Unit 5

Introduction to Functions

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Functions and Volume

Lesson 2

Expressions and Equations

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Let’s learn what a function is.

Unit 5 ● Lesson 2

Learning

Goal

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Square Me

Unit 5 ● Lesson 2 ● Activity 1

Here are some numbers in a list:

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1, -3, , 3, 2, , 0.5

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• How many different numbers are in the list?
• Make a new list containing the squares of all these numbers.
• How many different numbers are in the new list?
• Explain why the two lists do not have the same number of different numbers.

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Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Square Me

Unit 5 ● Lesson 2 ● Activity 1

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Can you think of other rules where different inputs can have the same output?

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Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

You Know This, Do You Know That?

Unit 5 ● Lesson 2 ● Activity 2

• A person is 60 inches tall. Do you know their height in feet?
• Do the rules in the diagrams match the justifications you just heard?

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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.

You Know This, Do You Know That?

Unit 5 ● Lesson 2 ● Activity 2

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Say ‘yes’ or ‘no’ for each question. If ‘yes’, draw an input-output diagram. If ‘no’, give examples of two different outputs that are possible for the same input.

• A person is 5.5 feet tall. Do you know their height in inches?
• A number is 5. Do you know its square?
• The square of a number is 16. Do you know the number?
• A square has a perimeter of 12 cm. Do you know its area?
• A rectangle has an area of 16 cm². Do you know its length?
• You are given a number. Do you know the number that is �as big?
• You are given a number. Do you know its reciprocal?

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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.

You Know This, Do You Know That?

Unit 5 ● Lesson 2 ● Activity 2

• Was the warm-up, where you have to square numbers, an example of a function?
• Is the reverse, that is knowing what number was squared to get a specific number, a function?

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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.

Using Function Language

Unit 5 ● Lesson 2 ● Activity 3

A person is 60 inches tall. Do you know their height in feet?

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Since the answer to this question is ‘yes’, we can write a statement like, "height in feet depends on the height in inches" or "height in feet is a function of height in inches."

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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.

Using Function Language

Unit 5 ● Lesson 2 ● Activity 3

Here are the questions from the previous activity. For the ones you said yes to, write a statement like, “The height a rubber ball bounces to depends on the height it was dropped from” or “Bounce height is a function of drop height.” For all of the ones you said no to, write a statement like, “The day of the week does not determine the temperature that day” or “The temperature that day is not a function of the day of the week.”

• A person is 5.5 feet tall. Do you know their height in inches?
• A number is 5. Do you know its square?
• The square of a number is 16. Do you know the number?
• A square has a perimeter of 12 cm. Do you know its area?
• A rectangle has an area of 16 cm². Do you know its length?
• You are given a number. Do you know the number that is as big?
• You are given a number. Do you know its reciprocal?

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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.

Using Function Language

Unit 5 ● Lesson 2 ● Activity 3

• Do any of you have a different response from your partner that you were not able to reach an agreement on?
• Invent a new question like the ones in the task that is not a function.

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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.

Same Function, Different Rule?

Unit 5 ● Lesson 2 ● Activity 4

Which input-output rules could describe the same function (if any)? Be prepared to explain your reasoning.

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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.

Same Function, Different Rule?

Unit 5 ● Lesson 2 ● Activity 4

• Do the latter two input-output rules describe the same function since they both take an input of 10 to an output of 100?
• Do any of the input-output rules describe the same function?

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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.

Introduction to Functions

Unit 5 ● Lesson 2

• How else could we describe the function 'double the input'?
• Is the rule 'the radius of a circle with circumference C' a function? Why or why not?
• Why does the description 'A person's age is 14 years old. What is their height in inches?' not define a function?

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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.

Unit 5 ● Lesson 2

• I know that a function is a rule with exactly one output for each allowable input.
• I know that if a rule has exactly one output for each allowable input, then the output depends on the input.

Learning

Targets

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Wait Time

Unit 5 ● Lesson 2 ● Activity 5

You are told that you will have to wait for 5 hours in a line with a group of other people. Determine whether:

• You know the number of minutes you have to wait.
• You know how many people have to wait.

For each statement, if you answer yes draw an input-output diagram and write a statement that describes the way one quantity depends on another.

If you answer no give an example of 2 outputs that are possible for the same input.

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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.

function

Unit 5 ● Lesson 2

A function is a rule that assigns exactly one output to each possible input.

The function y = 6x + 4 assigns one value of the output, y, to each value of the input, x. For example, when x is 5, then y = 6(5) + 4 or 34.

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Glossary

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).

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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).

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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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