Iowa Core Mathematics – Algebra I
Title: Ch1.3 Recognizing Algebraic and Graphical Representations of Functions
p.35-51 (2 periods)
Grade: HS-9 (Algebra 1- Linear Algebra).
Author: Larry Abrams, v1.1
Iowa Core Standards addressed in this lesson: (F.IF) Interpreting Functions, and (A.REI) Reasoning with
Equations and Inequalities.
(F.IF.1) Understand that a function from one set (the domain) to another set (the range) assigns to each
element of the domain exactly one element in the range. If “f” is a function and “x” is an element of its
domain, then “f(x)” denotes the output of “f” corresponding to the input “x”. The graph of “f” is the graph of
the equation y = f(x).
(F.IF.2) Use function notation, evaluate functions for inputs in their domains, and interpret statements that
use function notation in terms of a context.
(F.IF.5) Relate the domain of a function to its graph and, where applicable, to quantitative relationship it
describes. (For example, if the function f(x) gives the number of hours it takes to assemble “x” engines in a
factory, and then the positive integers would be an appropriate domain for the function).
(F.IF.7a) Graph functions expressed symbolically and show key features of the graph, by hand in simple cases
and using technology for more complicated cases.* (a) Graph linear and quadratic functions and show
intercepts, maxima, and minima.
(F.IF.9) Compare properties of two functions each represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an
algebraic expression for another, say which has the larger maximum.
A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which could be a line).
Math practices: MP.1, MP.2, MP.3, MP.4, MP.5, MP.8.
Math Habits of Mind: (1) Make Sense, (2) Justify, (4) Regularity, patterns, (5) Math Representations,
(6) Connections.
Math Habits of Interaction: (1) Private Reasoning Time, (2) Explain, (3) Listen to Understand, (7) Critique and
Debate.
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Iowa Core Standards for
Mathematical Practices
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1. Make sense of problems and persevere in solving them. (*)
2. Reason abstractly and quantitatively. (*)
3. Construct viable arguments and critique reasoning of others. (*)
4. Model with mathematics. (*)
5. Use appropriate tools strategically. (*)
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning. (*)
Place * next to portions of lesson where students use practice standards.
Student Friendly
Learning Goal
SWBAT: Write equations using function notation, and recognize multiple
representations of functions. Recognize characteristics of functions and
function families.
Grouping Strategies
Work will be done with a partner or in teams of 4 depending. All teams will
share out work to whole class.
LESSON SEQUENCE
(Include plans for adjustments to accommodate all learners)
Launch
Activities
1. State objectives of this lesson to students.
Read the SWBAT from above.
2. Refer to vocabulary on front (L) whiteboard.
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Notes
The SIOP objectives are posted on sideboard.
Materials
Whiteboards.
Function notation, increasing/ decreasing/
constant function, function family, linear
functions, exponential functions, absolute
minimum, absolute maximum, quadratic
functions, linear absolute value functions, and
linear piecewise functions.
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Explore – Part I
Activities
Problem #1: A New Way to Write Something.
1. Tell students to open to page 36 to start.1.
Write definition of a function on the front
whiteboard to open lesson.
2. Read paragraph 2 to students and do the
T-shirt problem to demonstrate a function.
Do a brief table in demo.
3. Have student volunteer read paragraph 1.
While student is reading, write the definition
of f(x) in the Public Domain sideboard.
4. Finish the rest of the page, indicating
ability to write f(x), g(x), h(x), C(s), etc.
5. Have teams consider the two Guiding
Questions for problem 1. Give them 1-2
minutes, and then share out.
6. Do the graphing calculator exercises on
page 37. Lead them through the steps and
use the guiding questions in left margin.
Problem #2 Up, Down, or Neither (p.38)
1. Read first sentence to class. They will need
to retrieve A-V graphs.
2. Have students read the next 3 paragraphs
about increasing, decreasing and constant
functions. Write on Public Domain. Ensure
understanding. Draw examples on board.
3. Have students do the next 1-3 items.
Check results after #1 as group. #2 is
graphing with calculator. They will need help.
Student do #3—split the 7 into 2 groups,
then share out.
4. I read top of p.40- definition of function
family. Write on vocab board. Have students
read the next 2 definitions, and write on
vocab board.
5. Partners complete #4 on previous table.
6. I do #5 on board. Representation of linear
function in slope-intercept form.
Transitioning to Iowa Core-Math
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Notes
Materials
Whiteboard.
A relation such that for every input there is
exactly one output. Vertical Line Test. (IF.1)
(IF.2) (IF.5) (A.REI.10)
Create a table.
(IF.1)
Public Domain.
So, yes, you can use any two letters to
represent a function (boy’s bubble question).
Public Domain.
1-2 minutes.
Graphing calculators. (IF.7a)
Calculators.
Students need all the graphs from previous
lesson A-V.
Students read.
Their graphs.
Public Domain.
Public Domain.
Work with partner. (IF.9)
Graphing calculators. (IF.7a)
Calculators.
Share out.
Function Family on vocab board.
Whiteboard.
Family of Linear Functions.
Family of Exponential Functions.
Do they know this from last year? Do I need to
remediate? (IF.1)
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Problem #3 Least, Greatest, or Neither?
1. Ask students to read first paragraph
definitions: absolute minimum and absolute
maximum. Discuss as a class.
2. Students finish 1-3 p.40-42. They will need
help with p.41 on calculators.
3. I lead top of p.42 writing on vocab board
as students read the last 2 definitions: family
of quadratic functions, and family of absolute
value functions.
4. Skip #4 Piecewise Functions p.42-44,
except I read the highlighted sentence on
page 44, elaborating about domain and
range.
Problem #5 We Are Family! (p.45-51).
1. I read the instructions on the top of page
45. Tell students to finish last pages with
partner, put name(s) on the pages and turn
them in. Write the names of the 5 function
families on the board as they start working.
2. Give them a copy of teacher’s page 52A as
homework exercise. Add the two questions
at the bottom of the page.
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Sorting graphs from problem 2 combination
category.
Draw a couple of simple graphs with minima
and maxima on board as example. (IF.9)
Combination
Graphs.
Calculators. (IF.7a)
Calculators.
Vocab board.
Two more families of functions.
Piecewise Functions.
(IF.5)
(IF.9)
Turn in pages 47-51.
Page 52A is homework.
p.47-51.
Homework.
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