright © Kendall Hunt Publishing Company Name Date First Names SAB • Grade 3 • Unit 1 • Lesson 1 Homework Careless Professor Peabody Professor Peabody lost his First Names data table.

**Use the graph to make a new data table. L Number of Letters S Number of Students 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 L Number of Letters Frequency of Letters in First Name Frequency of Letters in First Name S Number of Students 1 2 3 4 5 6 7 8 9 10 11 Student Activity Book — Page 9 MTB4_G3_TG_U01_FINAL.indd 11 7/29/13 2:00 PM**

12 This lesson introduces students to the class number line and their desk number line. These tools will be used by the class throughout the year. Students discuss the similarities and differences between the class number line and their desk number line. They play a game to practice addition and keep score using a number line. Content in this Lesson • Practicing addition. • Representing whole number sums on a number line [E6]. Assessment in this Lesson Assessment Expectation Assessed Observe Number Line Target Game Student Activity Book Page 11 E6. Represent whole number sums on number lines.

3.NBT.A Use place value understanding and properties of operations to perform multi-digit arithmetic. (3.NBT.A.2) MP2. Reason quantitatively. MP6. Attend to precision. Estimated Class Sessions: 1 TLP • Grade 3 • Unit 1 • Lesson 2 Number Line Target Number Line Target Lesson 2 MTB4_G3_TG_U01_FINAL.indd 12 7/29/13 2:00 PM

13 Materials List Materials for Students Daily Practice and Problems Lesson Homework Assessment Student Books Student Guide • Number Line Target Page 7 Student Activity Book • Number Line Target Game Page 11 • Number Line Target Game Boards Page 12 • Number Line Target Game Page 11 Teacher Resources Teacher Guide – digital • DPP Items G–H • Number Line Target Game Boards optional • Number Lines 0–30 2 per student • Number Lines 0–100 2 per student • Home Practice Parts 1–2 Supplies for Students • desk number line (0–100) Supplies for Student Pairs • scrap paper • paper clips, centimeter connecting cubes, or beans to use as markers Materials for the Teacher • Display of Number Line Target Game Boards (Student Activity Book) Page 12 • class number line (0–130) • Unit 1 Assessment Record Materials Preparation Number Lines.

Display the class number line (0–130) where all students can see it and can reach it with a pointer. Tape a number line (0–100) on each student’s desk for use throughout the year. Number Line Target Game Learning Center. Place scrap paper, game markers, and the game directions in a learning center to provide targeted practice. Laminate copies of the Number Line Target Game Boards Master so students can record the moves in a round with a non-permanent marker then wipe them clean for the new round (optional).

Number Line Target TLP • Grade 3 • Unit 1 • Lesson 2 MTB4_G3_TG_U01_FINAL.indd 13 7/29/13 2:00 PM

14 Teacher Planning Notes Teacher Planning Notes TLP • Grade 3 • Unit 1 • Lesson 2 Number Line Target MTB4_G3_TG_U01_FINAL.indd 14 7/29/13 2:00 PM

**15 Before the Lesson Prepare to display and discuss DPP item G: Skip Counting on the Number Line. Developing the Lesson Developing the Lesson Part 1. Introduce the Number Line Compare Number Lines. Direct students’ attention to the class number line and the number lines on their desk. **

Use the following discussion prompts to compare them: X Tell me what you see when you look at the class number line. (It is a line and it has all the numbers from 0 to 130. The numbers are written below dots or points.) X Describe what you see when you look at the number lines on your desk. (It is a line and it has all the fives and tens from 0 to 100. The numbers are written below marks on the line. The biggest marks are for the tens; there are medium marks for the fives, and smaller marks for the rest of the numbers.) X How are the two number lines the same? How are they different? (Possible responses: They are both lines with numbers in order.

The class number line goes up to 130 and my desk number line goes only to 100. The class number line has dots and all the numbers are written below the dots. The desk number line has only the fives and tens written under marks. The numbers for the tens are darker than the numbers for the fives.) X Are all the other counting numbers represented on your desk number line? If so, how? (Possible responses: The numbers are not written, but there are little marks for them. You have to think about what numbers go where for the numbers that are not fives or tens because they are not written below the little marks.) X Is 28 on your number lines? If so, how can you find it? (Possible response: Yes, just go three marks past 25.) X Show me 28 on your desk number line.

How should I count from 25? (Start at 25. Then on 26, say 26, then 27, 28.) Ask a student to point to 28 on the class number line and compare the location of where he or she is pointing to 28 on his or her desk number lines.

Skip Counting on the Number Line. Display and discuss DPP item G. As the class works through the questions, have one student model on the class number line while students use their desk number lines. TLP • Grade 3 • Unit 1 • Lesson 2 TIMS Tip! Use a pointer or meterstick if the class number line is hanging higher than can be easily reached. 11 Copyright © Kendall Hunt Publishing Company Name Date Number Line Target SAB • Grade 3 • Unit 1 • Lesson 2 Number Line Target Game This game is for two players. The object of the game is to be the player that covers the sum equal to or greater than the target number.

Materials: • Number Line Target Game Boards • game markers Directions 1.

Player 1 chooses a target number. Start with a small number, such as 20, and play on Game Board 1. 2. Player 1 covers a number and then Player 2 covers a number. Players track the sum of the covered numbers using the number line. 3. Take turns covering numbers. The winner covers the number that makes the sum equal to or greater than the target number. Variation Play the game using Game Board 2 with a larger target number, such as 100. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 + 5 + 6 + 4 + 8 Student Activity Book — Page 11 MTB4_G3_TG_U01_FINAL.indd 15 7/29/13 2:00 PM

**16 TLP • Grade 3 • Unit 1 • Lesson 2 Part 2. Play Number Line Target Model the Game. Display the game markers and Game Board 1 of the Number Line Target Game Boards page in the Student Activity Book. Referring to the rules on the Number Line Target Game page in the Student Activity Book, demonstrate how to play Number Line Target. Start by circling a target number, such as 20, on the number line. Working with a volunteer, alternate choosing and covering numbers on the game board and showing the sum of the numbers covered on the number line. A completed number line for a game with a target number of 20 is shown in Figure 1. **

Player A covered a 9, Player B covered a 3, and then Player A covered an 8. The winner is the player who covers the number that makes the sum equal to or greater than the target number. Therefore, each player should carefully select numbers so that his or her opponent will not be able to reach or exceed the target number.

Play the Game. Organize the class into pairs to play a few rounds with Game Board 1. Students can record their moves on a copy of the Number Lines 0–30 Master or they can sketch a number line on scrap paper. As students play, check to see that they recorded their moves correctly. After they have learned to record their moves using pencil and paper, they can play by simply moving a marker on the number line on the game board. Once students have played the game a few times with Game Board 1, tell them to play the game with Game Board 2. Students can first record their moves on the Number Lines 0-100 Master or sketch number lines showing only the fives and tens from 0 to 100.

When students are comfortable recording their moves, they can use a marker to track the sums on their desk number lines. Meeting Individual Needs Students can think of adding as hopping on the number line. To solve a problem such as 5 plus 3 they start at 5, then make 3 hops to 8. A common mistake is to include the starting point when they count hops, saying “5, 6, 7” and landing on 7 as the answer. Remind them that to solve 5 1 3, they should start at 5, then hop one move to 6, a second move to 7, and a third move to 8.

