Lesson 7: Comparing and Representing Functions in Different Forms
Unit Title: Linear Functions
Approx. time:
Lesson: 7 Comparing and Representing
2 days
Functions in Different Forms
A. Focus and Coherence
Students will know…
 Comparisons can be made between distinct linear
functions, whether they are modeled in equations,
tables, or graphs.
 The same linear function can be modeled as an
equation, in a table, and as a graph.
Students will be able to…
 Compare properties of two linear functions
(including proportional relationships) represented
in different ways (e.g. compare a distance-time
graph to a distance-time equation to determine
which of the two moving objects has greater
speed).
 Represent the same linear function as an equation,
in a table, and as a graph, given a scenario (i.e.
word problem).
CCSS-M Standards: 8.EE.5, 8.F.2, 8.F.4
B. Evidence of Math Practices
What will students produce when they are making sense,
persevering, attending to precision and/or modeling, in
relation to the focus of the lesson?
Students will provide three different representations of
the same linear function (by table, graphically, and
algebraically).
Students will make sense of problems through the
comparison of different linear functions.
Students will attend to precision by using the correct
academic language when defending their answers to their
classmates. Examples of this language include “slope”,
“graph”, “table”, “equation”, “y-intercept”, and “unit
rate”.
Student prior knowledge:
 Students are able to graph linear functions.
 Students are able to determine a function rule
from a table of data.
 Students are able to determine a function rule
from a graph.
 Students are able to identify the slope of a line.
Which math concepts will this lesson lead to?
 Systems of equations
Essential Question(s)
 What does slope mean and what does it represent?
 When is it appropriate to use rate of change?
 Why is it important to fit data to a linear function?
 In what kinds of situations is it appropriate to use a linear function as the model?
8th Grade
Linear Functions
Formative Assessments
Day 1: Use as an exit ticket out the door to establish whether more review is needed for the next day.
Directions: Make sure each function is represented as a table of values, graphically, and with an equation.
Table of Values
x
Graph
Equation
y
𝑦 = 3𝑥 + 2
x
y
x
y
-1
-2
1
2
3
6
Day 2:
Give as an end of the day quiz before the students leave.
(Please see number 10 on assessment piece 8b, and number 1 on 10b)
8th Grade
Linear Functions
Anticipated Student Preconceptions/Misconceptions
Choosing x-values to start the T-chart
Not having the skills to translate the solutions between the three display methods
Materials/Resources
Day 1: Matching cards cut up and placed in envelopes, pencil, paper, exit ticket
Day 2: Buying Movies – Shari, Buying Movies – Bret, Online vs. In Store comparison, pencil, paper
C. Rigor: fluency, deep understanding, application and dual intensity
What are the learning experiences that provide for rigor? What are the learning experiences that provide for evidence of
the Math Practices? (Detailed Lesson Plan)
Warm Up (5 minutes each day)
Warm-Ups are done on the weekly sheet that the student keeps and are collected at the end of the week.
Day 1:
Identify the slope and y-intercept of each equation:
a) 𝑦 = 3𝑥 + 6
b) 2𝑦 = −8𝑥 − 2
c) 3𝑥 + 2𝑦 = 14
Day 2:
Given the table below, provide both the corresponding equation and graph.
x
-1
0
1
-2
y
12
10
8
6
Lesson
Day 1:
 (5 minutes) Review Warm-Up

(35 minutes) Matching activity: Group the students into groups of three. Give each group an envelope with precut equations, graphs, and tables. Have the students match the appropriate graph to the appropriate equation
with the appropriate table. Each solution will have all three items, however, some of the cards are blank so that
the student will have to fill in the answers themselves. Teacher should be walking around, answering questions,
and directing conversation.

(10 minutes) Exit ticket problems
Day 2:
 (5 minutes) Review Warm-Up

(15 minutes) Buying Movies – Shari: Working in pairs, let the students try this problem for about 7 or 8 minutes
before jumping in to walk them through it. Teacher should be walking around, answering questions, and
directing conversation.
8th Grade
Linear Functions

(10 minutes) Buying Movies – Bret: Working in pairs, the students should be doing this worksheet without the
teacher leading. Teacher should be walking around, answering questions, and directing conversation.

(10 minutes) Online vs. In Store Comparison – Working in pairs, the students should be answering the questions
on the third worksheet.

(10 minutes) Formative Quiz
Closure
For both days, the closure items are the formative assessments that have been listed for this lesson.
Suggested Homework/Independent Practice
Day 1: Create your own ticket out the door that looks identical to the one we did in class today. Make three linear
functions, but only give one clue in each column. Show one of the functions as an equation, show one as a graph, and
show one as a table. Be ready to swap with a partner tomorrow so you can try to figure out each other’s functions!
Day 2:
8th Grade
Linear Functions