LESSON PLANNING GUIDE
Conyers Middle School – 2014-2015
Content Area
Math
Grade/Course
8
Unit of Study
Unit 6 Linear Models and Bivariate Data
Instructional Period
Week 26 Math Benchmark Week
Insert a standard(s) below (include code). HIGHLIGHT the SKILLS that students need to be able to do and
UNDERLINE the CONCEPTS that students need to know.
MCC.8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of
ordered pairs consisting of an input and the corresponding output.
MCC.8.F.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.
Use functions to model relationships between quantities.
MCC.8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of
the function from a description of a relationship or from two (𝒙, 𝒚) values, including reading these from a table or from a graph.
Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of
values.
MCC.8.F.5 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.
Investigate patterns of association in bivariate data.
MCC.8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two
quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
MCC.8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that
suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points
to the line.
MCC.8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope
and intercept.
MCC.8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative
frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from
the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.
List Behaviors
List Content
Determine DOK
(what students should be able to
do; focus on verbs)
(what students should know; focus on concepts)
(align to instruction and assessment)
Explore, compare, use
Strategy 1: Create a rigorous system of teaching and learning
Specific Results: Institutionalize Cycle for Results
plans
DOK Levels
DOK Ceiling
Action Steps: 1, 2, 3, 6
Performance Indicator: Teacher lesson
LESSON PLANNING GUIDE
Conyers Middle School – 2014-2015
Explore functions that arise from real-life
relationships where one variable determines
a unique value of another.
Use a variety of representations to have
students identify functions and relations that
are not functions
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.
DOK Level
2,3
Possible Aligned Activities and Questions
TAPS 2, 3, 4, 5
4
TAPS 1, 2
Resources
(on/offline)
1
Understand that functions describe relationships where one
variable determines a unique value of the other.
Math Textbook,
Worksheetworks.com
2
Recognize a graph of a function as the set of ordered pairs
consisting of an input and corresponding output.
Modeled on Whiteboard,
Student work
3
4
Write the equation of a line given two points, a graph, a table of
values, a geometric representation, or a story problem (verbal
description) of a linear relationship
Compare two linear functions each represented a different way
and describe similarities and differences in slopes, y-intercepts,
and values
Determine and interpret the initial value and rate of change given
two points, a graph, a table of values, a geometric
representation, or a story problem (verbal description) of a linear
relationship.
Standards (Primary)
DOK (Ceiling)
4
Various Teacher resources
Integrated
MCC.8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of
ordered pairs consisting of an input and the corresponding output
MCC.8.F.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………………………………
MCC.8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial
value of the function from a description of a relationship or from two (𝒙, 𝒚) values, including reading these from a table or from
a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its
graph or a table of values.
Strategy 1: Create a rigorous system of teaching and learning
Specific Results: Institutionalize Cycle for Results
plans
Action Steps: 1, 2, 3, 6
Performance Indicator: Teacher lesson
LESSON PLANNING GUIDE
Conyers Middle School – 2014-2015
KNOW/UNDERSTAND
Essential Question/Enduring Understanding:
TAPS 2, 3
How can I build on previous knowledge of scatter plots examine relationships
between variables.
How can I analyze scatterplots to determine positive and negative associations,
the degree of association, and type of association.
How can I examine outliers to determine if data points are valid or represent a
recording or measurement error
Enduring understanding
Collect, record, and construct a set of bivariate data using a scatter plot.
Determine whether the relationship between bivariate data is approximately linear
or nonlinear by examination of a scatter plot.
Interpret patterns on a scatter plot such as clustering, outliers, and positive,
negative, or no association
COMMON MISCONCEPTIONS FOR THE CURRENT
STANDARDS
****Taken From SLDS resources****
Strategy 1: Create a rigorous system of teaching and learning
Specific Results: Institutionalize Cycle for Results
plans
Action Steps: 1, 2, 3, 6
Performance Indicator: Teacher lesson
LESSON PLANNING GUIDE
Conyers Middle School – 2014-2015
Common misconceptions
Some students will mistakenly think of a straight line as horizontal or vertical only.
Some students will mix up x- and y-axes on the coordinate plane, or mix up the ordered
pairs. When emphasizing that the first value is plotted on the horizontal axes (usually x,
with positive to the right) and the second is the vertical axis (usually called y, with
positive up), point out that this is merely a convention: It could have been otherwise, but
it is very useful for people to agree on a standard customary practice.
Some students will mistakenly think of a straight line as horizontal or vertical only.
Some students will mix up x- and y-axes on the coordinate plane, or mix up the ordered
pairs. When emphasizing that the first value is plotted on the horizontal axes (usually x,
with positive to the right) and the second is the vertical axis (usually called y, with
positive up), point out that this is merely a convention: It could have been otherwise, but
it is very useful for people to agree on a standard customary practice.
Students often confuse a recursive rule with an explicit formula for a function. For
example, after identifying that a linear function shows an increase of 2 in the
values of the output for every change of 1 in the input, some students will
represent the equation as y = x + 2 instead of realizing that this means y = 2x + b.
When tables are constructed with increasing consecutive integers for input values,
then the distinction between the recursive and explicit formulas is about whether
you are reasoning vertically or horizontally in the table. Both types of reasoning—
and both types of formulas—are important for developing proficiency with
functions.
When input values are not increasing consecutive integers (e.g., when the input
values are decreasing, when some integers are skipped, or when some input
values are not integers), some students have more difficulty identifying the pattern
and calculating the slope. It is important that all students have experience with
such tables, so as to be sure that they do not overgeneralize from the easier
examples.
