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Scaling Two Dimensions: IM 8.5.18
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1. Lesson 8.5.18
- IM 8.5.18 Lesson: Scaling Two Dimensions
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2. Practice 8.5.18
- IM 8.5.18 Practice: Scaling Two Dimensions
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Scaling Two Dimensions: IM 8.5.18
IM 6 – 8 Math, GeoGebra Classroom Activities, Aug 17, 2020
“Scaling Two Dimensions” from IM Grade 8 by Open Up Resources and Illustrative Mathematics. Licensed under the Creative Commons Attribution 4.0 license.
Table of Contents
- Lesson 8.5.18
- IM 8.5.18 Lesson: Scaling Two Dimensions
- Practice 8.5.18
- IM 8.5.18 Practice: Scaling Two Dimensions
IM 8.5.18 Lesson: Scaling Two Dimensions
, , , , and all represent positive integers. Consider these two equations: and
Which of these statements are true? Select all that apply.
Create a true statement of your own about one of the equations.
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Clare sketches a rectangular prism with a height of 11 and a square base and labels the edges of the base s. She asks Han what he thinks will happen to the volume of the rectangular prism if she triples s.
Han says the volume will be 9 times bigger. Is he right? Explain or show your reasoning.
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A cylinder can be constructed from a piece of paper by curling it so that you can glue together two opposite edges (the dashed edges in the figure).
If you wanted to increase the volume inside the resulting cylinder, would it make more sense to double , , or does it not matter?
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If you wanted to increase the surface area of the resulting cylinder, would it make more sense to double , , or does it not matter?
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How would your answers to these questions change if we made a cylinder by gluing together the solid lines instead of the dashed lines?
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There are many cones with a height of 7 units. Let represent the radius and represent the volume of these cones.
Write an equation that expresses the relationship between and . Use 3.14 as an approximation for .
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Predict what happens to the volume if you triple the value of .
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Graph this equation.
What happens to the volume if you triple ? Where do you see this in the graph? How can you see it algebraically?
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Where do you see this in the graph?
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How can you see it algebraically?
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IM 8.5.18 Practice: Scaling Two Dimensions
There are many cylinders with a height of 18 meters. Let r represent the radius in meters and V represent the volume in cubic meters.
Write an equation that represents the volume as a function of the radius .
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Complete this table, giving three possible examples.
If the radius of a cylinder is doubled, does the volume double? Explain how you know.
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Is the graph of this function a line? Explain how you know.
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As part of a competition, Diego must spin around in a circle 6 times and then run to a tree. The time he spends on each spin is represented by s and the time he spends running is r. He gets to the tree 21 seconds after he starts spinning.
Write an equation showing the relationship between and .
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Rearrange the equation so that it shows as a function of .
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If it takes Diego 1.2 seconds to spin around each time, how many seconds did he spend running?
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The table and graph represent two functions. Use the table and graph to answer the questions.
For which values of is the output from the table less than the output from the graph?Font sizeFont size
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In the graphed function, which values of give an output of 0?
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A cone has a radius of 3 units and a height of 4 units.
What is this volume of this cone?
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Another cone has quadruple the radius, and the same height. How many times larger is the new cone’s volume?
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