Mathematics Success Level C

Transcription

1 T675 LESSON 2: Line Plot [OBJECTIVE] The student will measure lengths to the nearest fourth of an inch, create line plots of the data, and answer questions about line plots. [PREREQUISITE SKILLS] know the meaning of 1 2 and 1 [MATERIALS] Student pages S225 S233 Transparencies T686, T688, T691, T693, and T695 Copy Master T685 (1 per 6 student) Copy Master T690 (1 copy - cut apart to pass out to students) Painter s tape Overhead two-color counters (1 per student pair) Two-color counters (1 per student pair) Fraction Kits 1, 2, and 3 (1 per student pair) Overhead fraction strips Foldable from Lesson 22 [ESSENTIAL QUESTIONS] 1. What is the purpose of a line plot? 2. Describe how you know which length has the most objects on a line plot. 3. When an object you are measuring is not an exact measurement on the ruler, how do you know how long to say it is? [WORDS FOR WORD WALL] line plot, x-axis, y-axis [GROUPING] Cooperative Pairs (CP), Whole Group (WG), Individual (I) *For Cooperative Pairs (CP) activities, assign the roles of Partner A and Partner B to students. This allows each student to be responsible for designated tasks within the lesson. [LEVELS OF TEACHER SUPPORT] Modeling (M), Guided Practice (GP), Independent Practice (IP) [MULTIPLE REPRESENTATIONS] SOLVE, Graph, Verbal Description, Graphic Organizer, Pictorial Representation, Concrete Representation

2 T676 Mathematics Success Level C LESSON 2: Line Plot [WARM-UP] (5 minutes IP, WG, I) S225 (Answers are on T68.) Have students turn to S225 in their books to begin the Warm-Up. Students will answer questions based on a bar graph. Monitor students to see if any of them need help during the Warm-Up. Give students 3 minutes to complete the problems and then spend 2 minutes reviewing the answers as a class. {Pictorial Representation, Graph, Verbal Description} [HOMEWORK] (5 minutes) Take time to go over the homework from the previous night. [LESSON] (60 minutes M, GP, IP, CP, WG) SOLVE Problem (3 minutes WG, GP) T686, S226 (Answers on T687.) Have students turn to S226 in their books, and place T686 on the overhead. The first problem is a SOLVE problem. You are only going to complete the S step with students at this point. Tell students that during the lesson they will learn how to read and answer questions about line plots. They will use this knowledge to complete this SOLVE problem at the end of the lesson. {SOLVE, Graph, Graphic Organizer} Measuring to the Nearest Fourth of an Inch (15 minutes M, GP, WG, CP, IP) Copy Master T685, Copy Master T690, T686, T688, S226, S227 (Answers on T687, T689.) 10 minutes M, GP, WG, CP: Complete the steps on S226 and S227 with the students on the overhead. Have students work in partners and designate Partner A and Partner B. {Graph, Pictorial Representation, Verbal Description}

3 T677 LESSON 2: Line Plot MODELING Measuring to the Nearest Fourth of an Inch Step 1: Pass out a ruler from T685 to each pair of students. Tell students that the ruler measures in inches, and the distance between each whole number is an inch. Then ask the following questions about the ruler. Partner A, identify the point where zero inches would be. (at the beginning of the ruler) Record. Partner B, explain to Partner A how many equal parts the inch is split into. (four) Record. Tell students that this means that we can measure a distance to the nearest fourth. I see 1 and 3, why don t I see 2? (Because 2 is the same as 1 2.) Step 2: Model for the students how to measure the line segment in Problem using a transparent ruler on the overhead. Have Partner A measure with the ruler, while Partner B looks to make sure it is placed correctly. When I place the ruler correctly, the first point of the line segment is at zero, and the second point of the line segment tells you how long the line segment is. How long is this line segment? (1 inch) Record. Step 3: Now measure the line segment in Problem 5. Have Partner B use the ruler, while Partner A makes sure it is placed correctly. Partner A, explain how to place the ruler to measure the line segment. (so that the first endpoint lines up with zero) Partner B, how do we determine the length of the line segment? (Look at the second point and see what fraction is below it.) How long is the line segment? ( 1 2 of an inch) Record.

4 T678 Mathematics Success Level C LESSON 2: Line Plot Step : Now measure the line segment in Problem 6. Have Partner A use the ruler, while Partner B makes sure it is placed correctly. Partner A, determine if the line segment goes past the first inch. (Yes.) Partner B, explain how far past. (to the 1 ) Have partners discuss how long the line segment is. (1 1 Record. inches) Step 5: Now measure the line segment in Problem 7. Have Partner B use the ruler, while Partner A makes sure it is placed correctly. Partner A, determine if the line segment lands exactly on one of the lines of the ruler. (No) Record. Partner B, explain which two lines it is between. ( 1 2 and 3 ) Record. Have partners discuss which mark on the ruler the line segment is closer to. ( 3 of an inch) Record. When we say that we are going to measure a line segment to the nearest fourth of an inch, what do you think that means? (If it doesn t fall exactly on a line of the ruler, we choose the one that it is closest to.) Record.

