Common Core High School Functions Teaching and Learning Resources
Domain: LE: Linear, Quadratic, and Exponential Models
Select the cluster for resources on this page:
LEA: Construct and compare linear
and exponential models and solve problems
Standards:
 LEA.1. Distinguish between situations that
can be modeled with linear functions and with exponential functions.
 LEA.1.a. Prove that linear functions
grow by equal differences over equal intervals, and that
exponential functions grow by equal factors over equal
intervals.
 LEA.1.b. Recognize situations in which
one quantity changes at a constant rate per unit interval
relative to another.
 LEA.1.c. Recognize situations in which
a quantity grows or decays by a constant percent rate per unit
interval relative to another.
 LEA.2. Construct linear and exponential
functions, including arithmetic and geometric sequences, given a
graph, a description of a relationship, or two inputoutput pairs
(include reading these from a table).
 LEA.3. Observe using graphs and tables
that a quantity increasing exponentially eventually exceeds a
quantity increasing linearly, quadratically, or (more generally) as
a polynomial function.
 LEA.4. For exponential models, express as
a logarithm the solution to ab^{ct} = d where
a, c, and d are numbers and the base b
is 2, 10, or e; evaluate the logarithm using technology.
Technologyenhanced investigations:
Mathwords.com: Math Dictionary:
Key vocabulary for this domain. Use
with LEA, LEB:
CK12: Algebra: Concepts, videos, and practice problems for learners
to complete:
NCTM Illuminations:
Shedding Light on a Subject: This unit has four lessons in which
learners explore "the development of a mathematical model for the decay
of light passing through water. The goal of this investigation is
a rich exploration of exponential models in context." Movie clips and
simulations are included, along with virtual manipulatives (interactive
grapher for data and line of best fit), which help learners to identify
a function that models their data. Use with LEA.
Ohio Resource Center on YouTube: Tutorials for High School
Mathematics: Logarithms.
Definition of and computation with both common logarithms and base e
natural logarithms.
LearnZillion:
 Lesson set:
Distinguish
between linear functions and exponential functions: This is a
series of seven video lessons that also include guided practice on this
topic. Videos demonstrate how to model exponential growth
situations with 2 variables; how to determine the end behavior of a
polynomial or exponential function, and the greater of two polynomial
functions; how to compare polynomial and exponential growth; name the
3rd ordered pair belonging to a linear or exponential function. Aligns
with LEA.1.
 Lesson set:
Prove how linear
functions grow (and exponential functions): This is a series
of two video lessons that also include guided practice on this topic of
how linear and exponential functions grow. Aligns with LEA.1.a.
 Lesson set:
Prove that,
over equal intervals, linear functions grow by equal differences
and exponential functions grow by equal factors. Five
video lessons: Identify linear functions by linking equal
differences to equal intervals, graph an exponential function,
understand the rate of change in exponential functions,
distinguish between linear and exponential functions by
examining intervals and using tables. Aligns with
LEA.1.a.
 Lesson set:
Recognize when
one quantity changes at a constant rate per unit interval of
another. Four video lessons: Compare relationships
between quantities using linear models, interpret d=rt by
graphing its linear function, find average rates of change using
data in tables, calculate average rate of change using d=rt.
Aligns with LEA.1.b.
 Lesson set:
Understand exponential growth and decay: This is a series
of four video lessons that also include guided practice on this topic.
Videos demonstrate writing exponential growth and decay functions,
determining which of two growing quantities will exceed the other at a
given point in time. Aligns with LEA.1.c.
 Lesson set:
Recognize when
one quantity grows or decays by a constant percent rate per unit
interval of another. Four video lessons: Graph
depreciation and halflife of an element using an exponential
decay model, graph the spread of behaviors using an exponential
growth model, compare exponential growth models using graphs.
Aligns with LEA.1.c.
 Lesson set:
Express
solutions to exponential models as logarithms; evaluate using
technology. Five video lessons: Evaluate logarithms
using exponentials, solve for time in a continuously compounding
function, solve realworld problems using properties of
logarithms, use an exponential formula to solve a population
problem, solve a halflife model. Aligns with LEA.4.
MIT BLOSSOMS: Video lessons with additional teacher
and learner resources. Descriptions are from the video summaries.
 Flu Math Games:
"This video lesson shows students that math can play a role in
understanding how an infectious disease spreads and how it can
be controlled." Additional simulations are included.
Aligns with Algebra standards SSEB.3.c and REIA.1; Function
standards IFC.8.b, BFB.4.a, and LEA1.(a, c); and Statistics
and Probability standards IDB.6.a, ICA.1, ICB.4, CPA.2, and
MDA.1.
 Free Fall: "This video lesson is an example of "teaching for
understanding" in lieu of providing students with formulas for
determining the height of a dropped (or projected) object at any
time during its fall. The concept presented here of creating a
chart to organize and analyze data collected in a simple
experiment is broadly useful." Aligns with Function
standards IFB.6, IFC.7.a, LEA.1.a, and
Algebra standard CEDA.2.
