Mathematics Success Level F

Transcription

1 T691 [OBJECTIVE] The student will find the volume of rectangular prisms. [MATERIALS] Student pages S236 S242 Transparencies T699, T701, T703 Centimeter cubes (50 cubes per pair) Colored paper for foldable (1 per student or foldable made during Lesson 22) [ESSENTIAL QUESTIONS] 1. What does volume measure? 2. Why is volume measured in cubic units? 3. Describe how the area of the base of a prism is related to the volume of the prism. [WORDS FOR WORD WALL] volume, rectangular prism [GROUPING] Cooperative Pairs (CP), Whole Group (WG), Individual (I) [LEVELS OF TEACHER SUPPORT] Modeling (M), Guided Practice (GP), Independent Practice (IP) [MULTIPLE REPRESENTATIONS] SOLVE, Algebraic Formula, Verbal Description, Pictorial Representation, Concrete Representation, Graphic Organizer [WARM-UP] (5 minutes IP, I, WG) S236 (Answers on T698.) Have students turn to S236 in their books to begin the Warm-Up. Students will find the area of rectangles to prepare for finding the volume of rectangular prisms. Monitor students to see if any of them need help during the Warm-Up. Give students 4 minutes to complete the problems and then spend 1 minute reviewing the answers as a class. {Algebraic Formula, Pictorial Representation} [HOMEWORK] (5 minutes) Take time to go over the homework from the previous night.

2 T692 Mathematics Success Level F [LESSON] (50 60 minutes M, GP, IP, WG, I) SOLVE Problem (3 minutes GP, WG) T699, S237 (Answers on T700.) Have students turn to S237 in their books, and place T699 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 find the volume of prisms. They will use this knowledge to complete this SOLVE problem at the end of the lesson. {SOLVE} Discovery Activity Volume of Rectangular Prisms (15 minutes M, GP, WG) T699, S237 (Answers on T700.) Pass out the cubes to each pair of students. Use the following activity to complete the steps on S237 with your students. {Concrete Representation, Algebraic Formula, Verbal Description}

3 T693 MODELING Volume of a Rectangular Prism Step 1: Model creating a rectangle out of the cubes that is 3 cubes long and 2 cubes wide on the overhead. Be sure to point out that there is no space between the cubes. Step 2: Find the area of the bottom of the rectangle by counting the squares on the bottom, or by using the area formula: A = lw = 3(2) = 6 square units. Remind students that the area is the number of squares the shape covers. Step 3: Tell students that since you used cubes to make the figure, it not only has length and width, but also height. It is a three-dimensional figure. Record the number of cubes for each dimension: height (1), length (3), and width (2). Step 4: Count the number of cubes that make up the prism with students (6). Add another layer to your prism by adding 6 more cubes on top of the first layer. Step 5: Ask students to tell you the area of the bottom (or base). Ask, Has it changed? (No, it is still 6 square units.) Ask students to find the height (2), length (3), and width (2) of the prism. Count the number of cubes that make up the prism with students (12). Step 6: Add another layer to your prism by adding 6 more cubes on top of the first two layers. Step 7: Ask students to tell you the area of the bottom (or base). Ask, Has it changed? (No, it is still 6 square units.) Ask students to find the height (3), length (3), and width (2) of the prism. Count the number of cubes that make up the prism with students (18).

4 T694 Mathematics Success Level F Step 8: Explain to students that the number of cubes it takes to make a rectangular prism is called the prism s volume. Ask students to look at the pattern of the number of cubes that made up the prism each time a layer was added. Each time a layer was added, 6 more cubes were added, and the volume increased by 6. Step 9: Ask students to look at the pattern created by the height, length, and width at Steps 3, 5, and 7. Fill in the chart below with students. Length Width Height Number of Cubes (Volume) Step Step Step Ask students what formula they could use to find the volume of a rectangular prism (V = lwh or V = Bh). Practice Volume of Rectangular Prisms (12 minutes M, GP, IP, WG, I) T701, S238 (Answers on T702.) 5 minutes M, GP, WG: Have students turn to S238 in their books, and place T701 on the overhead. Use the following activity to help students complete S238. {Pictorial Representation, Algebraic Formula, Verbal Description

