Unit Overview
Content Area: Math
Unit Title: Expressions and Functions
Unit: 4
Target Course/Grade Level: Eighth Grade
Timeline: 3/4 weeks
Unit Summary: Students are introduced to expressions, relations, and functions as they analyze words,
tables, graphs, and equations. Patterns are used to help students write algebraic expressions and translate
between verbal, tabular, graphical, and algebraic representations of linear functions. Students extend their
analysis to nonlinear functions.
Primary interdisciplinary connections: Language Arts and Technology
9.1 21st-Centuries Life & Career Skills
Standard 9.1 All students will demonstrate the creative, critical thinking, collaboration, and
problem-solving skills needed to function successfully as both global citizens and workers in
diverse ethnic and organizational cultures.
Strand: A. Critical Thinking and Problem Solving
B. Creativity and Innovation
C. Collaboration, Teamwork and Leadership
Content Statement:
9.1.8: A The ability to recognize a problem and apply critical thinking skills and problem
solving skills to solve the problem is a lifelong skill that develops over time.
9.1.8: B Gathering and Evaluating knowledge and information from a variety of sources,
including global perspective, fosters creativity and innovative thinking.
9.1.8: C Collaboration and team work enable individuals or groups to achieve common goals
with greater efficiency.
Leadership abilities develop over time through participation in group and or teams that
that are engaged in challenging or competitive activities.
st
21 Century themes and skills: Critical Thinking and Problem Solving, Collaboration, Teamwork and
Leadership, Creativity and Innovation
Mathematical Practices:
8.MP.1 Make sense of problems and persevere in solving them.
8.MP.2 Reason abstractly and quantitatively.
8.MP.3 Construct viable arguments and critique the reasoning of others.
8.MP.4 Model with mathematics.
8.MP.5 Use appropriate tools strategically.
8.MP.6 Attend to precision.
8.MP.7 Look for and make use of structure.
8.MP.8 Look for and express regularity in repeated reasoning.
Learning Targets
Domain: Functions
Cluster: Define, evaluate, and compare functions. Use functions to model relationships between
quantities.
Standard #
Standards
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.
8.F.3
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight
line; give examples of functions that are not linear. For example, the function A = s2
giving the area of a 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.
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.
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.
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.
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. For example, collect data from students in your
class on whether or not they have a curfew on school nights and whether or not they have
assigned chores at home. Is there evidence that those who have a curfew also tend to have
chores?
9.1.8.A.1
Develop strategies to reinforce positive attitudes and productive behaviors that impact
critical thinking and problem-solving skills.
9.1.8.A.2
Implement problem-solving strategies to solve a problem in school or the community.
9.1.8.B.2
Assess data gathered to solve problems for which there are varying perspective (e.g., cross
cultural, gender specific, generational, etc.) and determine how the data can best be used to
design the multiple solutions.
9.1.8.C.1
Determine an individual’s responsibility for personal actions and contributions to group
activities.
9.1.8.C.2
Demonstrate the use of compromise, consensus and community building strategies for
carrying out different task, assignments and projects.
9.1.8.C.3
Model leadership skills during classroom and extracurricular activities.
Unit Essential Questions
 How can words, tables, graphs, and equations be
used to show the relationship between two
quantities?
 How are functions, formulas, equations, tables,
and graphs related?
 What are some ways in which functions and
Unit Enduring Understandings
 Coordinate geometry can be used to represent and
verify geometric/algebraic relationships.
 The symbolic language of algebra is used to
communicate and generalize the patterns in
mathematics.
 In order to make inferences about the world we
relations can be represented?
 How are the graphs of linear functions and
quadratic functions different?
communicate representations and generalizations
of patterns verbally, numerically, symbolically and
graphically.
Unit Learning Targets
Students will ...
 Graph ordered pairs on the coordinate plane and use the coordinate plane to represent relations.
 Find a rule for a given pattern.
 Translate information in tables and graphs to expressions.
 Translate tables and graphs into linear equations.
 Determine whether a relation is a function.
 Complete function tables.
 Represent linear functions using function tables and graphs.
 Determine whether a function is linear or nonlinear.
 Graph quadratic functions.
Evidence of Learning
Summative Assessment
 Create and interpret tables, graphs, and models to represent, analyze, and solve problems related to
linear equations.
 Analyze domain and range.
 Given a table, graph, or verbal description, write an equation and make a prediction.
 Translate among verbal, tabular, graphical, and algebraic representations of linear functions.
 Determine whether a function is linear or nonlinear from a table.
 Compare the graphs of linear and nonlinear functions.
 Graph quadratic functions.
Equipment needed: coordinate grids, number cubes, ruler, Smart Board, white boards, calculators, Elmo
Teacher Instructional Resources: Textbook (TBD)
Study Island
Khan Academy Videos
Formative Assessments
 Skill sheets
 Quizzes/Tests
 Student workbook
 Homework
 Math games
 Study Island
Integration of Technology:
 Smart Board to play online games, utilize online resources, generate models with Smart Software.
 Kahn Academy Videos
 Elmo – for demonstration
 Study Island
Technology Resources:
http://www.purplemath.com
http://www.khanacademy.org – Interactive 2.0 instructional and practice site. Students can view
instructional videos and complete practice modules for additional practice/remediation.
http://www.studyisland.com/ - Web-based instruction, practice, assessment and reporting built from NJ
standards.
http://www.ixl.com/math/grade-8 - IXL 8th grade online interactive activities for the students to
complete
http://www.aaamath.com/grade8.html - AAA math 8th grade – online interactive activities and
problems for the student to complete.
http://www.adaptedmind.com/Math-Worksheets.html?type=hstb – Grade level material for practice,
lessons, games, etc.
Opportunities for Differentiation:
Decelerate: Students create patterns of squares with sides 1, 2, 3, and so on, using toothpicks. Students
make tables for perimeter, total number of squares, total number of toothpicks used, as they extend the
pattern. Then they write the rule for each pattern.
Students gather price information for snacks available in their cafeteria. Working in pairs, they create a
table and then graph the data for the cost of buying one to six of the item.
Students play the game ”Function or Not?” – Display a table of values. Students decide whether it is a
function or not and are awarded points accordingly.
Students use a template (showing all work) as they graph quadratic functions.
Accelerated: Students bring in graphs from newspapers or magazines that represent real-world data. The
graphs should represent a linear equation. The students will determine the linear equation using the text
and examining the points. Give the graph to another student who will try to determine the equation.
Given two equations, the students will determine the solution for the system.
Students create different quadratic functions, graph them and then determine what in the function made the
shape change.
Teacher Notes: Before the chapter begins, review translating verbal phrases into algebraic expressions
and then evaluating them. Review writing linear equations from tables and graphs.