Unit 5
Filling Containers
Functions and Volume
Lesson 11
8.F.B.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (πΉ, πΊ) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
8.F.B: Use functions to model relationships between quantities.
Expressions and Equations
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Warm Up
Unit 5 β Lesson 11
1 min individual - 1 min team share - 3 mins class share
Page 172
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 5 β Lesson 11
We will be able to collect data about a function so that we can represent and describe it as a graph.
Learning
Goal
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Where were we? Where are we? Where are we going?
Unit 5 β Lesson 11
Agenda Review
You are successful today when...,
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.2 Activity: Height and Volume
You can describe the graph of a function in words
10 mins total
3 mins class demonstration - 4 minutes group - 3 mins class share
pg 172-3
Your teacher will demonstrate filling a cylinder with water to investigate the height of water in the cylinder as a function of the water volume.
1) Before we get started, make a prediction about the shape of the graph.
2) As you watch the demonstration, record the data in the table.
0 | 28.27 | 56.5 | 84.8 | 113.1 | 127.2 |
0 | 1 | 2 | 3 | 4 | 4.5 |
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.2 Activity: Height and Volume
You can describe the graph of a function in words
The point (51.2,2.6) means that the volume of water in a cylinder with a 5 cm diameter is 51.2 ml when the height of the water is 2.6 cm.
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.2 Activity: Height and Volume
You can describe the graph of a function in words
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.2 Activity: Height and Volume
You can describe the graph of a function in words
As the radius is larger, the slope is less steep. This is because for a cylinder with a larger base, the same volume of water will not fill as high up the side of the cylinder.
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.3 Activity: What Is the Shape?
You can describe the graph of a function in words
10 mins total
4 mins individual - 3 minutes group - 3 mins class share
pg 173-4
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.3 Activity: What Is the Shape?
You can describe the graph of a function in words
A shape in the form of two cylinders stacked on top of each other, with the upper cylinder having a greater radius. The height grows linearly with the volume in each cylinder, but as the water level rises into the second container, the height will begin to grow less quickly
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.3 Activity: What Is the Shape?
You can describe the graph of a function in words
3 cylinders stacked on top of each other. The bottom cylinder should be the tallest. The middle cylinder should be shorter and have a smaller radius than the bottom. The top cylinder should be the shortest but have the largest radius.
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.3 Activity: What Is the Shape?
You can describe the graph of a function in words
Both containers are made up of cylinders stacked on top of each other. The containers are different because the first container is made up of two parts, while the second is made up of three parts.
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Filling Containers
You can describe the graph of a function in words
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Lesson Synthesis
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Which Cylinder?
You can describe the graph of a function in words
Cylinder b. A cylinder with a large radius would have a smaller change in height (slope) for the same volume of water added when compared to a cylinder with a smaller radius. Since the line for b has the smaller slope, it must be the cylinder with the larger radius.
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Cool-down
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 5 β Lesson 11
Learning
Targets
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.
All curriculum excerpts are under the following licenses:
IM 6β8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6β8 Math Curriculum is available at https://openupresources.org/math-curriculum/.
Adaptations and updates to IM 6β8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.
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