Model Mathematics Curriculum
Unit Implementation Plan
UNIT COVER SHEET
Name:
Rhonda Zielsdorf
Unit Title:
M3 U4 L2: Representing Functions
Dates of Instruction:
Grade Level:
Algebra 2 (Grade 11)
March 2016
Timeframe (Add lessons and space as needed):
Unit Timeframe: 6-7 days
Lesson 1 Title:
Graph Stories
Timeframe: 1 day
Lesson 2 Title:
Key Features
Timeframe: 2 days
Lesson 3 Title:
Key Features
Timeframe: 2 days
Lesson 4 Title:
Transformations
Timeframe: 2 days
Lesson 5 Title:
Transformations
Timeframe: 2 days
Standards Alignment
Content Standards:
F-IF.4: For a function that models a relationship between two quantities, interpret key features of graphs
and tables in terms of the quantities sketch graphs showing key features given a verbal description of the
relationship. Key features include: intercepts; intervals where the function is increasing, decreasing,
positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple
cases and using technology for more complicated cases.
F.BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific
values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and
illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd
functions from their graphs and algebraic expressions for them.
Standards for Mathematical Practice:
MP3: Construct viable arguments and critique the reasoning of others
MP4: Model with mathematics
MP5: Use appropriate tools strategically
MP6: Attend to precision
MP7: Look for and make use of structure
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: M3 U4 L2
DAY: 1
DAILY PLAN For Lesson: Graph Stories; Popcorn; Roller Coaster
Objectives
These are an introduction to using a graph from the real world and discussing its
key features.
Content
Standards
F-IF.4
F.IF.7
Mathematical
Practices
MP #2 Reason abstractly and quantitatively. Students interpret total distance
traveled over time from picture of a coaster.
MP #4 Model with mathematics. Students will model the total number of kernels
popped in relationship to the length of time it takes to pop with a graph.
MP #3 Construct viable arguments and critique the reasoning of others. Students
will compare and contrast graphs with other students to decide what a “good”
graph looks like.
Materials
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Preparation
Create groups
Lesson
Activities
1. Play the video and ask students to describe the rate at which the popcorn pops
by listening for the “pops.” Replay the video and have students independently
sketch a graph of the total number of kernels popped over time to pop the bag.
Video
Popcorn handout
Roller Coaster handout
2. In small groups, have students compare graphs, defend their graph, and
comment on the graphs of others. Groups should decide which graph is the
most realistic.
3. Using the group’s choice, they should answer the questions about the graph.
4. Coming back to the whole group, debrief student responses.
5. Answer questions #1-4 on the Roller Coaster handout with a Think-Pair-Share
format. Bring the whole class together for a discussion of #5. Continue with
Think-Pair-Share for #6-7.
Assessments
Independent Practice (Homework):
Find a graph online, in a magazine, etc., comparing two quantities with a real-world
context. Describe the key features mathematically.
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?
MP #2 Reason abstractly and quantitatively. Students interpret total distance traveled over time from
picture of a coaster.
MP #4 Model with mathematics. Students will model the total number of kernels popped in relationship
to the length of time it takes to pop with a graph.
MP #3 Construct viable arguments and critique the reasoning of others. Students will compare and
contrast graphs with other students to decide what a “good” graph looks like.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: M3 U4 L2
DAY: 2
DAILY PLAN For Lesson : Key Features
Objectives
Students will be introduced to key features of functions by using multiple
representations for each feature.
Content
Standards
F-IF.4
F.IF.7
Mathematical
Practices
MP #3 Construct viable arguments and critique the reasoning of others. Students
attempt to convince each other their answer choices are correct when reviewing
independent practice (see Key Features Practice & Teacher Notes for useful questions.)
MP #6 Attend to precision. Students carefully indicate key features of functions.
Materials
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Key Features Definitions
Key Features Representations
Key Features Practice & Teacher Notes
Key Features Enrichment
Graph Selfies
Polling Clickers
Preparation
Lesson
Activities
Assessments
1. Using the Key Features Definitions handout, discuss as a whole group the
definitions of key features and identify them on the graph provided.
2. After independent practice, use questions provided in Key Features Practice &
Teacher Notes to anonymously poll the class (e.g. www.socrative.com or
www.polleverywhere ) . After initial responses are visible to the class, say
“Find someone who answered differently and convince them you are correct.”