 The Power of Exponentials, Big and Small:
"Exponential growth is keenly applicable to a variety of
different fields ranging from cell growth in biology, nuclear
chain reactions in physics to computational complexity in
computer science. In this lesson, through various examples and
activities, [the presenters] have tried to compare exponential
growth to polynomial growth and to develop an insight about how
quickly the number can grow or decay in exponentials."
Aligns with Algebra standards SSEB.3.c and CEDA.2 and Function
standards IFA.3, IFC.7.(a, c, e), IFC.8.b, and LEA.1.(a, c).
 The Towers of Hanoi: Experiential Recursive Thinking:
"This lesson is about the Towers of Hanoi problem, a classic
famous problem involving recursive thinking to reduce what
appears to be a very large and difficult problem into a series
of simpler ones. The learning objective is for students to
begin to understand recursive logic and thinking, relevant to
computer scientists, mathematicians and engineers."
Aligns with Algebra standard SSEB.3.c, and Function standards
IFC.8.b and LEA.1.a.
 Tragedy of the Commons:
"This lesson introduces students to the “Tragedy of the
Commons,” an extended metaphor for problems of shared
environmental or manmade resources that are overused and
eventually depleted. In this metaphor, shared resources are
compared to a common grazing pasture, or “commons,” on which any
dairy farmer can graze as many cows as he/she wishes. If too
many cows are added to the commons, they will overeat the grass
in the pasture and the shared resource will become depleted – a
disadvantage to everyone. In this lesson, students will be
inspired to think about possible solutions to this problem."
Aligns with Algebra standard SSEB.3.c and Function standards
IFB.4, IFC.8.b, LEA.1.a, LEA.3, and LEB.5.
Zweigmedia.com: Tutorials and examples using
fillin or multiple choice to test understanding. Learners can
also choose to do game versions of some topics. Use with LEA.1
and LEA.2:

Functions and Models: Part A: Cost, revenue, and profit models;
Part B: Demand, supply, and timechange models

Linear functions and models: In three parts, learners get the
basics of slope and intercepts; finding the equation of a line; then
applications of linear models.
Wolfram Demonstrations Project:
Download the free Wolfram CDF player
to interact with the following manipulatives. Note: Within the
Wolfram Demonstration Project are
9 manipulatives addressing LEA.1,
19 manipulatives for LEA.2,
1 manipulative for LEA.3, and
3 manipulatives for LEA.4. Among those:
Multiple Choice:
ACT Academy and OpenEd:
Khan Academy: Practice questions with videos.
Constructedresponse:
Khan Academy: Practice questions with videos.
Performance tasks:
Illustrative Mathematics:
Functions:
Inside Mathematics: MARS Task:
Functions (pdf) or see all MARS Tasks: Functions &
Relations: Course 1 Algebra: Scroll down the page to select
Functions: Learners work with graphs of linear and nonlinear
functions. This task aligns with function standards IFC.7, IFC.9 and LEA.3.
Mathematics Assessment Project: Standards: High School: Functions:
https://www.map.mathshell.org/stds.php?standardid=1448
Mathematics Common Core Toolbox:
PARCC Prototype Project: Under High School Tasks, select:
 Cellular growth: "Students write geometric
sequences both recursively and with an explicit formula and use
the two representations to model situations. In this task,
students consider the use of one or more representations to
solve a realworld problem and choose the type of sequence to
represent a situation." This fourpart task aligns with function
standards BFA.2 and LEA.2 and mathematical practice standards
MP.2 and MP.4.
 Golf balls in water: "Students model
approximately linear data with a linear function. To do so, they
must use contextual information and construct representations of
linear relationships as well as interpret parameters of the
linear models in the context. It makes use of common sense
understandings of volume as it relates to changing the
dimensions of a glass jar; thus, the mathematics is presented in
a context that is novel, yet has multiple entry points for
students." This threepart task aligns with function standards BFA.1,
LEA.2, LEB.5, and mathematical practice standards MP.1, MP.2
and MP.4.
 Rabbit populations: "Students analyze
the situation (rabbit population growth) and create a
mathematical model that represents it. Students are then
presented with a second rabbit population that is slightly
different and asked to compare the models for the two
populations. This requires students to identify which function
parameters and key features of the graph will change based on
the adjustment in context. Students then use the two models
together to answer mathematical questions." This threepart task aligns
with function standards BFA.1, LEA.2, LEB.5, and mathematical
practice standard MP.4.
Mathematics Vision Project,
Secondary 1 Student Edition:
Module
3: Arithmetic and Geometric Sequences: This module
contains 10 classroom tasks. Function standards addressed in
Module 2 include LEA.1, LEA.2, LEB.5, and BFA.1.