Some students may not pay attention to the scale on a graph, assuming that the
scale units are always “one.” When making axes for a graph,
Some students may not using equal intervals to create the scale.
Some students may infer a cause and effect between independent and dependent
variables, but this is often not the case.
Some students graph incorrectly because they don’t understand that x usually
represents the independent variable and y represents the dependent variable.
Emphasize that this is a convention that makes it easier to communicate.
Strategy 1: Create a rigorous system of teaching and learning
Specific Results: Institutionalize Cycle for Results
plans
Action Steps: 1, 2, 3, 6
Performance Indicator: Teacher lesson
LESSON PLANNING GUIDE
Conyers Middle School – 2014-2015
KNOWLEDGE & SKILLS
(Key Vocabulary)
Vocabulary- Tier 1
Tier 3
Academic vocabulary
across content-areas
Words using to teach
Tiers 2-3
function, input,
output, dependent,
independent
Demonstrate,
identify, explain,
describe
Content-specific, domain-specific
.
Recognize, Compare,
Debate/Defend,
Pre-assessment to Inform Instruction
Benchmark 4.5
Unit 6 pretest
Daily Formal assessments
TAPS 2, 3, 5
A.P.P.
First Period
a. Use this time to provide the students with team-planned remediation
through a LearnZillion video or other video directly related to the standard, or a
hands-on experience that will expose the standard misconception and
reinforce the expectations of the standard. Videos should be paused at key
points to assess student learning and understanding.
b. After interacting with the video, students should work together on a
focused practice activity directly related to the video that will provide both
students and teachers with progress toward achievement of the
standards. LearnZillion videos and lessons provide practice worksheets.
DO
Content
Process
Product
Students will
explain the
relationship
between domain
range and function
rule.
1. Guide students to
understanding how
to apply real life
situations with
bivariate data.
1. Students will explain
the relationship
between 2 linear
functions and
determine the greater
rate of change.
Advanced
TAPS 2, 3, 4
BENCHMARK
3-11
PI Day 3-12
Students will relate
Real world
situations with 𝜋
Strategy 1: Create a rigorous system of teaching and learning
Specific Results: Institutionalize Cycle for Results
plans
Students will solve
complex problems with
Bivariate data
Students will utilize
Choice Boards.
(This includes
Problem solving,
Action Steps: 1, 2, 3, 6
Performance Indicator: Teacher lesson
LESSON PLANNING GUIDE
Conyers Middle School – 2014-2015
vocabulary, and
Writing)
Ready
Benchmark
3-11
PI Day 3-12
Students will relate
Real world
situations with 𝜋
Teacher will help
guide students on
calculating bivariate
data.
Students will identify
domain and range.
How to use
function rules to
determine
outputs.
Need
Prerequisites
Benchmark
3-11
Teacher will
guide students
PI Day 3-12
with finding the
Students will relate
slope and Y
intercept of a line
Real world
utilizing various
situations with 𝜋
methods.
Students need
to understand
how to
differentiates
the formulas for
finding slope
Solve problems
with bivariate data
Students will utilize
Choice Boards.
(This includes
Problem solving,
vocabulary, and
Writing)
Find the slope using
various methods ,
including tables,
graphs, and given
coordinate points.
Students will utilize
Choice Boards.
(This includes
Problem solving,
vocabulary, and
Writing)
How to
understand the
coordinate
plane.
Strategy 1: Create a rigorous system of teaching and learning
Specific Results: Institutionalize Cycle for Results
plans
Action Steps: 1, 2, 3, 6
Performance Indicator: Teacher lesson
LESSON PLANNING GUIDE
Conyers Middle School – 2014-2015
How to plot
points from a
function table
Subtract
negative
integers when
finding the
change in Y
over change in
X
TAPS 2, 3, 5, 6, 8
Steps to Deliver the Lesson Using WICOR
Engage
(Hook, introduction to lesson
concepts)
AVID
®
1. Practice subtracting and dividing integers
WICOR:
Explore/Explain
(teaching content all students need to
know, understand and be able to do
as determined by unpacked standard)
1. Understand that functions have an input, output, and a rule.
2. Students will find the errors in their peers work, and explain how to
correct the mistakes.
3. 3. Students will Use P. A C. E. organizer. P- Problem, A – Answer, C –
Calculate, E - Explain
WICOR:
Enrich/Elaborate
(differentiation of process )
.
Students will solve problems by comparing functions writing in their own words
in a Writing Across Curriculum activity. Students will also show diagrams for their
writing.
Strategy 1: Create a rigorous system of teaching and learning
Specific Results: Institutionalize Cycle for Results
plans
Action Steps: 1, 2, 3, 6
Performance Indicator: Teacher lesson
LESSON PLANNING GUIDE
Conyers Middle School – 2014-2015
WICOR:
Evaluation
(Formative assessment)
Students will evaluate and grade their peer’s work after they have created their
own problems. Students will complete assessment with Volume and area.
WICOR:
Resources
Math Workbook, Worksheetworks.com, studyisland.com, gameaquarium.com
Classroom Performance System (Clickers.) Learnzillion, kahoot, plickers, QR code
generator
Strategy 1: Create a rigorous system of teaching and learning
Specific Results: Institutionalize Cycle for Results
plans
Action Steps: 1, 2, 3, 6
Performance Indicator: Teacher lesson