5 T695 MODELING Practice with Volume Step 1: Have students look at Example 1 on S238. Remind students that to find the volume, they can multiply the length, width, and height of the figure. Label the length (5), the width (3), and the height (2). Remind them to always start by writing the formula and then substituting in the values. Explain that because the unit of measure of the prism in the example is not specified, students will use unit. The answer will be in units cubed (u 3 ). If students have difficulty understanding the units cubed, remind them that each unit is a cube. If they were to count the number of cubes in Example 1, there would be 30 cubes. Each cube is 1 cubic unit, so that will be a total of 30 cubic units. (If you used cm cubes, that measurement would be 30 cm 3.) Step 2: In the second column, model for students how to write the formula for the volume of a rectangular prism (V V = lwh). Step 3: Look at Example 2 with students. Point out the length (20), width (6), and height (7). Model writing the formula and then substituting the values to find the volume in cubic millimeters. Also have students write the formula in the middle column. Step 4: Look at Example 3 with students. After reading the problem, underline each of the dimensions in the problem. Then model writing the formula and substituting the values to find the volume. Also have students write the formula in the middle column. Step 5: Look at Example 4 with students. After reading the problem, underline each of the dimensions in the problem. Ask students how they think you should find the volume, if you know the area of the base, and not the length and width. Remind them that area = length times width, so they need to multiply the base area by the height. (You can also refer back to the cube activity, where the area of the base was always the same, and the height changed when students added another layer.) 7 minutes IP, WG, I: Have students complete Problems 5 8 in the third column on S238. Give students 5 minutes to complete the problems and then go over the answers as a class. {Pictorial Representation, Algebraic Formula, Verbal Description}

6 T696 Mathematics Success Level F Foldable (10 minutes M, GP, WG) Give students a piece of colored paper. Follow the steps below to have each student make a foldable. The foldable will include finding the volume of rectangular prisms. (If you completed Lessons 22 25, the students have already made the foldable. Skip to Step 2 to add information on finding the volume of a rectangular prism to the foldable that is already started). {Algebraic Formula, Graphic Organizer} MODELING Foldable Step 1: Fold one corner of the piece of paper down to the edge of the other side of the paper. Cut off the strip at the bottom. A square should be left. Step 2: Open the square. Fold each corner into the center. Write Volume of Rectangular Prisms on one outside flap. Three outside flaps will be blank to be written on later. Step 3: Pull up the flap that says Volume of Rectangular Prisms. On the triangle that sticks up, draw a rectangular prism, with the length, base, and height labeled. Underneath the prism, write the formula. On the square portion, draw another prism, with values for the dimensions. Find the volume using the formula. See your foldable for the information.

7 T697 SOLVE Problem (7 minutes GP, WG) T703, S239 (Answers on T704.) Have students turn to S239 in their books, and place T703 on the overhead. 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. (Students should say that they need to use the volume formula.) {SOLVE, Algebraic Formula, Verbal Description} If time permits (10 minutes IP, I) S240 (Answers on T705.) Have students complete the six volume problems on S240. Give students 8 minutes to complete the problems, and take 2 minutes to go over the answers. {Algebraic Formula} [CLOSURE] (3 minutes) To wrap up the lesson, go back to the essential questions and discuss them with students. What does volume measure? (Volume measures the capacity of a 3-D figure.) Why is volume measured in cubic units? (When finding volume, three measurements are multiplied, and a unit times a unit times a unit is units cubed, or units to the third power.) Describe how the area of the base of a prism is related to the volume of the prism. (The base is the area of the bottom of the prism, and the volume is the base times the number of layers in the prism.) [HOMEWORK] Assign S241 and S242 for homework. (Answers on T706 and T707.) [QUIZ ANSWERS] T708 T710 The quiz can be used at any time as extra homework or to see how students did on finding the volume of rectangular prisms.