12 Copyright © Kendall Hunt Publishing Company Name Date SAB • Grade 3 • Unit 1 • Lesson 2 Number Line Target Number Line Target Game Boards 10 15 25 35 45 55 65 75 85 95 5 20 30 40 50 60 70 80 90 100 Game Board 1 Game Board 2 1 2 3 4 5 6 7 8 9 5 5 10 10 20 20 30 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Student Activity Book — Page 12 TIMS Tip! Laminate the Number Line Target Game Boards so students can record their number line moves with a non-permanent marker then wipe them clean for the next round. Ongoing Assessment Observe students as they are playing the Number Line Target Game.

Note their ability to add whole numbers using a number line [E6]. Put the Number Line Target Game in a learning center to provide targeted practice.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 + 9 + 3 + 8 Figure 1: Keeping track of sums for the game with a target of 20 MTB4_G3_TG_U01_FINAL.indd 16 7/29/13 2:00 PM

**17 TLP • Grade 3 • Unit 1 • Lesson 2 Summarizing the Lesson Summarizing the Lesson Play a game of Number Line Target with a student and ask him or her to explain his or her choices of numbers. Discuss strategies for moving on the number line. Use prompts similar to the following: If a student chooses 20 when the sum is at 30, ask: X How can you move 20 on the number line without counting each one? (Possible response: I count two more tens, 40, 50.) If a student chooses 30 when the marker is on 25, ask: X How can you move 30 on the number line without counting each one? (Possible response: I count by tens starting at 25. **

I know that they will all end in 5, so 35, 45, 55.) Refer students to the vignette on the Number Line Target page in the Student Guide. After describing the game plays between Tanya and Jerome, ask student pairs to discuss Questions 1–3. Homework and Practice X Students can take home the Number Line Target Game Board and related directions from the Student Activity Book and play the game with their families.

X Assign Home Practice Parts 1 and 2. X Assign DPP items G and H. DPP Bit G and Task H develop number sense. Math Facts. Home Practice Parts 1 and 2 provide practice with addition and subtraction math facts. Extension Place the Number Line Target Game in a center for students to play using one of the following game board variations: X Create a game board without twos and threes. After playing, ask students to name a few sums that cannot be made with these numbers missing. X Create a game board with only even numbers and ask students to describe the patterns they notice in the sums. X Create a game board with only odd numbers and ask students to describe the patterns they notice in the sums.

7 Play Number Line Target with a partner. Directions and game board are in the Student Activity Book.

Game Board 1 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 +9 +4 Jerome and Tanya are playing a game called Number Line Target. They are trying to reach or go over the target number of 20 by moving on the number line. Jerome started the game by covering 9 on the game board. He showed his move on the number line. Tanya decided to cover the number 4 on the game board. The sum of 9 and 4 is 13. She added her move to Jerome’s on the number line and landed on 13. Jerome studied the number line.

1. What number should Jerome choose next to reach or go over the target? Explain your thinking.

2. Jerome decides to cover 2 on his next move. Does he reach or go over his target? 3. If Jerome covers 2 on his move, what number should Tanya cover to reach or go over the target? Explain. Number Line Target Lesson 2 Number Line Target SG • Grade 3 • Unit 1 • Lesson 2 Student Guide — Page 7 Teacher Guide — Home Practice Parts 1 and 2 MTB4_G3_TG_U01_FINAL.indd 17 7/29/13 2:00 PM

18 3.MD.B Represent and interpret data. (3.MD.B.3) 3.NBT.A Use place value understanding and properties of operations to perform multi-digit arithmetic. (3.NBT.A.2) MP1. Make sense of problems and persevere in solving them. MP2. Reason quantitatively. MP3. Construct viable arguments and critique the reasoning of others. MP4. Model with mathematics. MP7. Look for and make sense of structure. Students make predictions and generalizations about a population by studying a sample. In the Kind of Bean Lab, students take a scoopful of dry beans from a population of beans. After students sort and count the beans, they record, organize, graph, and analyze their data.

**Content in this Lesson • Representing and using variables of an investigation [E1]. • Drawing scaled bar graphs from a table [E2]. • Reading a table or scaled graph to find information about a data set [E3]. • Making predictions and generalizations about a population from a sample using data tables and graphs [E4]. • Communicating reasoning and solutions verbally and in writing [MPE5]. • Representing whole number sums on number lines [E6]. Assessment in this Lesson Assessment Expectation Assessed Math Practices Expectation Assessed Kind of Bean Lab Picture Student Activity Book Page 13 E1. **

Represent the variables and procedures of an investigation in a drawing.

Kind of Bean Lab Graph Student Activity Book Page 14 E2. Draw scaled bar and picture graphs from a table. Kind of Bean Lab Check-In: Questions 7–11 with Feedback Boxes Student Activity Book Pages 16–19 E2. Draw scaled bar and picture graphs from a table. E3. Read a table or scaled graph to find information about a data set. E4. Make predictions and generalizations about a population from a sample using data tables and graphs. MPE5. Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking.

DPP Item L Playing Number Line Target Teacher Guide – digital E6.

Represent whole number sums on number lines. TLP • Grade 3 • Unit 1 • Lesson 3 Kind of Bean Estimated Class Sessions: 3 Kind of Bean Lesson 3 MTB4_G3_TG_U01_FINAL.indd 18 7/29/13 2:00 PM

19 Vocabulary in this Lesson • certain event • horizontal axis • impossible event • likely event • population • sample • scaled graph • unlikely event • value • variable • vertical axis Materials List Materials for Students Daily Practice and Problems Lesson Homework Assessment Student Books Student Guide • Kind of Bean Pages 8–11 • Math Practices Reference Student Activity Book • Kind of Bean Lab Pages 13–19 • Toni’s Candy Grab Page 21 • Kind of Bean Lab Picture Page 13 • Kind of Bean Lab Graph Page 14 • Kind of Bean Lab Check-In: Questions 7–11 Pages 16–19 Teacher Resources Teacher Guide – digital • DPP Items I–N • DPP Item L Playing Number Line Target Supplies for Student Groups • small container such as a margarine tub or yogurt cup Materials for the Teacher • Display of the Kind of Bean Lab Graph (Student Activity Book) Page 14 • large container of mixed beans • 1 4–cup scoop or 4-oz.

paper cup • 3 kinds of beans. See Materials Preparation. • self-adhesive notes • Unit 1 Assessment Record Materials Preparation Create a Bean Population. Create a bean population by selecting three different types of beans. Label a large container “bean population.” Fill a large container with the three types of beans and mix them thoroughly. Students should not be told this recipe. Each type of bean should be approximately the same size, and each type should be easily distinguishable from the others. It is important that the mixture have one type of bean that is most common, e.g., 1 pound of red beans, 2 pounds of navy beans, and 4 pounds of pinto beans.

**Kind of Bean TLP • Grade 3 • Unit 1 • Lesson 3 MTB4_G3_TG_U01_FINAL.indd 19 7/29/13 2:00 PM**

20 Developing the Lesson Developing the Lesson Part 1. Analyze Population Problems Use Sampling and the TIMS Laboratory Method to Study Populations. This lab involves learning about a population through sampling. Students will sample a collection of three types of beans to model sampling an animal population. Begin by discussing important applications such as estimating wildlife populations. Explain that sampling may be applied to situations closer to students’ lives.

For example, they can estimate the number of squirrels, pigeons, cats, or dogs in their neighborhoods.

