2014-2015 Curriculum Blueprint ... Course: MJ2 ADV Unit #14: Functions

2014-2015 Curriculum Blueprint
Grade: 7
Course: MJ2 ADV
10 Days
Unit #14: Functions
Learning Goal
Students will be able to calculate the slope of a linear function, and determine where the line
crosses the x and y axes in real-world problems. Students will also be able to solve systems of
equations in real-world problems to determine a common solution.
Link to Learning Scale: Functions, Interpret Functions
Essential Question(s)
How do we recognize linear functions?
When graphing real world data, what does the slope and intercepts tell us?
When would a system of equations with two unknowns have no solution or an infinite
number of solutions?
Approximate Time:
Unit Overview
In this unit, the term function is formally introduced for both linear and non-linear functions.
Students model functions in different ways (algebraically, graphically, numerically in tables, or
by verbal descriptions) and interpret those representations qualitatively and quantitatively.
For this unit, students will be introduced to non-linear functions so that they are able to identify
whether or not a function is linear, but they will not be required to generate their own examples
until later.
Understanding how functions model (MP.4) relationships requires that student’s reason
abstractly and quantitatively (MP.2) while looking for and making use of structure (MP.7).
Focus Standards
Vertical Progression:
Bullets are the deconstructed standards These should be used to develop concise learning
http://www.turnonccmath.net/ K-8 Learning Trajectories (This could be used to determine
statements/daily objectives/scales. Standards below are not intended to be followed in the order they remediation needs or enrichment opportunities)
are listed. See unit sequence for intended order. Grade 8 Mathematics Item Specifications
7th Grade - Students decide whether two quantities are in a proportional relationship.
MAFS.8.F.1.1 (DOK 2):
Understand that a function is a rule that assigns to each input exactly one output. The graph of a
High School - Students will learn function notation, explore many examples of functions, interpret
function is the set of ordered pairs consisting of an input and the corresponding output.
functions, and translate between representations.
MAFS.8.F.1.2 (DOK 2):
Compare properties of two functions each represented in a different way (algebraically,
graphically, numerically in tables, or by verbal descriptions). For example, given a linear function
represented by a table of values and a linear function represented by an algebraic expression,
determine which function has the greater rate of change.
Identify functions algebraically including slope and y-intercept.
Identify functions using graphs, tables and verbal descriptions.
Compare and contrast 2 functions with different representations.
Draw conclusions based on different representations of functions.
Unit Sequence
Be selective in choosing problems aligned to the
standards within each lesson
Slope, Intercepts, and Linear Functions Rule
McDougal Littell 7-7 – 7-8
Engage NY Module 5
Lesson 1 (Page 9)
More Examples of Functions
MAFS.8.F.1.3 (DOK 2):
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give
Engage NY Module 5
examples of functions that are not linear. For example, the function A = s² giving the area of a
Lesson 4 ( Page 45)
square as a function of its side length is not linear because its graph contains the points (1,1), (2,4)
and (3,9), which are not on a straight line.
Graphs of Functions
Recognize that a linear function is graphed as a straight line.
Engage NY Module 5
Lesson 5 (Page 57)
Recognize the equation y = mx + b is the equation of a function whose graph is a straight
line where m is the slope and b is the y-intercept.
Compare the characteristics of linear and nonlinear functions using various
Provide examples of nonlinear functions using multiple representations.
Essential Vocabulary
slope-intercept form
linear function
function notation
systems of equations
solutions of systems of equations
Higher Order Questions/Stems
How did you identify the function?
What are the characteristics of a __________?
What are some different ways you can
recognize a non-linear function?
Writing Connections
Compare and contrast 2 functions.
Compare the characteristics of linear and
nonlinear functions.
2014-2015 Curriculum Blueprint
Grade: 7
Course: MJ2 ADV
10 Days
Unit #14: Functions
MAFS.8.F.2.5 (DOK 3):
Describe qualitatively the functional relationship between two quantities by analyzing a graph
(e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that
exhibits the qualitative features of a function that has been described verbally.
Analyze a graph and describe the functional relationship between two quantities using
the qualities of the graph.
Interpret the relationship between x and y values by analyzing a graph.
Sketch a graph, given a verbal description of its qualitative features.
Mathematical Practice Standards
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.2.1: Reason abstractly and quantitatively.
MAFS.K12.MP.4.1: Model with mathematics.
MAFS.K12.MP.7.1: Look for and make use of structure.
Approximate Time:
Supplemental Resources
8th Grade Flip Book – A user-friendly resource
for understanding the specifications of the
Common Core Standards.
EngageNY Grade 8 Module 5 – Word documents
can be found using this link
*You can access all of the following material from
the Module 5 page as the links below may be
slow to load
o Teacher Materials
o Student Materials - The student materials
consist of the student pages for each lesson
in Module 5.
o Copy Ready Materials - A collection of the
module assessments, lesson exit tickets and
fluency exercises from the teacher materials.
Writing Template Tasks These template tasks
are designed from the Mathematical Practice
Standards. When filled in, these templates
become teaching tasks that create
opportunities for teaching literacy skills in
Georgia Unit 4: Functions Tasks aligned to
8.F.1.1 and 8.F.1.2:
o Secret Codes and Number Rules – Page 9
o Foxes and Rabbits – Page 36
o The Vending Machine – Page 41
o Order Matters – Page 47
o Battery Charging – Page 57
o Which is Which? – Page 64
o Create Matching Function Cards – Page 72
o Sorting Functions – Page 100
Georgia Unit 5: Linear Functions Tasks aligned to
8.F.1.2 and 8.F.1.3
o Analyzing Linear Functions – Page 54
MARS Task: Modeling Situations with Linear
Equations – a formative assessment lesson in
which students will explore relationships
between variables in everyday situations, find
unknown values from known values, find
relationships between pairs of unknowns, and
express these as tables and graphs, find general
relationships between several variables, and
express these in different ways by rearranging
formulae. (PowerPoint at the bottom of the page)
Draw conclusions based on different
representations of functions.
Explain how you verified that for each input
there was exactly one output.
Link to Problem Solving Rubric
Link to Webb’s DOK Guide
2014-2015 Curriculum Blueprint
Grade: 7
Course: MJ2 ADV
Unit #14: Functions
Math Formative Assessment System (MFAS)
These formative assessments could be used
before instructing a lesson on similar content
to help formulate small groups or they may be
used however PLCs see best for their students.
Each formative assessment comes with a rubric
and instructional implications based on the
level of student understanding.
Illustrative Mathematics – 8th grade tasks
developed under the direction of writers of the
CCSS at the University of Arizona.
RTTT Item Specifications – page 45
Teaching Channel Video: Graphing Linear
Equations Full Body Style – 4 minute video
featuring students graphing a line given slopeintercept on a giant coordinate plane.
Teaching Channel Video 2 minute video with a
focus on Improving Participation with Talk
Moves (Personalized Learning Opportunity).
Approximate Time:
10 Days