Curriculum / Math / 8th Grade / Unit 4: Functions / Lesson 4
Math
Unit 4
8th Grade
Lesson 4 of 12
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Represent functions with equations.
The core standards covered in this lesson
8.F.A.1 — Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8.
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 (x, y) 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.
The foundational standards covered in this lesson
7.RP.A.2.B — Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
7.RP.A.2.C — Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Water flows from a faucet into a bathtub at a constant rate of 7 gallons of water pouring out every 2 minutes. The bathtub is initially empty and the plug is in.
a. Determine a rule that describes the volume of water in the tub as a function of time. Write your rule as an equation.
b. If the tub can hold 50 gallons of water, how long will it take to fill the tub?
Grade 8 Mathematics > Module 5 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
You are filling the same tub (from Anchor Problem 1) with water flowing in at the same constant rate, but there were initially 8 gallons of water in the tub.
a. Determine a new rule that describes the volume of water in the tub as a function of time. Write your rule as an equation.
b. The tub can still hold 50 gallons of water. How long will it take now to fill the tub?
Water flows from a faucet at a constant rate. Assume that 6 gallons of water are already in a tub by the time we notice the faucet is on. This information is recorded in the first column of the table below. The other columns show how many gallons of water are in the tub at different numbers of minutes since we noticed the running faucet.
a. What is the rate of change? Explain what this means in the context of the situation.
b. Write an equation that describes the volume of water in the tub as a function of time.
c. How long was the faucet on before it was noticed?
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Edwin purchased a used car to drive himself back and forth from his new job. He only uses the car to drive to work and back home, and he takes the same route each time. The table below shows the mileage of the car and the number of days that Edwin has taken the car to work.
a. How many miles does Edwin drive on a workday, round trip?
b. How many miles were on the car when Edwin bought it?
c. Write an equation that describes the number of miles on the car as a function of the number of days that Edwin drives it to work.
d. What will be the mileage of Edwin’s car after he drives it to and from work 100 days?
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 3
Lesson 5
Topic A: Defining Functions
Define and identify functions.
8.F.A.1
Use function language to describe functions. Identify function rules.
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Topic B: Representing and Interpreting Functions
Identify properties of functions represented in tables, equations, and verbal descriptions. Evaluate functions.
8.F.A.1 8.F.A.2 8.F.B.4
8.F.A.1 8.F.B.4
Read inputs and outputs in graphs of functions. Determine if graphs are functions.
Identify properties of functions represented in graphs.
Topic C: Comparing Functions
Define and graph linear and nonlinear functions.
8.F.A.3
Determine if functions are linear or nonlinear when represented as tables, graphs, and equations.
8.F.A.1 8.F.A.3
Compare functions represented in different ways (Part 1).
8.F.A.2
Compare functions represented in different ways (Part 2).
Topic D: Describing and Drawing Graphs of Functions
Describe functions by analyzing graphs. Identify intervals of increasing, decreasing, linear, or nonlinear activity.
8.F.B.5
Sketch graphs of functions given qualitative descriptions of the relationship.
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