Use the Kind of Bean pages in the Student Guide to depict the use of the sampling process and the four steps of the lab method to investigate a population. These pages illustrate an important point: Even when a population cannot be directly studied, we can still draw some conclusions about that population by sampling it and doing some clever thinking. Content Note Meanings of “Population.” The word population has more than one meaning. In statistics (and in this lesson), a population is the group of people or things being studied, such as the group of people who live in a particular city or animals in the rain forest.

Students may be more familiar with the use of population to mean the number of people who live in a country, city, or other region, such as the population of Seattle.

Represent Sample Population Data. Questions 1–3 discuss the variables in the scientists’ investigation of animals in the rain forest. Identifying the variables is an important part of any experiment. Questions 4–5 help students distinguish between the variables and the values of those variables. In the Robinsons’ experiment, the values of the variable Type of Animal are the names of the animals they chose to study: spider monkeys, squirrels, river otters, armadillos, and jaguars. The values of the variable Number of Animals are the numbers of the animals they counted while conducting the experiment.

These are recorded in the second column of the data table.

**Question 6 asks students to examine the vertical axis and the way it is scaled. Make sure students understand that there are values between each of the points on the vertical axis. For example, the bar representing 230 Spider Monkeys stops slightly above the value of 225. TLP • Grade 3 • Unit 1 • Lesson 3 8 Sampling a Population What is a population? A population is a group or collection of things. The population of your city or town is the group of people who live there. Sometimes, a population is too big to study or too hard to count. Then you study a sample of the population. A sample is a smaller group or part of the whole population.**

Say you want to learn about the population of pets in your town. You can begin by counting the number of dogs, cats, birds, and other pets on your block. Using this information, you can predict the kinds of pets that people have in your town. You can also use your data to predict which pet is the most common in your town or neighborhood. Kind of Bean SG • Grade 3 • Unit 1 • Lesson 3 Kind of Bean Lesson 3 Student Guide — Page 8 9 A Sample of Animals Betty Robinson and her scientist parents are studying animals in the Amazon Rain Forest. The population of animals in the rain forest is very large, so Betty and her parents study a sample of the animals.

They have chosen a small area of the forest to investigate. They identify the types of animals they see in this area and count the number of each type of animal. The two main variables in their experiment are the type of animal and the number of each type.

They use the TIMS Laboratory Method to help them solve problems. First, they draw a picture of the steps they will follow in the experiment. Then, they collect and organize the data in a data table. Next, they graph their data. Finally, they analyze and discuss their results. When you have a problem, you, too, can use the tools of science to solve it. We call these tools of science the TIMS Laboratory Method. Kind of Bean SG • Grade 3 • Unit 1 • Lesson 3 Number of Each Animal Type Student Guide — Page 9 MTB4_G3_TG_U01_FINAL.indd 20 7/29/13 2:00 PM

21 Make Predictions about the Population.

Question 7 provides practice in reading a bar graph similar to the one students will make and read later in the lesson. Question 8 asks them to make a prediction about the population from the sample data. Draw attention to the features of the data table and graph: X column headings in the data table indicate the variables—type of animal and number of animals X the symbols N and T are used to stand for the variables X the labels on the horizontal axis and vertical axis indicate the variables being studied X the values for type of animal on the horizontal axis X the scaling for the values on the vertical axis X bars that accurately reflect the data X title of the graph Part 2.

Kind of Bean Lab Identify the Variables. Distribute a small container to each pair of students. One student from each pair should take a 1 4-cup scoop of beans from the large container you prepared and put it in their small container. Tell students that this is their sample of the population of beans. Relate the bean sample population in their container to the animal sample population in the rain forest. Tell students they are going to study their population of beans the same way the Robinsons studied the animals in the rain forest. The following questions can help guide the discussion: X How can we classify or sort the beans? (We can sort by color or by kind of bean.) X What kinds of beans are in the population? (Students may not know the name of the different beans but may distinguish them by color.) X The Robinsons studied a population of animals in the rain forest.

**We want to conduct an experiment to study our population of beans. If our experiment is like the Robinsons’, what two variables would we study? (Kind of Bean and Number of Beans) X What are the values of the variable “Kind of Bean”? (In our example, the values are black, navy, and pinto.) X What are the values of the variable “Number of Beans” before we do the experiment? (We don’t know. We can take a sample from the population of beans and count the number of each kind of bean.) TLP • Grade 3 • Unit 1 • Lesson 3 10 SG • Grade 3 • Unit 1 • Lesson 3 Kind of Bean Here is the graph of the Robinsons’ data. **

Spider Monkeys Squirrels River Otters Armadillos Jaguars A Sample of Animals T Type of Animal N Number of Animals Discuss Discuss 1. What variables do the letters T and N stand for? 2. What variable is on the horizontal axis ( )? 3. What variable is on the vertical axis ( )? 4. At the beginning of the experiment, the Robinsons chose values for the variable Type of Animal. Two of these values are Spider Monkeys and Jaguars. What are the other values for this variable? 5. What values for the variable Number of Animals did the Robinsons record in their data table?

6. Look at the vertical axis on the graph the Robinsons made to display their data. How did they scale this axis? Why do you think they chose to do it this way? 7. What is the most common animal in the sample? Least common? 8. Predict which two animals are the most common in the whole population. Conduct a similar experiment using a bean population instead of different animals in the rain forest. Use the Kind of Bean Lab pages in the Student Activity Book and the TIMS Laboratory Method. Pull a sample of beans from a container and count the number of each kind of bean. Use the data to predict which kind of bean is the most common and which is the least common in the bean population.

Student Guide — Page 10 Content Note Scaling a Graph. Since the range of values for the Number of Animals is so large, the vertical axis of the graph must be scaled so that all values can be represented. For this graph a scale of 25 was chosen. When a graph is scaled by a value other than 1, it is understood that there are values between each of the points on the vertical axis. For example, the bar representing 230 Spider Monkeys stops slightly above the value of 225.

MTB4_G3_TG_U01_FINAL.indd 21 7/29/13 2:00 PM

22 X How can we predict the most common kind of bean or the least common kind of bean without counting all the beans? (Count each kind of bean in a sample. If there is a lot more of one kind of bean in the sample, then it is likely there is a lot more of that kind of bean in the population.) Draw the Picture. Refer students to the Kind of Bean Lab pages in the Student Activity Book. To begin, explain to students that they will draw a picture of the experiment that shows the variables and what they will do to collect their data.

This is the first step in the TIMS Laboratory Method.

**Discuss what makes a good picture. Although aesthetics is part of what makes a good picture, it is more important scientifically to communicate procedures, show equipment, identify variables, and establish notation. See Figure 1. Note that this student showed the three kinds of beans, the procedure of filling the scoop with beans, and sorting them by kind. He also labeled the variables with “K” for Kind of Bean and “N” for Number of Beans. Direct students to each complete a drawing in the Draw section on the Kind of Bean Lab page.**

Figure 1: A sample picture Collect the Data. Collecting the data is step two of the TIMS Laboratory Method.

Begin by having students fill out the first column of the data table with the names of the kinds of beans. Since students have already taken a sample of the population, the pair should sort and count them and complete the data table in the Collect section in the Student Activity Book. Ongoing Assessment Use the picture on the Kind of Bean Lab in the Student Activity Book to assess students’ abilities to represent the variables and procedures of an investigation in a drawing [E1].

