Unit 5
Connecting Representations of Functions
Functions and Volume
Lesson 7
8.F.A.2: Compare properties of two functions each represented in a different way.
8.F.A.3: Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear..
Expressions and Equations
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Which are the Same? Which are Different?
Unit 5 ● Lesson 6
1 min individual - 1 min team share - 3 mins class share
Page 162
The graph & equation are the same function but the variables are different.
The table has opposite outputs for the same input as the first two. The graph would be a line reflected across the y-axis as compared with the first two. y= -2x
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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.
Let’s connect tables, equations, graphs, and stories of functions.
Unit 5 ● Lesson 7
We will be able to identify connections between different representations of functions so that we can compare inputs and outputs of functions that are represented in different ways.
Learning
Goal
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Where were we? Where are we? Where are we going?
Unit 5 ● Lesson 7
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.
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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.
7.1 Activity: Comparing Temperatures
I can compare inputs and outputs of functions that are represented in different ways.
10 mins total
3 mins individual - 2 minutes group - 4 mins class share
pg 163
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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.
7.1 Activity: Comparing Temperatures
I can compare inputs and outputs of functions that are represented in different ways.
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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.
7.1 Activity: Comparing Temperatures
I can compare inputs and outputs of functions that are represented in different ways.
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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.
7.1 Activity: Comparing Temperatures
I can compare inputs and outputs of functions that are represented in different ways.
Let's discuss how we used the two different representations (graph & table) to get our answers.
The graph, since I just have to find the highest part. In the table I have to read all the values in order to find the highest temperature.
The table is quicker since the numbers are given and I only have to subtract. In the graph I had to figure out the temperature values for both times before I could subtract.
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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.
7.2 Activity: Comparing Temperatures
I can compare inputs and outputs of functions that are represented in different ways.
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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.
7.2 Activity: Comparing Volumes
I can compare inputs and outputs of functions that are represented in different ways.
10 mins total
3 mins individual - 2 minutes group - 3 mins class share
Cube
Sphere
pg 164
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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.
7.2 Activity: Comparing Volumes
I can compare inputs and outputs of functions that are represented in different ways.
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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.
7.2 Activity: Comparing Volumes
I can compare inputs and outputs of functions that are represented in different ways.
Let's discuss how we used the two different representations (graph & equation) to get our answers.
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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.
Connecting Representations of Functions
I can compare inputs and outputs of functions that are represented in different ways.
Graphs require estimation but easily let us identify important features such as highest point or steepest section.
Tables immediately let us find output values but only for limited input values.
Equations let us precisely compute outputs for all inputs but only one at a time.
We used each representation to find outputs for different inputs.
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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.
Comparing Different Areas
I can compare inputs and outputs of functions that are represented in different ways.
Less than. From the table the area of a square of side length 2 inches is 4 square inches,whereas from the equation the area of a circle with radius 1.2 inches is about 4.52 square inches.
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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 ● Lesson 7
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.
10 things that require zero talent to be successful
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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.
Glossary
A function is a rule with exactly one output for each allowable input
Domain
Range
y depends on x
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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.
Glossary
Unit 5 ● Lesson 1-2
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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.
Glossary
Unit 5 ● Lesson 1-2
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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 6–8 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 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.
Adaptations and updates to IM 6–8 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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