Lesson three. Scale Factors. Terminal Objective. Lesson 3

Students will be asked find the volume of a triangular prism and rectangular prism. Given a prism with its dimensions multiplied by a scale facr, you will find the new volume without using a formula. Students will use a table explore the effects of scale facrs on rectangular prisms.

1 Lesson three Terminal Objective Given the volume of a prism in which the dimensions have been multiplied by a scale facr, students will be able accurately determine the new volume without using a formula. Content Standard Reference: Grade 7 Measurement & Geometry 2.3 Compute the length perimeter, the surface area faces, and the volume of a threedimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale facr, the surface area is multiplied by the square scale facr and the volume is multiplied by the cube scale facr. Materials 1. Centimeter cubes 2. Box 3. PowerPoint Time Required 1 class scale facrs 23

2 Introduction of Lesson Anticipary Set: Students will be asked find the volume of a triangular prism and rectangular prism. Student Objective: Given a prism with its dimensions multiplied by a scale facr, you will find the new volume without using a formula. Purpose: Architects and engineers need know the effect of scale facrs on volume when they make scale models of buildings. Shippers who come through the Port of Long Beach may need know the effect of scale facrs on volume when they load cargo ships. Lesson Keyword 1. Scale facr - A number that multiplies a quantity. Input Describe a scale facr. A scale facr is a number that multiplies a quantity. Modeling Fill a box with centimeter cubes and show the students what a scale facr is. Ask students predict the number of cubes that would be needed if the dimensions box were doubled. Use the cubes find the volume new box. 24 scale facrs

3 Check for Understanding Ask the students write a description of a scale facr in their own words. Students will share their descriptions with their partner and the teacher will randomly call on members of each pair share with the class. Input Students will use a table explore the effects of scale facrs on rectangular prisms. Modeling We know that the volume of a 40 foot container is 2,752 ft 3. What do you suppose would happen the volume if we multiplied the length, width and height by a scale facr of 2? Or by a scale facr of 3? Or by a scale facr of 4? Complete the table when multiplying the dimensions by a scale facr of 2. hx2 lx2 wx2 Length Width Original ,752 ft 3 Same x ,016 ft or 8 x 3 scale facrs 25

4 Now, multiply the dimensions by a scale facr of 3 and complete the table. Length Width Original ,752 ft 3 Same x ,016 ft or 8 x ,304 ft or 27 Let s complete the entire table. Length Width Original ,752 ft 3 Same x ,016 ft or 8 x ,304 ft or ,128 ft or ,000 ft or 125 Check for Understanding Display five true/false questions. Students will answer by giving a thumbs up if the statement is true and a thumbs down if the statement is false. 1. Whenever the length, width, and height are multiplied by a scale facr of 2, the volume is multiplied by scale facrs Answer: True

5 2. Whenever the length, width, and height are multiplied by a scale facr of 3, the volume is multiplied by 3 4. Answer: False 3. Whenever the length, width, and height are multiplied by a scale facr of 23, the volume is multiplied by Answer: False. 4. Whenever the length, width, and height are multiplied by a scale facr of 54, the volume is multiplied by Answer: True. 5. Whenever the length, width, and height are multiplied by a scale facr of x, the volume is multiplied by x 3. Answer: True. Input Students will use a table explore the effects of scale facrs on triangular prisms. 5f 4f 5f 14f 6f scale facrs 27

6 Modeling Show how complete the table when multiplying the dimensions by a scale facr of 2. Base prism Original ft 3 Same x ,344 ft or 8 x 3 Show how complete the table when multiplying the dimensions by a scale facr of 2, 3, 4 and 5. Base prism Original ft 3 Same x ,344 ft or 8 x ,536 ft or ,752 ft or ,000 ft or 125 Check for Understanding Display five true/false questions. Students will answer by giving a thumbs up if the statement is true and a thumbs down if the statement is false. 28 scale facrs

7 1. The volume of a triangular prism is 100m 3. If the dimensions are multiplied by a scale facr of 2, the new volume will be 800m 3. Answer: True. 2. The volume of a triangular prism is 310 ft 3. If the dimensions are multiplied by a scale facr of 2, the new volume will be 620 ft 3. Answer: False. 3. The volume of a rectangular prism is 10 km 3. If the dimensions are multiplied by a scale facr of 4, the new volume will be 270 km 3. Answer: False 4. The volume of a rectangular prism is 21 yd 3. If the dimensions are multiplied by a scale facr of 3, the new volume will be 567 yd 3. Answer: True 5. The volume of a rectangular prism is 50 m 3. If the dimensions are multiplied by a scale facr of x, the new volume will be 50x 3 m 3. Answer: True Guided Practice Display the following problems: 1. Suppose the volume of a rectangular prism is 40 ft 3. Find the new volume, if the dimensions are multiplied by a scale facr of 3. Answer: 1,080 ft 3 scale facrs 29

8 2. Suppose the dimensions of a triangular prism are multiplied by a scale facr of 2 and the new volume is 432 cm 3. What was the volume? Answer: 54 cm 3 3. Suppose the volume of a triangular prism is 120 m 3 and the new volume is 3,240 m 3. What scale facr were the dimensions multiplied by? Answer: 3 Partners will be asked check each other s work. Closure Students will be asked write a brief explanation of what would happen the volume of a triangular prism if the dimensions were multiplied by a scale facr. Students will share their responses with their partner and several students will be selected share with the class. 30 scale facrs

9 Worksheet Lesson three Solve Using scale facrs for rectangular prisms. Base prism Original ,752 ft 3 Same x 2 x 3 Using scale facrs for triangular prisms. Base prism Original ft 3 Same x 2 x 3 scale facrs 31