TLP • Grade 3 • Unit 1 • Lesson 3 13 Copyright © Kendall Hunt Publishing Company Name Date Kind of Bean SAB • Grade 3 • Unit 1 • Lesson 3 Kind of Bean Lab Use the TIMS Laboratory Method to investigate the population of beans. Draw Draw a picture of the lab setup. Show the variables and the materials you will use. 1. What are the two main variables in your experiment? and Collect Collect the data. Use your scoop to take a sample from the container. Record the number of each kind of bean in the table. N Kind of Bean Student Activity Book — Page 13 14 Copyright © Kendall Hunt Publishing Company Name Date SAB • Grade 3 • Unit 1 • Lesson 3 Kind of Bean Graph Make a bar graph of your results.

Remember to label the graph. Student Activity Book — Page 14 MTB4_G3_TG_U01_FINAL.indd 22 7/29/13 2:00 PM

23 Graph the Data. The third step of the TIMS Laboratory Method is graphing the data. Many relationships between variables become more evident on a graph. Remind students to label their graph with an appropriate title and to label each axis with the name of the variable and a letter to stand for the variable. Students should label the horizontal axis with the names of the three types of beans in their population. Remind students that because the range of data for the Number of Beans is so large the vertical axis will need to be scaled by something other than one. Ask students to discuss how the vertical axis could be scaled so that all of their data can be accurately shown on their graphs.

Students should use the dotted lines as guides and the bars should accurately reflect the data in the table. See Figure 2. Ask the class to compare students’ graphs.

**X Which bar is the tallest on most of the graphs? (Since there are different quantities of each type of bean in the mixture, you can expect that the tallest bar will represent the type of bean that has the largest quantity in the mixture.) X Which is the shortest? Why? (The shortest bar will likely represent the bean that was the smallest quantity in the mixture. It is reasonable to expect the sample to be similar to the total population being studied.) Ongoing Assessment Use the graph from the Kind of Bean Lab pages in the Student Activity Book to assess students’ abilities to draw a scaled bar graph from a table [E2].**

Explore the Data. The fourth step in the TIMS Laboratory Method is exploring the data through a series of questions. Questions 2–6 in the Student Activity Book ask students to interpret the data literally. The answers can be found either in the data table or on the graph. Since student groups will have different data, their answers will differ. A Second Sample. In Check-In: Questions 7–10, students are asked to make predictions about the beans represented in a second sample using the same scoop. Before asking students to work on Question 7, use the Math Practices page in the Reference section of the Student Guide and the following prompts to guide a discussion about the math practices: X What tools or strategies can you use to guide your predictions? (Students can use their data table and their graph from their first sample to help guide their predictions.) X What should you remember when you are writing about your predictions? (Explanations should be clear and complete so that other people can tell what students are thinking.) TLP • Grade 3 • Unit 1 • Lesson 3 467 Reference SG • Grade 3 Math Practices Solving a problem: Showing or telling how I solve a problem: 1.

Know the problem. I read the problem carefully. I know the questions to answer and what information is important. 2. Find a strategy. I choose good tools and an efficient strategy for solving the problem. 3. Check for reasonableness. I look back at my solution to see if my answer makes sense. If it does not, I try again. 4. Check my calculations. If I make mistakes, I correct them.

5. Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking. 6. Use labels. I use labels to show what numbers mean. The question tells me . I need to find out . I used convenient numbers to estimate like this . Then I compared my answer to my estimate. To check this: 715 – 350 = 365 I did this: 365 + 350 = 715 ✓ Cars 1 2 3 Cost 3 6 9 Step 1 . Step 2 . Step 3 . Is there a pattern? What operations should I use? Is there a more efficient way? What tools should I use? 0 2 4 6 Cars 1 2 3 Cost 3 6 9 I check my calculations with a calculator. $5 12 cars 36 inches 155 miles 9 days 4 apples 3 $ 1 2 58 + 19 = 77 chairs Graphs Tables Words Number Sentences I show each step of my work using: “First, I added up the total number of chairs because .

” Student Guide — Reference Kind of Bean A Sample of Beans Number of Beans Black Navy Pinto 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 N K Figure 2: A sample graph MTB4_G3_TG_U01_FINAL.indd 23 7/29/13 2:00 PM

24 Ask students to answer Questions 7A–C independently. While students are working, prepare for groups to take a second sample by putting their first samples back into the large population container. Student responses for Question 7C should be straightforward and include using their data table and/or their graph of the first sample to make their predictions. A possible prediction: X “I used my graph to make my predictions. The tallest bar on my graph showed the most common bean was the Black Bean and the shortest bar was for the Navy Bean. Since the second sample will come from the same container, I think the same thing will happen.” Question 8 directs students to take a second sample using the same scoop.

Ask one student from each pair to take a second sample of beans from the large container holding the bean population. After sorting and counting the beans in their sample bean population, students are asked to represent their sample population data in a table (Question 8) and a graph (Question 9) and to describe the most common kind of bean in the sample (Question 10). Ongoing Assessment Use Check-In: Questions 7–11 and the Feedback Box on the Kind of Bean Lab pages in the Student Activity Book to assess students’ abilities to draw a scaled bar graph from a table [E2]; use a data table and graph to find information about a data set [E3]; and make predictions and generalizations about a population from a sample using a data table and graph [E4].

**Use Check-In: Question 7C to assess students’ abilities to show or tell how they arrived at their answer so someone else can understand their thinking [MPE5].**

In Question 11, students are asked to tell if their predictions for their second sample were correct and to explain why or why not. A scientist would expect another pull from the same bean sample to be similar to the first pull. However, it is possible that a second sample could yield different results. Even if this does happen, it is the reasoning behind the prediction that is important. The following paragraph shows a sample student response for a student whose prediction was not accurate. X “I predicted that I would have the most Black Beans and the least Navy Beans. When I took the second scoop I did have the most Black Beans but this time my least was Pinto Beans.

I think this happened because the beans weren’t mixed up all the way.” TLP • Grade 3 • Unit 1 • Lesson 3 15 Copyright © Kendall Hunt Publishing Company Name Date Kind of Bean SAB • Grade 3 • Unit 1 • Lesson 3 Explore Answer the following questions using your data table and graph. 2. A. What kind of bean is most common in your sample? B. How many do you have of this kind of bean? 3. A. What kind of bean is least common in your sample? B. How many do you have of this kind of bean? 4. How many more of the most common beans do you have than the least common? Show or tell how you know.

5. What is the total number of beans in your sample? 6. Show or tell how you found the answer to Question 5. Student Activity Book — Page 15 16 Copyright © Kendall Hunt Publishing Company Name Date SAB • Grade 3 • Unit 1 • Lesson 3 Kind of Bean A Second Sample Check-In: Questions 7–11 7. You are going to collect a second sample with the same size scoop. A. Predict which kind of bean will be the most common. B. Predict which kind of bean will be the least common. C. Show or tell how you decided.

8. Collect a second sample with the same size scoop. Count the beans and record your data in the table.

C N Second Sample Student Activity Book — Page 16 MTB4_G3_TG_U01_FINAL.indd 24 7/29/13 2:00 PM

25 Population Predictions. In Questions 12–13, students use their sample data to make predictions about the bean population. Students can work with their groups to discuss their thinking before completing the questions. In Question 13, students are asked to think about how the data in their data table and graph will change if they used a larger scoop to pull their sample. Students should articulate that while the number of beans pulled will be larger, the most and least common type of bean would likely remain the same for this sample. This will be reflected in both the data table and the graph.

