Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Warm Up:
Evaluate each expression for the given value of the variable.
1. 2x ­ 5 when x = 6
2. 13 ­ c + 4 when c = 2
3. 45 ÷ z when z = 9
4. y2 + 14 when y = 3
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Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Agenda:
1. Launch Question
2. Notes on Lesson 4­1 Using Two
Variables to Represent a
Relationship.
3. Independent Practice on Lesson
4­1.
4. Homework
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Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Launch:
Think inside and outside the box. Inside the box, write three things that relate to the weight of the box. Outside the box, write three things about the box that do not relate to its weight.
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Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Focus Question:
What does it mean for one
quantity to depend on another?
How do you represent such a
relationship?
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Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Lesson 4 ­ 1
Using Two Variable to Represent a Relationship
Suppose you are going to buy 12 pieces of
fruit and you only buy apples and pears.
equation ­
There are two related and unknown
quantities in this situation: number of apples
and number of pears. A change in one
affects a change in the other. The more
apples you buy, the fewer pears you buy.
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Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Lesson 4 ­ 1
Using Two Variable to Represent a Relationship
Example 1: A fruit basket business takes 103 orders in
one month. Orders can be placed online or over
the phone. Identify the related and unknown
quantities.
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Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Lesson 4 ­ 1
Using Two Variable to Represent a Relationship
Suppose you are going to buy 12 pieces of
fruit and you only buy apples and pears.
equation ­
You can assign a variable to each of the
related quantities.
a = number of apples
p = number of pears
You can write an equation to represent the
relationship.
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Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Lesson 4 ­ 1
Using Two Variable to Represent a Relationship
Example 2: After­school practice is 90 minutes long.
Some of that time is spent doing warm­ups and the
rest is spent doing drills. Write an equation to
represent the situation.
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Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Lesson 4 ­ 1
Using Two Variable to Represent a Relationship
Vocabulary:
equation ­
Dependent
Variable:
A value that changes in response to
another variable.
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Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Lesson 4 ­ 1
Using Two Variable to Represent a Relationship
Vocabulary:
equation ­
Independent
Variable:
A value that affects change on the
dependent variable.
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Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Lesson 4 ­ 1
Using Two Variable to Represent a Relationship
The growth of a plant depends on how much
water it receives.
equation ­
Amount of growth and amount of water are
related and unknown quantities.
The amount of growth is the dependent
variable and the amount of water is the
independent variable.
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Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Lesson 4 ­ 1
Using Two Variable to Represent a Relationship
Example 3: Classify each highlighted quantity as an
independent or dependent variable.
a.) You biked m miles to the store and burned c
Calories.
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Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Lesson 4 ­ 1
Using Two Variable to Represent a Relationship
Example 3: Classify each highlighted quantity as an
independent or dependent variable.
b.) The category of a hurricane is related to the
wind speed of the hurricane.
c.) The population of a state determines the
number of representatives from the state in the
U.S. Congress.
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Lesson 4­1 Using Two Variables to Represent a Relationship.notebook
April 03, 2017
Classwork:
1.
2.
3.
Lesson 4­1 Student Companion
Lesson 4­1 Homework Worksheet
Lesson Check
Lesson Check: In each situation, identify the independent and dependent variables.
1. The wind chill factor is related to the wind speed.
2. The amount of merchandise bought determines the amount of sales tax charged.
3. You earned d dollars for working h hours.
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