5 T679 LESSON 2: Line Plot 5 minutes IP, CP: Give pairs one or two line segments to measure from Copy Master T690 so that all the segments are being measured. Have each pair measure the line segments to the nearest fourth of an inch with the ruler and write the measurement below the line segment. Tell Partner A to measure the first one, while Partner B checks, and then switch places for the second line segment. The line segments will be checked as a group when you make the line plot. {Pictorial Representation, Verbal Description} Creating Line Plots (9 minutes M, GP, WG, CP) T688, S227 (Answers on T689.) 9 minutes M, GP, WG, CP: Show students how to make a line plot on the board (or wall) using their line segments. Have them copy what you are doing on the board into the line plot at the bottom of page S227. {Concrete Representation, Graph, Verbal Description} MODELING Creating Line Plots Step 1: Use painter s tape to make an x-axis and y-axis for the line plot on the whiteboard. Explain that just like a bar graph, a line plot is a way to display data, and you start with an x-axis and a y-axis. Step 2: Tell students that the measurements of the line segments will be used as the labels for the x-axis. Partner A, explain what numbers are marked on the x-axis. (the same numbers that are on the ruler) Step 3: Tell students that the frequency (number of lines) will be on the y-axis. Count up by ones, making sure you have at least 8 lines. Label the y-axis as Number of Lines. Step : Have students discuss what a good title for the graph would be. (Line Segment Lengths)

6 T680 Mathematics Success Level C LESSON 2: Line Plot Step 5: Tell students that they are going to bring their line segments up to the board to make the line plot. Ask pairs who have a segment that is 1 of an inch to bring it up to the board. (Rectangles should come up.) Tape the line segments to the board above the 1 portion of the x-axis, one on top of the other Step 6: Tell students that on their line plots, instead of a rectangle, they will use an x to represent one of the line segments. The number of x s represents the number of line segments that are that length. Step 7: Have students bring up the line segments for each measurement and add them to the line plot. For 1 2 of an inch rectangles 23 25; for 3 of an inch rectangles 19 22; for 1 inch rectangle 18; for 1 1 inches rectangles 15 17; for inches rectangles 11 1; for 1 3 inches rectangles 10; and for 2 inches rectangles 1 3. Step 8: Complete the line plot. Interpreting Line Plots (10 minutes M, GP, WG, IP, CP) T691, S228 (Answers on T692.) 5 minutes M, GP, WG, CP: Have students turn to S228 in their books, and place T691 on the overhead. Read the first three questions together and model how to read the line plot to answer them. {Pictorial Representation, Graph, Verbal Description}

7 T681 LESSON 2: Line Plot MODELING Interpreting Line Plots Step 1: Read Question 1. Partner A, explain how we know how many line segments are about inches long. (Look to see how many x s are above 1 1 on the plot.) 2 Partner B, identify how many line segments are about 1 1 inches long. 2 (four) Record. Step 2: Read Question 2. Partner A, explain how we know how many line segments are about 1 of an inch long. (look to see how many x s are above 1 on the plot) Partner B, identify how many line segments are about 1 of an inch long? (five) Record. Step 3: Read Question 3. Partner A, explain what it means to be longer than 1 inch. (any segments that are more than 1 inch) Partner B, determine if we should include segments that are 1 inch. (No.) Why not? (If they are 1 inch, they are not more than 1 inch.) How many line segments are longer than 1 inch? (seventeen) Record.

8 T682 Mathematics Success Level C LESSON 2: Line Plot 3 minutes CP, IP: Have students answer Questions and 5 on S228 with a partner. {Graph, Verbal Description} 2 minutes WG: Go over the answers for the last two questions. {Graph, Verbal Description} Creating Line Plots (12 minutes CP, IP, WG) T691, T693, S228, S229 (Answers on T692, T69.) 10 minutes CP, IP: Students will now work in pairs to measure the objects on S229. Make sure students are using the line segment under or above the object to measure. Have partners take turns measuring and then make a line plot of the data on S228. Circulate around the room to be sure students are measuring and making the line plot correctly. {Pictorial Representation, Graph, Verbal Description} 2 minutes WG: Go over the lengths and line plot as a whole group. {Pictorial Representation, Graph, Verbal Description} Foldable Line Plots ( minutes M, WG) Have students take out the foldable they began in Lesson 22. {Graph, Graphic Organizer, Verbal Description, Pictorial Representation} MODELING Foldable - Line Plots Step 1: Students should take out their foldable, and the teacher should record information on the transparency created for the foldable. Step 2: Label the last flap Line Plots. On the inside, complete the section for Line Plots. Refer to your foldable for the information.

9 T683 LESSON 2: Line Plot SOLVE Problem (5 minutes GP, WG) T695, S230 (Answers on T696.) Remind students that the SOLVE problem is the same one from the beginning of the lesson. Complete the SOLVE problem with your students. Ask them for possible connections from the SOLVE problem to the lesson. (They will read a line plot and answer questions.) {SOLVE, Graph, Verbal Description, Graphic Organizer} If time permits (10 minutes IP, CP) S231 (Answers on T697.) Give pairs of students the materials listed in the chart on S231 to measure. Have partners take turns measuring the objects. After measuring, they should make the line plot and answer the questions. Students will need to share your overhead fraction kits. [CLOSURE] (2 minutes) To wrap up the lesson, go back to the essential questions and discuss them with students. What is the purpose of a line plot? (to show how many objects fit into the same category) Describe how you know which length has the most objects on a line plot. (The measurement with the most x marks has the most objects with that length.) When an object you are measuring is not an exact measurement on the ruler, how do you know how long to say it is? (Find the two measurements it is in between; whichever one it is the closest to is the estimated measurement.) [HOMEWORK] Assign S232 and S233 for homework. (Answers on T698 and T699.) [QUIZ ANSWERS] T700 T703 The quiz can be used at any time as extra homework or to see how students progress on understanding and creating line plots.