Part 3. Describe Events: Impossible, Unlikely, Likely, and Certain Define Descriptions. Display the words “impossible,” “unlikely,” “likely,” and “certain” from left to right across the board. Explain that they can be used to describe whether something will happen. Students should discuss what the words mean with a partner or in small groups. After allowing time to think about the words, ask groups to share their definitions. Here are some sample answers: X Impossible: “I am sure it cannot happen.” X Unlikely: “It probably will not happen” or “It will not happen very often.” X Likely: “It probably will happen” or “It will happen most of the time.” X Certain: “I am sure it will happen.” Brainstorm a class list of events that are impossible, unlikely, likely, and certain.

As students suggest events, write some on self-adhesive notes and ask volunteers to place the notes near the appropriate word on the board. After a few examples, have students write their own events and place their notes on the board. They might not agree on how to classify some events. For example, in one class a student was certain that “I will do my homework tonight.” It was difficult for her to imagine that unforeseen circumstances such as a power failure, illness, etc., could prevent that. Words such as “very likely” and “very unlikely” might help the class reach a consensus. Adhesive notes can be moved toward the right or left side of the board depending on how likely the events are.

**Here are some sample events: X Impossible: “I will grow wings tonight” or “My dog will swim across the ocean.” X Unlikely: “It will snow in Chicago in May” or “Three students will be named José in one classroom.” X Likely: “We will have school on Tuesday” or “We will eat lunch today.” X Certain: “The sun will come up tomorrow” or “Ice cubes will melt if I leave them outside on a hot day.” TLP • Grade 3 • Unit 1 • Lesson 3 17 Copyright © Kendall Hunt Publishing Company Name Date Kind of Bean SAB • Grade 3 • Unit 1 • Lesson 3 9. Graph your data.**

10. A. What kind of bean is most common in this sample? B. What kind of bean is least common in this sample? Student Activity Book — Page 17 18 Copyright © Kendall Hunt Publishing Company Name Date SAB • Grade 3 • Unit 1 • Lesson 3 Kind of Bean 11. Were your predictions in Question 7 correct? Why or why not? Population Predictions 12. Use your data to make predictions about the bean population (all of the beans in the class container). Predict which bean is the most common and which bean is the least common. Tell why you think so. 13. Suppose you use a much larger scoop to take a sample. A.

How will the data in your data table change? B. How will your graph change?

Student Activity Book — Page 18 MTB4_G3_TG_U01_FINAL.indd 25 7/29/13 2:00 PM

26 Describe Kind of Bean Events. Discussion Questions 9–10 in the Student Guide follow a short paragraph containing definitions of the terms used to describe the likihood of an event. Question 9 asks each group to imagine pulling out one bean from the bean population. They use their data to predict what type of bean is most likely to be pulled out. Encourage each group to be ready to explain their prediction. The type of bean that is most common in their sample and in the bean population is the most likely to be pulled—the type of bean with the highest bar on their graph.

Question 10 then asks each student to pull out just one bean from the bean population and return it. Most students will pull the type they predicted, but some might not. Since the event “pulling out the most common bean” is likely but not certain, it may not happen every time, but it will happen most of the time. Summarizing the Lesson Summarizing the Lesson To review the big ideas of the lesson, ask students to look back at Betty Robinson’s data in the Sample of Animals section in the Student Guide. Ask students to discuss the following questions in groups and then be ready to share their thinking with the rest of the class.

X What variables are Betty and her parents investigating? (Type of Animal and Number of Animals) X Explain the Robinsons’ investigation. If they had to draw a picture to show their investigation, what would they draw? (They should show the two variables. They would show pictures of each Type of Animal in the study and label that part of the picture with a T. Then to show that they counted to find the Number of Animals, they could show tallies beside the animals and label the tallies with an N.) X If you were able to help Betty collect data on the animals in the same area of the forest, which is more likely—that you would see an armadillo or a river otter? How do you know? (It would be more likely to see an armadillo because the Robinsons recorded seeing more armadillos than otters in the data table.

**The armadillo bar is taller than the river otter bar.) TLP • Grade 3 • Unit 1 • Lesson 3 19 Copyright © Kendall Hunt Publishing Company Name Date Kind of Bean SAB • Grade 3 • Unit 1 • Lesson 3 Kind of Bean Lab Check-In: Questions 7–11 Feedback Box Expectation Check In Comments Draw a scaled bar graph from a table. [Questions 8–9] E2 Read a table or scaled graph to ﬁnd information about a data set. [Questions 10 A–B] E3 Make predictions and generalizations about a population from a sample using data tables and graphs. [Questions 7A–B and 11] E4 Yes .**

. . Yes, but . . . No, but . . . No . . . MPE5. Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking. [Question 7C] Student Activity Book — Page 19 11 Kind of Bean SG • Grade 3 • Unit 1 • Lesson 3 A Sample of Beans: Impossible, Unlikely, Likely, and Certain Some things are certain. You know they will definitely happen. Other things are likely. They will probably happen, but they might not. Still other things are unlikely. They can happen, but they will not happen very often. Finally, some things are impossible. They can never happen. Discuss Discuss After you have completed the Kind of Bean Lab, discuss the questions below.

9. Imagine you pull out one bean from the bean population container. What type of bean are you most likely to pull out? Use your data to predict. Be ready to explain your thinking. 10. Now test your prediction by pulling out one bean and returning it. A. Was it the type you predicted? B. Discuss with your class what happened when other groups pulled one bean. Did every group pull the bean that was most likely? C. If an event is likely, will it happen every time? Most of the time? Student Guide — Page 11 MTB4_G3_TG_U01_FINAL.indd 26 7/29/13 2:00 PM

27 X How many more armadillos than river otters did the Robinsons see? How do you know? How can you use the graph to solve the problem? (125 more armadillos than otters.

Possible strategy: I looked at the data table and knew that I needed to subtract 75 from 200. I thought of money and counted up by 25. You need one more 25 to get to 100 and four 25s to get to 200, so 125 more armadillos. Each line on the graph stands for 25, so you can count up by 25s from the top of the otter bar to the top of the armadillo bar.) X Is it certain that you would see a spider monkey? Why or why not? (No, it is not certain, but since the spider monkeys were the most common animals in the sample, it is likely.) X How likely is it that you would see a dinosaur in the Amazon rain forest? Why or why not? (Since dinosaurs are extinct, this is impossible.) Homework and Practice X Assign the Toni’s Candy Grab page in the Student Activity Book.

This page requires students to graph and analyze sample data just like the lab.

X Assign DPP items I–N. DPP Bit I provides practice with elapsed time. Task J provide practice with adding on number lines.Tasks L and N develop mental math strategies for addition. Math Facts. DPP Bits K and M provide practice with mental math strategies for addition. TLP • Grade 3 • Unit 1 • Lesson 3 21 Copyright © Kendall Hunt Publishing Company Name Date Kind of Bean SAB • Grade 3 • Unit 1 • Lesson 3 Toni’s Candy Grab Homework 1. Toni filled a bag with red, green, and blue candy. She reached inside and took out a sample. Graph the data she wrote in the table. 2. How many candies did she grab in her sample ? 3.

