Transformations of Graphs
Topic/Title of Lesson:
Transformations
Class Name and Level(s):
Algebra 2/ 10th -11th grade
Learning Goal, Theme or Question for
Lesson
Goal:
Students are able to connect graphs, tables and
equations given one of the three.
Students should also be able to predict how the
graph of a function should shift left, right, up, or
down given a certain change to the original
equation.
Date:
Adjustments to ensure equity:
This lesson will incorporate the use of multiple
teaching strategies, visual aids, auditory elements,
and kinesthetic elements. This lesson, also, allows
for students to collaborate on some class work but
also have the opportunity to work on their own.
Key Vocabulary for Lesson:
 Linear/ non-linear
 X-axis/ y-axis
 Shift
 Y-intercept/ x-intercept
 X and Y coordinates
Content Standard(s) and/or Content Objectives:
 NCTM Algebra: Understand patterns, relations, and functions.

NCTM Geometry: Apply transformations and use symmetry to analyze mathematical
situations.

Montana Content Standard: Represent functions in a variety of ways including tables,
graphs, or diagrams, verbal descriptions, and symbolic expressions in recursive and
explicit form. Select and justify an appropriate form for solving a given problem with and
without technology.
Motivation or Hook for the Lesson:
Transformations of graphs is an interesting topic. I would start this lesson by showing the students
graphs that they are somewhat familiar with but not completely. Graphs such as y= –IxI and y= x2 +2. I
would hope that students recognize that the original functions are functions that they are familiar with.
That is recognize y = IxI and y= x2 . This should link students’ understanding of those common functions to
this lesson about shifts and transformations of functions.
Strategies you will use to link prior knowledge/personal experience to this lesson:
Transformations of these graphs are important since so many graphs they will encounter are
transformations of other graphs.
Accommodations for special needs->accelerated learners:
Special needs students can be paired with other students to help them better understand the material.
Students can also better understand the material by offering them some technological assistance such as
graphing calculators. The teacher can challenge accelerated learners to make a documentary using
cameras to explain why certain changes to the equation will alter the graph.
Materials and or technology needed for this lesson:
Teacher: Whiteboard, dry erase markers, projector, power point, computer, video camera, and TI-83
graphing calculators.
Student: Graph paper and pencil.
Learning Objectives: What should students know Assessment and Performance Levels: How
and be able to do to demonstrate mastery of this
concept/standard?
will you assess your students’ attainment of the
learning objectives?
1. Students will be able to identify the connections
between the graphs, tables, and equations of
important functions such as y=X2 and y=X3 as well
as several other important non-linear functions.
2. Students will be able to identify what changes
must be made to the equations of the functions in
order to shift the function left, right, up or down a
specific amount of units.
3. Students will be able to understand and convey
why certain changes to the equations will transform
the graph. And also be able to identify what changes
have been made to the equation given the graph
with the changes made.
At the end of this lesson there will be a Jeopardy
game. The students will be split into teams of 3-4
students. The students will be expected to work in
groups as well as individually to demonstrate that
they understand the material. There will be 1
category that requires the students to work in
groups. This category will require the students to do
multiple things such as given a graph. Write the
equation of the function and make a table for at least
10 points. There will also be several categories:
graphs, functions, tables,
transformations/explanations and groups. This
jeopardy game will assess all three learning
outcomes. The categories require students to make
connections between the graphs, tables, and
functions and to identify them. The transformation
category obligates the students to identify the
changes of graphs given the function or vice-versa.
This category will also force students to demonstrate
that they understand what changes made to one
form will make to the other.
Last, there will be an explanations category that will
require students to verbally explain why certain
changes made will make certain changes. This
requires students to have a deeper understanding of
why things change the way that they do.
Procedure/Sequencing of Lesson and Teaching Strategies
Strategy/Minutes: Please indicate which strategy you will you use how much time you will devote to each
__30_ mins. Modeling/ Whole Class work (includes Jeopardy activity)
__10 _mins. Small Group/ independent practice (part of jeopardy activity)
__10_ mins Partner Work (students will explore the graphs of equations in partners)
Procedure for Lesson: Please describe a step by step procedure for your lesson
1. Introduction/ attention getter with interesting non-linear graphs.
2. Partner work.
 Students will be split into groups of 2-3 students. Each group of students will be given several
equations to graph (this will require students to make a table for each function as well). An example
would be y= x2 , y= (x-2)2, y= x2 – 2, y=(x+2)2, y=x2 +2, and y=(1/2x)2. Each group would get a
different function. Then, I would have the students come up with the plain function first to sketch a
graph of their function to show the class what their function looks like. This will happen for a couple
of functions such as the square root function and x cubed as well.
3. As a class, we will explore why the changes to the graphs occur and thus get an idea of why certain
shifts or changes happen.
4. Last, the Jeopardy game. Split students into 3 approximately even groups. The students will rotate
threw so that only one student from each group will participate at a time (except for during the group
category).
5. Here is an outline of what is expected for each category:
a) Graphs- In this category, the students will be given the graph of a function. The students must
come up with the equation of the graph or make a table of 10 points. The table must include the yintercepts and x-intercepts where appropriate.
b) Tables- In this category, the students will be given a table of the function. The students will then
have to give the function or make a graph of the function. The question will prompt which answer
is wanted.
c) Functions- This category will give the students the function. The students will have to either graph
the function or make a table of the value of the function. The table must include the x-intercepts
and y-intercepts where appropriate.
d) Transformations/ Explanations- This category will make certain transformations to common
graphs. This category will have a couple of different types of questions. The first type of question
will give the students either a graph or a table of a function. The students are to come up with
what the original function is and then verbally explain what shifts or changes have been made to
the function to get the graph or table that is given. The second type of question will give the
students the function and tell them what changes have occurred (ex. Shifted 3 units up). The
students are to graph the function and verbally explain why their graph fits the given criteria.
e) Groups- When the group category is selected, all members of the group can participate. The
students will be given either a graph or the function itself. If they are given the function, then they
are expected to make a table of 10 points (must include the y-intercept and the x-intercept where
appropriate) and also make a graph of the function. When given the graph, the students are to
make a table with 10 points (include the y-intercept and x-intercept where appropriate) and come
up with the function that fits the graph.
When students believe that they have the right answer, they are to bring their graph/table to the
teacher to check before telling the rest of the students. This is to ensure that there are no hints are
given if the students do not have the right answer and the rest of the groups have an opportunity to come
up with the correct answer.
At home work: Approximate time this work should take: __15- 20 minutes__
If desired, students can have some practice interpreting what changes will be made to the graph given the
function or the original function and the shifts that are made. Students should practice graphing these nonlinear functions and shifts that are made.
Reflection on Lesson/Notes to self:
This lesson incorporates the use of technology as an assessment tool. The PowerPoint Jeopardy game
enhances student learning by allowing for students to work together as well as individually to demonstrate
that they understand the material. The technology incorporates a different aspect of the classroom that
students do not get to use very often.
Using the PowerPoint game is a great way for the teacher to evaluate where their students are at with
learning the material. It also allows for the teacher to pay more attention to who is participating and who is
not as well as to what extent each student understands the material since all students should have the
opportunity to participate in the game.