After time for discussion (3-5 minutes), poll the class again on the same
question.
Classroom Discussion
Independent Practice
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?
MP #3 Construct viable arguments and critique the reasoning of others. Students attempt to convince each
other their answer choices are correct when reviewing independent practice (see Key Features Practice &
Teacher Notes for useful questions.)
MP #6 Attend to precision. Students carefully indicate key features of functions.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: M3 U4 L2
DAY: 3
DAILY PLAN For Lesson : Key Features
Objectives
Students will be introduced to key features of functions by using multiple
representations for each feature.
Content
Standards
F-IF.4
F.IF.7
Mathematical
Practices
MP #3 Construct viable arguments and critique the reasoning of others. Students
attempt to convince each other their answer choices are correct when reviewing
independent practice (see Key Features Practice & Teacher Notes for useful questions.)
MP #6 Attend to precision. Students carefully indicate key features of functions.
Materials
Preparation
 Key Features Definitions
 Key Features Representations
 Key Features Practice & Teacher Notes
 Key Features Enrichment
 Graph Selfies
Group students heterogeneously by ability for a base group.
During jigsaw, the teacher facilitates by questioning students and providing
guidance as needed.
Lesson
Activities
Assessments
3. Group students heterogeneously by ability for a base group. Explain the
purpose of the activity: to learn formal mathematical language to identify key
features of functions.
4. Jigsaw students to new groups which are arranged homogeneously by ability.
Give the lowest ability group “easier” words (suggested x-intercept, y-intercept,
increasing, etc.) In the jigsaw group, students will collaborate to develop the 3
missing representations for each feature. The teacher could model this process
with a chosen feature before beginning the jigsaw. During jigsaw, the teacher
facilitates by questioning students and providing guidance as needed.
5. When groups have completed their key features, students should return to their
base groups. Students will independently fill out a flipbook of the key features
with information provided by each group member from the jigsaw.
Students will independently fill out a flipbook of the key features with
information provided by each group member from the jigsaw.
Key Features Practice (after Definitions) & Teacher Notes
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?
MP #3 Construct viable arguments and critique the reasoning of others. Students attempt to convince each
other their answer choices are correct when reviewing independent practice (see Key Features Practice &
Teacher Notes for useful questions.)
MP #6 Attend to precision. Students carefully indicate key features of functions.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: M3 U4 L2
DAY: 4
DAILY PLAN For Lesson : Transformations Sort & Effects
Objectives
Students will determine the effects of transformations on key features of graphs.
Content
Standards
F-IF.4
F.IF.7
F.BF.3
Mathematical
Practices
MP #3 Construct viable arguments and critique the reasoning of others. Students will
explain their method in choosing which graphs to group together, defending their
method to other students.
MP #6 Attend to precision. Students carefully indicate key features of functions.
Materials
Transformations Sort & Effects Document
Preparation
Cut the graphs into cards for students to sort.
Create student pairs.
Lesson
Activities
Assessments
1. Sort graphs.
2. Ask pairs to share out to the whole class the graphs they grouped together and
why.
Ask pairs to share out to the whole class the graphs they grouped together and
why.
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?
MP #3 Construct viable arguments and critique the reasoning of others. Students will explain their method
in choosing which graphs to group together, defending their method to other students.
MP #6 Attend to precision. Students carefully indicate key features of functions.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT: M3 U4 L2
DAY: 5
DAILY PLAN For Lesson : Transformations Sort & Effects
Objectives
Students will determine the effects of transformations on key features of graphs.
Content
Standards
F-IF.4
F.IF.7
F.BF.3
Mathematical
Practices
MP #3 Construct viable arguments and critique the reasoning of others. Students will
explain their method in choosing which graphs to group together, defending their
method to other students.
MP #6 Attend to precision. Students carefully indicate key features of functions.
Materials
Transformations Sort & Effects Document
Preparation
Lesson
Activities
Assessments
2. Transition to the Debriefing Handout by referencing families of graphs.
Identify parent graphs and transformations.
3. In pairs, students answer the questions regarding how key features are
affected by transformations. Ask pairs to share out to the whole group,
debriefing and clarifying any misconceptions.
Independent Practice (Homework):
Homework handout included
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?
MP #3 Construct viable arguments and critique the reasoning of others. Students will explain their method
in choosing which graphs to group together, defending their method to other students.
MP #6 Attend to precision. Students carefully indicate key features of functions.