**Toni reaches inside her bag again and pulls out only one candy. Use the words impossible, unlikely, likely, or certain to describe the following events: A. She pulls out a blue candy. B. She pulls out a red candy. C. She pulls out a piece of candy. D. She pulls out a yellow candy. red green blue 39 12 5 Toni’s Data • Title the graph. • Label the axes. • Scale the vertical axis. Student Activity Book — Page 21 MTB4_G3_TG_U01_FINAL.indd 27 7/29/13 2:00 PM**

28 Students analyze and graph bean population data similar to the Kind of Bean Lab data from Lesson 3. Students compare data representations to determine which data matches a mystery tub of beans. Content in this Lesson • Reading a table or scaled graph to find information about a data set [E3]. • Making predictions from samples [E4]. • Communicating solution strategies verbally and in writing [MPE5]. • Demonstrating fluency with the addition facts [E7]. Assessment in this Lesson Assessment Expectation Assessed Math Practices Expectation Assessed Which Tub? with Feedback Box Teacher Guide – digital MPE5.

Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking.

DPP Item O Addition Facts Quiz: Doubles, 2s, and 3s Teacher Guide – digital E7. Demonstrate fluency with the addition facts. Vocabulary in this Lesson • population • sample 3.MD.B Represent and interpret data. (3.MD.B.3) MP2. Reason quantitatively. MP3. Construct viable arguments and critique the reasoning of others. MP4. Model with mathematics. MP7. Look for and make sense of structure. Estimated Class Sessions: 1 Lesson 4 Who Is Right? TLP • Grade 3 • Unit 1 • Lesson 4 Who Is Right? MTB4_G3_TG_U01_FINAL.indd 28 7/29/13 2:00 PM

29 Materials List Materials for Students Daily Practice and Problems Lesson Homework Assessment Student Books Student Guide • Who Is Right? Page 12 • Math Practices Reference Teacher Resources Teacher Guide – digital • DPP Items O–P • Home Practice Parts 3–4 • Which Tub? • Which Tub? Feedback Box • DPP Item 0 Addition Facts Quiz: Doubles, 2s, and 3s Materials for the Teacher • Display of the first page of the Which Tub? Assessment Master (Teacher Guide) • Unit 1 Assessment Record • Math Facts Class Record Who Is Right? TLP • Grade 3 • Unit 1 • Lesson 4 MTB4_G3_TG_U01_FINAL.indd 29 7/29/13 2:00 PM

30 Teacher Planning Notes Teacher Planning Notes TLP • Grade 3 • Unit 1 • Lesson 4 Who Is Right? MTB4_G3_TG_U01_FINAL.indd 30 7/29/13 2:00 PM

31 Developing the Lesson Developing the Lesson Compare Samples. Use the Who Is Right? page in the Student Guide to extend students’ understanding of taking a sample from a population. In the vignette, two groups of students each take a sample from the same bean population. When the two groups sort their samples, they find that their results are slightly different. Students work with a partner or in a small group to discuss Questions 1 and 2.

**After they have had time to work, ask students to share their thinking with the whole class.**

Students’ responses to Question 1 will vary. Look for the following points in explanations: X The numbers for the same type of bean in their data tables are close. X Pinto beans are the most common in both samples. Navy beans are the least common in both samples. X The total number of beans in both samples is close, since both pairs used the same scoop. Tara and Kim pulled 211 and Mark and Jason pulled 217. In Question 2, students are asked to decide if one of the groups could have made a mistake. Ask: X Did one of the pairs make a mistake? Or could they both have correct data? (The data for both the girls and the boys are correct.

Each pair took their own sample, so Tara and Kim should not expect their numbers for each type of bean to be exactly the same as Mark and Jason’s. The numbers should be close since they were both taken from the same container of beans with the same scoop.) Students should understand that since the answers depend on data collected, different data can often lead to different answers. Which Tub? Provide each student with a copy of the Which Tub? Assessment Master from the Teacher Guide. Introduce the problem by reading and displaying the short vignette at the top of the page. Refer to the Math Practices page in the Reference section of the Student Guide to review Math Practices Expectation 5, Show my work.

Ask: X What do you need to include so someone else will be able to understand your thinking? (Possible student responses: I need to make sure I answer the question that is asked; tell what tools I use to decide which tub was Tara and Kim’s; or tell or show each step I take to answer the question.) Ask individuals to work on the Which Tub? page while keeping Math Practices Expectation 5 in mind. Use the Feedback Box to provide students feedback on their ability to show their thinking. TLP • Grade 3 • Unit 1 • Lesson 4 12 SG • Grade 3 • Unit 1 • Lesson 4 Who Is Right? Lesson 4 Who Is Right? Discuss Discuss A third-grade class did the experiment Kind of Bean.

Tara and Kim were partners, and Mark and Jason were partners.They used the same container of beans and the same scoop. Each pair took their own sample. Their data tables are below. The girls and boys compared their data. The girls said, “Oh, no! One of us must have done it wrong. Our answers do not match!” K Kind of Bean N Number of Beans Pulled Pinto Black Navy 112 73 26 Tara and Kim K Kind of Bean N Number of Beans Pulled Pinto Black Navy 114 75 28 Mark and Jason 1. Look at both data tables. What patterns do you notice? 2. Did one of the pairs make a mistake? Or could they both have correct data? Show or tell your thinking.

Student Guide — Page 12 Ongoing Assessment Use the Which Tub? Assessment Master and the Feedback Box to assess students’ progress toward showing or telling how they arrived at an answer so someone else can understand their thinking [MPE5]. TIMS Tip! Students can use the feedback you provide on the Which Tub? Feedback Box to make revisions to their work. MTB4_G3_TG_U01_FINAL.indd 31 7/29/13 2:00 PM

32 TLP • Grade 3 • Unit 1 • Lesson 4 Summarizing the Lesson Summarizing the Lesson Ask students to look back at Who Is Right? in the Student Guide. Ask: X Tara and Kim’s data was different from Mark and Jason’s data, but both of their data tables were correct.

**How can that be? (Possible response: Each of the pairs took their own sample, so the numbers will not be exactly the same, just close.) X What are some of the patterns in the data table that help you know that both data tables are correct? (Possible response: Both groups pulled about the same amount of beans for their samples. In both samples, Pinto beans were the most and Navy beans were the least. The numbers for all three kinds of beans were similar in both samples.) X How can a graph help you decide which tub of beans was used? (Possible response: The tallest bar on the graph was for Pinto beans and it was 112. **

The data table for the Second Tub had Pinto beans as the largest number and it was 115. That is close to 112. The smallest bar on the graph was for Navy beans and it was 26. The data table for the Second Tub also had Navy beans as the smallest number and it was 24. That is close to 26. Both the graph and the data table for the Second Tub had Black beans in the middle, and the numbers 70 and 73 for Black beans were close. The data table for the First Tub was totally different because it had Black beans as the most.) Homework and Practice X Assign Home Practice Parts 3 and 4. Home Practice Parts 3 and 4 develop number sense by asking students to partition a number and locate the number on a number line.

X Assign DPP items O–P. DPP Task P asks students to write a story to match a number sentence. Math Facts. DPP Bit O assesses students’ fluency with addition facts for doubles, twos, and threes. 467 Reference SG • Grade 3 Math Practices Solving a problem: Showing or telling how I solve a problem: 1. Know the problem. I read the problem carefully. I know the questions to answer and what information is important. 2. Find a strategy. I choose good tools and an efficient strategy for solving the problem. 3. Check for reasonableness. I look back at my solution to see if my answer makes sense. If it does not, I try again.

