Scaling Dimensions: How Changing Length, Width, or Height Affects Volume

Mathematics Grades 7th Grade 4:16 Video
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Lesson Description

Explore how altering the dimensions of a rectangular prism impacts its volume. This lesson uses a Khan Academy video to demonstrate the relationship between dimension changes and volume scaling.

Video Resource

How volume changes from changing dimensions

Khan Academy

Duration: 4:16
Watch on YouTube

Key Concepts

  • Volume of a rectangular prism
  • Proportional relationships
  • Scaling dimensions

Learning Objectives

  • Calculate the volume of a rectangular prism.
  • Explain how changing one dimension of a rectangular prism affects its volume.
  • Explain how changing multiple dimensions of a rectangular prism affects its volume.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the formula for the volume of a rectangular prism: Volume = length × width × height. Briefly discuss what happens to the area of a rectangle if you double its length. Introduce the concept that we'll be exploring similar changes but in three dimensions with volume.
  • Video Viewing (10 mins)
    Watch the Khan Academy video: 'How volume changes from changing dimensions'. Encourage students to take notes on the examples presented.
  • Guided Practice (15 mins)
    Work through example problems similar to those in the video. Start with changing one dimension, then move to changing two, and finally all three. Emphasize the multiplicative effect on the volume. For example, doubling one dimension doubles the volume; doubling all three dimensions multiplies the volume by 2x2x2 = 8.
  • Independent Practice (15 mins)
    Provide students with practice problems where they need to calculate the new volume of a rectangular prism after one or more dimensions have been changed. Include problems where dimensions are halved or tripled.
  • Wrap-up (5 mins)
    Review the key concepts of the lesson. Ask students to summarize the relationship between dimension changes and volume changes in their own words.

Interactive Exercises

  • Dimension Slider
    Use an online interactive tool or a spreadsheet to allow students to adjust the dimensions of a rectangular prism and see the corresponding changes in volume in real-time.
  • Volume Calculator
    Present real-world problems and use calculators to compute the outcome of volume and scaling.

Discussion Questions

  • If you triple the height of a rectangular prism, what happens to its volume?
  • If you halve the length and double the width of a rectangular prism, what happens to its volume?
  • Why does doubling all three dimensions result in an eightfold increase in volume?

Skills Developed

  • Calculating volume
  • Proportional reasoning
  • Problem-solving

Multiple Choice Questions

Question 1:

A rectangular prism has a volume of 24 cubic units. If you double the height, what is the new volume?

Correct Answer: 48 cubic units

Question 2:

A rectangular prism has dimensions 2x3x4. If you double all the dimensions, what is the new volume?

Correct Answer: 192

Question 3:

If you halve the length of a rectangular prism, what happens to the volume?

Correct Answer: The volume halves

Question 4:

A cube has sides of 5cm. If you double all the sides, by what factor does the volume increase?

Correct Answer: 8

Question 5:

The volume of a prism is 100 cubic meters. If the length is doubled and the width is halved, what is the new volume?

Correct Answer: 100 cubic meters

Question 6:

A rectangular prism has a base of 10 inches and a height of 4 inches. By how much will the volume increase if the height is doubled?

Correct Answer: 2

Question 7:

A box has width 2, depth 2, height 2. What is the volume?

Correct Answer: 8

Question 8:

If the volume of a rectangular prism is 36 and you double two of the dimensions, what is the new volume?

Correct Answer: 144

Question 9:

What does it mean to scale an object?

Correct Answer: To change the size

Question 10:

Which of the following is the formula to calculate the volume of a rectangular prism?

Correct Answer: Length * Width * Height

Fill in the Blank Questions

Question 1:

The volume of a rectangular prism is found by multiplying length, _____, and height.

Correct Answer: width

Question 2:

If you double one dimension of a rectangular prism, the volume is __________.

Correct Answer: doubled

Question 3:

If you double all three dimensions of a rectangular prism, the volume is multiplied by __________.

Correct Answer: eight

Question 4:

Halving a dimension of a rectangular prism __________ the volume.

Correct Answer: halves

Question 5:

The volume is always measured in ________ units.

Correct Answer: cubic

Question 6:

If one dimension is multiplied by 3, the volume is multiplied by _____.

Correct Answer: 3

Question 7:

When all sides of a cube are equal, the volume equals side * side * _______

Correct Answer: side

Question 8:

The formula for finding volume is length * ______ * height.

Correct Answer: width

Question 9:

When more than one dimension is doubled, we _________ the scaling factor.

Correct Answer: multiply

Question 10:

The act of changing an object's dimensions is called _______

Correct Answer: scaling

Educational Standards

7.GM.1:Develop and understand the concept of surface area and volume of rectangular prisms with rational-valued edge lengths. 7.A.1:Explain the concept of proportionality in mathematical models and situations and distinguish between proportional and non-proportional relationships. 7.A.2:Identify and justify proportional relationships using mathematical models and situations; solve problems involving proportional relationships and interpret results in the original context.

Teaching Materials

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