 Task 1: Growing Dots; Task 2: Growing, Growing Dots; Task 3: Scott’s
Workout; Task 4: Don’t Break the Chain; Task 5: Something to Chew
On; Task 6: Chew On This; and Task 7: What Comes Next? What Comes
Later? align to both standards LEA.1 and LEA.2.
 Task 8: What Does It Mean?; and Task 9: Geometric Meanies;
Task 10: I Know … What Do You Know? align to standard LEA.2.
Mathematics Vision Project,
Secondary 1 Student Edition:
Module
4: Linear and Exponential Functions: This module contains
10 classroom tasks. Function standards addressed in Module 3
include IFA.3, IFC.7, LEA.1, LEA.2, LEA.3, LEB.5, and BFA.1,
BFA.2. Five of those include function standards LEA.1,
LEA.2, LEA.3.
 Task 2: Sorting Out The Change; and Task 3:
Where’s My Change? align to standards LEA.1 and LEA.2.
 Task 5: Getting Down to Business aligns to standards LEA.2
and LEA.3.
 Task 4: Linear, Exponential or Neither aligns to
standard LEA.3.
 Task 6: Growing, Growing, Gone align to standards
LEA.1, LEA.2, and LEA.3.
Mathematics Vision Project,
Secondary
3 Student Edition:
Back to top
LEB: Interpret expressions for
functions in terms of the situation they model
Standards:
 LEB.5. Interpret the parameters in a
linear or exponential function in terms of a context.
Technologyenhanced investigations:
NCTM Illuminations:
Function Matching: Students see the graph and determine parameters.
A. Dendane: Analyze Math:
Exponential Functions: HTML5 applet to
explore the properties of the graphs of exponential functions.
Learners change parameters a, b, c, d, and B in equations of the form f(x)=
a(B^{b(x+c)})+ d.
MIT BLOSSOMS: Video lesson with additional teacher and learner
resources. Description is from the video summary.
Tragedy of the Commons:
"This lesson introduces students to the “Tragedy of the
Commons,” an extended metaphor for problems of shared
environmental or manmade resources that are overused and
eventually depleted. In this metaphor, shared resources are
compared to a common grazing pasture, or “commons,” on which any
dairy farmer can graze as many cows as he/she wishes. If too
many cows are added to the commons, they will overeat the grass
in the pasture and the shared resource will become depleted – a
disadvantage to everyone. In this lesson, students will be
inspired to think about possible solutions to this problem."
Aligns with Algebra standard SSEB.3.c and Function standards
IFB.4, IFC.8.b, LEA.1.a, LEA.3, and LEB.5.
Wolfram Demonstrations Project:
Download the free Wolfram CDF player
to interact with the following manipulative:
Final number of bacteria cells. Aligns with LEB.5.
Multiple Choice:
Constructedresponse:
Performance tasks:
Illustrative Mathematics:
Functions:
Mathematics Assessment Project: Standards:
High School: Functions:
https://www.map.mathshell.org/stds.php?standardid=1448
Mathematics Common Core Toolbox:
PARCC Prototype Project: Under High School Tasks, select:
 Golf balls in water: "Students model
approximately linear data with a linear function. To do so, they
must use contextual information and construct representations of
linear relationships as well as interpret parameters of the
linear models in the context. It makes use of common sense
understandings of volume as it relates to changing the
dimensions of a glass jar; thus, the mathematics is presented in
a context that is novel, yet has multiple entry points for
students." This threepart task aligns with function standards BFA.1,
LEA.2, LEB.5, and mathematical practice standards MP.1, MP.2
and MP.4.
 Rabbit populations: "Students analyze
the situation (rabbit population growth) and create a
mathematical model that represents it. Students are then
presented with a second rabbit population that is slightly
different and asked to compare the models for the two
populations. This requires students to identify which function
parameters and key features of the graph will change based on
the adjustment in context. Students then use the two models
together to answer mathematical questions." This threepart task aligns
with function standards BFA.1, LEA.2, LEB.5, and mathematical
practice standard MP.4.
Mathematics Vision Project,
Secondary 1 Student Edition:

Module
3: Arithmetic and Geometric Sequences: This module contains
10 classroom tasks. Six of those tasks include function standard
LEB.5. Function standards addressed in Module 2 include LEA.1,
LEA.2, LEB.5, and BFA.1.

Module
4: Linear and Exponential Functions: This module contains 10
classroom tasks. Function standards addressed in Module 3 include
IFA.3, IFC.7, LEA.1, LEA.2, LEA.3, LEB.5, and BFA.1, BFA.2. Task
4: Linear, Exponential, or Neither; Task 5: Getting Down to Business;
Task 7: Making My Point; Task 9: Up a Little, Down a Little align
to function standard LEB.5.
Mathematics Vision Project,
Secondary
3 Student Edition:
Back to top Common Core Math:
Intro  HS Functions Domain:
IF  BF  LE  TF 