4. Check my calculations. If I make mistakes, I correct them.

5. Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking. 6. Use labels. I use labels to show what numbers mean. The question tells me . I need to find out . I used convenient numbers to estimate like this . Then I compared my answer to my estimate. To check this: 715 – 350 = 365 I did this: 365 + 350 = 715 ✓ Cars 1 2 3 Cost 3 6 9 Step 1 . Step 2 . Step 3 . Is there a pattern? What operations should I use? Is there a more efficient way? What tools should I use? 0 2 4 6 Cars 1 2 3 Cost 3 6 9 I check my calculations with a calculator. $5 12 cars 36 inches 155 miles 9 days 4 apples 3 $ 1 2 58 + 19 = 77 chairs Graphs Tables Words Number Sentences I show each step of my work using: “First, I added up the total number of chairs because .

” Student Guide — Reference Teacher Guide — Home Practice Parts 3 and 4 MTB4_G3_TG_U01_FINAL.indd 32 7/29/13 2:00 PM

33 Estimated Class Sessions: 1–2 Students solve one- and two-step word problems using sample data represented in scaled picture graphs and tables. Content in this Lesson • Using picture graphs to solve problems and make predictions [E4, E5]. • Drawing scaled picture graphs from a table [E2]. • Reading a table or scaled graph to find out information about a data set [E3]. • Making predictions and generalizations about a population from a sample using data tables and graphs [E4]. • Solving one- and two-step problems involving addition and subtraction [E5]. • Demonstrating fluency with addition facts [E7].

**• Communicating reasoning and solutions verbally and in writing [MPE5]. Assessment in this Lesson Assessment Expectation Assessed Picture Graphs Check-In: Questions 5–10 with Feedback Box Student Activity Book Pages 24–26 E2. Draw scaled bar and picture graphs from a table. E3. Read a table or scaled graph to find information about a data set. E4. Make predictions and generalizations about a population from a sample using data tables and graphs. E5. Solve one- and two-step problems using data in scaled bar and picture graphs.**

DPP Item Q Addition Facts Quiz: More Addition Facts Teacher Guide – digital E7.

Demonstrate fluency with the addition facts. DPP Item R Sample of Beans Teacher Guide – digital E2. Draw scaled bar and picture graphs from a table. E3. Read a table or scaled graph to find information about a data set. E5. Solve one- and two-step problems using data in scaled bar and picture graphs. Vocabulary in this Lesson • picture graph • scaled graph 3.MD.B Represent and interpret data. (3.MD.B.3) MP1. Make sense of problems and persevere in solving them. MP2. Reason quantitatively. MP3. Construct viable arguments and critique the reasoning of others. MP5. Use appropriate tools strategically.

MP6. Attend to precision.

MP8. Look for and express regularity in repeated reasoning. Using Picture Graphs TLP • Grade 3 • Unit 1 • Lesson 5 Using Picture Graphs Lesson 5 MTB4_G3_TG_U01_FINAL.indd 33 7/29/13 2:00 PM

34 Materials List Materials for Students Daily Practice and Problems Lesson Homework Assessment Student Books Student Guide • Using Picture Graphs Pages 13–14 Student Activity Book • Picture Graphs Pages 23–26 • Picture Graphs Check-In: Questions 5–10 Pages 24–26 Teacher Resources Teacher Guide – digital • DPP Items Q–R • DPP Item Q Addition Facts Quiz: More Addition Facts • DPP Item R Sample of Beans Materials for the Teacher • Display of first Picture Graphs page (Student Activity Book) Page 23, optional • Unit 1 Assessment Record • Math Facts Class Record • Individual Assessment Record TLP • Grade 3 • Unit 1 • Lesson 5 Using Picture Graphs MTB4_G3_TG_U01_FINAL.indd 34 7/29/13 2:00 PM

35 Teacher Planning Notes Teacher Planning Notes Using Picture Graphs TLP • Grade 3 • Unit 1 • Lesson 5 MTB4_G3_TG_U01_FINAL.indd 35 7/29/13 2:00 PM

36 TLP • Grade 3 • Unit 1 • Lesson 5 Developing the Lesson Developing the Lesson Introduce Picture Graphs. Have students open their Student Guide to the Using Picture Graphs pages. Use the following questions to begin a discussion about using picture graphs (graphs that use pictures to display data). Ask: X Look at the picture graph on this page. Where else have you seen picture graphs? (Students have likely seen picture graphs in their social studies books or in student newspapers.) X How is the picture graph similar to a bar graph? (Possible response: The symbols are lined up and look like bars.) X How is it different from the bar graphs we made for Kind of Bean? (Some possible responses include: The pictures are arranged horizontally instead of vertically.

**There are no numbers on the graph to show the values for the number of students.) X What is the value of each of the symbols? How do you know? (Possible response: Each symbol is equal to 3 students. There is a key that tells you the scale at the bottom of the graph.) Content Note Picture Graphs in Earlier Grades. Teachers in the primary grades often use picture graphs to organize information about their classroom. For example, they may do a picture graph showing how children come to school either by bus, in a car, or by walking.**

Students work with a partner or in a small group to discuss Questions 1–5. After they have had an opportunity to discuss the problems, use the questions to guide a class discussion. Read and Use Picture Graphs. To answer Questions 1–3, students need to understand that each symbol on the graph is equal to 3 students. Students can skip count by 3s or use addition to solve each of these questions. In Question 4, students compare the number of students who have a dog as a pet with the number who have a bird. Some students will find the total number of students who have a dog and the total number of students who have a bird and then use subtraction to find this answer.

Others will realize that there are 5 more symbols for dogs than there are for birds and will skip count by 3s or use repeated addition to find their answer.

13 Ana and Frank were thinking about their school as a population. They decided to use their classroom as a sample of the population to collect data about the types of pets their schoolmates have in their homes. After they collected the data, they decided to organize it using a picture graph. dog Frequency of Pets cat bird fish K Kind of Pet = 3 students Discuss Discuss Use Ana and Frank’s picture graph to answer the following questions. Be ready to share your answers. 1. This picture graph shows that more students have a dog as a pet than any other animal.

A. If each stick person symbol represents 3 students, how many students have a dog? B.

Show or tell how you know. 2. The picture graph shows that a bird is the pet for the fewest number of students. A. How many students have a bird for a pet? B. Show or tell how you know. 3. Use the graph to find out how many students have a cat or a fish for a pet. 4. What is the difference between the number of students who have a dog and the number who have a bird? 5. Ana and Frank collect the same pet data from a different third-grade class in their school. Which pet do you think is most common? Why do you think so?

Using Picture Graphs SG • Grade 3 • Unit 1 • Lesson 5 Lesson 5 Using Picture Graphs Student Guide — Page 13 23 Copyright © Kendall Hunt Publishing Company Name Date Using Picture Graphs SAB • Grade 3 • Unit 1 • Lesson 5 Picture Graphs 1. Linda’s mom is a baker. Linda decided to use a picture graph to show the different flavors of cake her mother baked during a day. Linda finished her data table but forgot to finish the graph. Use the information in the data table to finish the picture graph. 2. What scale did Linda use to make her picture graph? 3. A. How many cake symbols did you have to draw on the graph to show 10 vanilla cakes?

**B. Show or tell how you know. 4. Write a number sentence to show the difference between the number of chocolate cakes Linda’s mom baked and the number of spice cakes she baked. Vanilla Chocolate Lemon Spice F Flavor of Cake Cakes Baked Today Cakes Baked Today = 2 Cakes Chocolate Vanilla Lemon Spice 12 10 6 2 N Number of Cakes Baked F Flavor of Cake Student Activity Book — Page 23 MTB4_G3_TG_U01_FINAL.indd 36 7/29/13 2:00 PM**

37 TLP • Grade 3 • Unit 1 • Lesson 5 Students are asked to predict the results of a second sample in Question 5. Since both of the third-grade classrooms are part of the total population of the school, it would be reasonable to expect that the largest number of students will have a dog as a pet and the fewest number of students will have a bird.

Practice with Picture Graphs. The Picture Graph pages in the Student Activity Book provide additional practice with picture graphs. Students work with a partner or in a small group to complete Questions 1–4. Ask individuals to share their answers. Use this discussion to check for understanding before assigning Check-In: Questions 5–10.

For Question 1, draw the incomplete picture graph on the board or display a copy of the page. Ask students to use the information in the data table to complete the picture graph. In Questions 2–3, the scale used on this graph is one cake symbol equals 2 cakes. This means that students will draw 5 cake symbols to show that ten vanilla cakes were baked. Students write a number sentence to show the difference between the number of spice cakes baked and the number of chocolate cakes baked in Question 4.

Ask students to complete Check-In: Questions 5–10 independently to assess their understanding of picture graphs.

Ongoing Assessment Use Check-In: Questions 5–10 and the corresponding Feedback Box to assess student progress toward drawing scaled picture graphs from a table [E2]; reading a table and graph to find out information about a data set [E3]; making predictions and generalizations about a population from a sample using data tables and graphs [E4]; and solving one- and two-step problems using data in picture graphs, including scaled data [E5]. A Sample of Problems. Students complete Questions 6–13 in the A Sample of Problems section of the Using Picture Graphs pages in the Student Guide.

These word problems provide practice with computation, estimation, and critical-thinking skills. Many problems challenge students to use their knowledge of mathematics in new situations. This will encourage students to think through each problem rather than simply applying the same procedure to several problems. 24 Copyright © Kendall Hunt Publishing Company Name Date SAB • Grade 3 • Unit 1 • Lesson 5 Using Picture Graphs Check-In: Questions 5–10 5. The students in third grade were selling popcorn to raise money. They started to draw a data table and a picture graph to show how many bags of popcorn they sold each day.

**Use the information below to complete the missing parts of the data table and picture graph. Use your graph and data table to answer the following questions. 6. A. How many popcorn bag symbols did you need to draw on the graph to show the number of bags sold on Tuesday? B. Show or tell how you know.**

7. A. How many bags of popcorn did the students sell on Friday? B. Show or tell how you know. C Popcorn Sales Tuesday Monday Wednesday Thursday Friday D Day of the Week Popcorn Sales = 5 Bags of Popcorn D Day of the Week Monday Tuesday Wednesday Thursday Friday 10 20 5 N Number of Bags Sold Student Activity Book — Page 24 25 Copyright © Kendall Hunt Publishing Company Name Date Using Picture Graphs SAB • Grade 3 • Unit 1 • Lesson 5 8. A. How many bags of popcorn did the students sell on Monday and Tuesday? B. How does the total for Monday and Tuesday compare to the amount sold on Friday?

C.

Show or tell your thinking. 9. A. Write a number sentence to show how many bags of popcorn the students sold during all five days. B. Show or tell how to use your graph to answer Question 9A. Student Activity Book — Page 25 MTB4_G3_TG_U01_FINAL.indd 37 7/29/13 2:00 PM

38 TLP • Grade 3 • Unit 1 • Lesson 5 Content Note Computing Fluently. NCTM’s Principles and Standards for School Mathematics states: “Part of being able to compute fluently means making smart choices about which tools to use and when. Students should have experiences that help them learn to choose among mental computation, paper-and- pencil strategies, estimation, and calculator use. The particular context, the question, and the numbers involved all play roles in those choices . Students should evaluate problem situations to determine whether an estimate or an exact answer is needed, using their number sense to advantage, and be able to give a rationale for their decision” (p.

36). Summarizing the Lesson Summarizing the Lesson Organize students to share their problem solutions and strategies with a partner. Discussion of students’ strategies reminds students that there are often many ways to solve a problem and that communicating a solution path is important. To encourage students to listen to one another’s strategies, ask students to explain their strategies for a problem to a partner. Each member of a pair must explain his or her strategy well enough so that the partner can then show or tell how the problem was solved to the rest of the class.

Question 13 asks, “About how many animals are in the sample?” It is more efficient to use mental math to estimate the total number of animals in the sample than to find the exact answer. One way is to use desk number lines to find convenient numbers and then quickly add them. TIMS Tip! Having students work with a partner or in a small cooperative group provides students with the opportunity to talk about their problem-solving strategies. Make sure students understand that when working in a group all students need to be able to explain how a problem is solved.

**Homework and Practice X Assign DPP items Q–R. **

DPP Task R provides practice and an assessment opportunity with using a data table and graph to solve problems. Math Facts. DPP Bit Q provides fluency practice with addition facts and can be used to assess fluency with the addition facts. 14 SG • Grade 3 • Unit 1 • Lesson 5 Using Picture Graphs Use the Picture Graphs pages in the Student Activity Book to practice drawing, reading, and using picture graphs. A Sample of Problems Show or tell how you solve each problem. 6. Alex wants to print name cards for the four students in his group. The other members of his group are Beth, Karl, and Todd.

How many letters will he print?

7. Make a list of the first names of five students from your class. How many letters are in this list? 8. Choose some first names from your class so that the total number of letters is twenty-two. Write a number sentence for this problem. 9. A. Four students are playing a game of Number Line Target. The target number is 25. Alex covered an eight. Jacob covered a five. Then Keenya covered a three. What is the sum of their numbers? B. Now it is John’s turn. What number does he need to cover to win the game?

C. Sketch a number line and show each move for this game. 10. Kathy, Beth, Jay, and Joanie were playing Number Line Target.

They each covered one number. The sum of their numbers was 26. Kathy covered a 5. Beth covered an 8. What could Jay and Joanie have covered? 11. Professor Peabody took a sample of sixteen beans from a container. He recorded two lima beans and nine pinto beans. He forgot to record the number of navy beans before he dumped them back into the container. How many navy beans were in his sample?

12. In Rachel’s sample there were fifteen pinto beans, four lima beans, and seven navy beans. Shannon said, “I pulled the same number of navy beans as you. I have two more pinto beans than you. I have one less lima bean than you.” How many beans did Shannon pull? 13. Betty Robinson and her parents collected data on a small sample of animals. They saw 22 spider monkeys, 18 squirrels, 9 river otters, 20 armadillos, and 5 jaguars. About how many animals are in the sample? Student Guide — Page 14 26 Copyright © Kendall Hunt Publishing Company Name Date SAB • Grade 3 • Unit 1 • Lesson 5 Using Picture Graphs 10.

**The students decide to sell popcorn during a second week. A. Predict the day of the week that will have the most sales. B. Show or tell how you know.**

Picture Graphs Check-In: Questions 5–10 Feedback Box Expectation Check In Comments Draw scaled picture graphs from a table. [Q# 5] E2 Read a table or scaled graph to ﬁnd information about a data set. [Q# 5–6] E3 Make predictions and generalizations about a population from a sample using data tables and graphs. [Q# 10] E4 Solve one- and two-step problems using data in scaled picture graphs. [Q# 7–9] E5 Student Activity Book — Page 26 MTB4_G3_TG_U01_FINAL.indd 38 7/29/13 2:00 PM