Grade 8 Unit 6: Function and Slope of a Line, Inequalities

Roselle School District

Mathematics Curriculum

Grade 8 Unit 6: Function and Slope of a Line, Inequalities

Essential Question(s) / Enduring Understanding(s)
What are the characteristics of a function?
What is the difference between an input and an output of an equation?
In what ways can you represent a function? / A function is a rule that assigns exactly one output to each input.
Functions can be represented algebraically, graphically, in tables numerically, and verbally.
Summative Assessment Task
See attached document
Common Core Standards, 2010
Define, evaluate, and compare functions.
·  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.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.
·  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.
·  W8.2 Write informative/explanatory texts to examine a topic and convey ideas, concepts and information through the selection, organization, and analysis of relevant content.
Learning Expectations
TLWBAT… / Activities/Resources / Student Strategies/Modifications/Differentiation / Formative Assessments / Technology Infusion/Resources
Understand that a function is a rule that assigns to each input exactly one output. / Day 1:
Introductory activity of students creating coordinate graphs on graph paper or in notebooks using plots given by teacher.
Each quadrant will be identified along with positive and negative integers.
Students will complete practice problems of graphing functions in a function table in order to determine a set of ordered pairs consisting of an input and output.
Independent practice:
Students completed university stations (Seton Hall University, Rutgers University etc). Each station represents previous learned material (i.e. graphing coordinates, determine a solution set, distance formula, identifying coordinates). Once a student completes the first university level with a B or higher, they are allowed to move on to the next round.
Day 2:
Math stations:
Students are grouped in teams of two or three where they must answer questions on finding the x and y coordinate along with the distance of any coordinate pair using the distance formula around the room on math station easels (taped to the walls) for various rigorous levels of learning. Each group will be graded for classwork. All work will be shown on an answer key.
Day 3:
Interpreting graphs:
Students receive a power point on interpreting graphs with various guided practice examples and independent work created by the teacher.
Once students grasp the concept of vertical and horizontal lines for graphs, they will then choose graphs from various options and create a graph based on a real world scenario. For example, students must create a graph for the following: “Jordan gets off to a good start, and continues through the course with speed”. They will use various horizontal and vertical lines to create a mathematical relationship.
Students have 12 options to choose from: two have to be real world scenarios, one is a chart given where they must plot on a graph, and the last is a situation where they must create a chart along with the graph.
Students learn to represent functions with tables, graphs, or equations. Introduction to important vocabulary terms such as domain, range, and vertical line test.
Students will be shown a function machine. The box is made out of a shoe box and aluminum foil. Students will be given equation where it will be displayed on the front of the box. They will input (x) into the machine and output (y) an answer. Once they receive all the domain and ranges and make a table out of it, they will then graph it on a coordinate plane. / Small group instruction/working with partner:
Math stations for coordinate graphing: use easel paper or construction paper around the room
Individualized instruction: allow students to work by themselves on any activity if needed
Peer tutoring: break groups up into different levels of learning expectations (jigsaw method) for math station or group work.
Use of manipulatives
Smart board graphs and interactive dots
Computer activities for remediation
Find various interactive activities for remediation: look under technology use
Chunking information
Rephrasing of questions
Video tutorials from textbook
Choice activities/Math stations: university stations for various levels of rigor
UDL choice activities: create a menu allowing students to choose different practice work
Use of manipulatives
Reference sheets
Classroom posters
Guided practice of transformations
Choice activities/Chunking information
Reference sheets for each transformation
Small group instruction
Review of printed notes from smart board.
Activities completed in small group for more of an understanding
Individualized instruction
Peer tutoring
Team up stronger math skills with lower math skills
Use of manipulatives
Reference sheets
Classroom posters / Exit ticket: vocabulary words from 3-1 and 3-2
Create a function table and complete it
Journal entry
What are the similarities and differences between a continuous graph and a discrete graph?
Do now
POD from LOTI
Quiz
Interpreting graphs quiz
Function tables and distance formula quiz
Math university stations
Test: Summative assessment for unit 4
Oral questioning: test students orally on any formative assessment.
One-sentence summary:
Where is the x-axis?
Where is the y-axis?
What is the first number in a coordinate point?
What is the second number in the coordinate point?
Where is the origin located?
What is a continuous graph?
What is a discrete graph?
Transfer and apply
Students read real world scenarios and apply graphing to create these scenarios
Homework handouts
3-1 a, b, c
3-2 a, b, c
3-3 a, b, c
3-4 a, b, c
3-5 a, b, c
Or independent work from text book
Exit Pass (5 minutes) each day
Students will solve and graph five questions pertaining to solving multi-step equations. / 3-2 video tutorial:
http://my.hrw.com/math06_07/nsmedia/lesson_videos/msm3/player.html?contentSrc=13418/13418.xml
Interpreting graphs video tutorial:
http://my.hrw.com/math06_07/nsmedia/lesson_videos/msm3/player.html?contentSrc=13420/13420.xml
Know-it-notebook move on mini agenda:
http://my.hrw.com/math06_07/student/osp/msm3_2010/content/0302_mthc3_kin.pdf
ordered pairs and coordinate graphing universities:
http://wilday.roselleschools.org/res_view_folder.aspx?id=96eb61d2-f57d-4b1d-b2c0-30a69337278a&userGroupId=cd19f26a-b879-473f-ade8-0b10061164b7&userGroupType=C
Power point on interpreting graphs
The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. / Examples will be shown in a power point or Smart board activity and all work will be graphed. Various examples can be taken from textbook guided practice and power point lessons
Day 1:
Introduction to domains and ranges notes:
http://www.coolmath.com/algebra/15-functions/01-whats-a-function-domain-range-05.htm
Function Notation notes:
http://www.coolmath.com/algebra/15-functions/02-function-notation-01.htm
Function sets notes:
http://www.coolmath.com/algebra/15-functions/04-functions-with-sets-02.htm
Vertical line test notes:
http://www.mathwarehouse.com/algebra/relation/vertical-line-test.php
Interactive game for needed assistance: http://www.ixl.com/math/grade-8/complete-a-function-table
Creating very own functions using the function machine (alternate interactive website):
http://www.shodor.org/interactivate/activities/FunctionMachine/
Open ended responses must be answered in accordance to student work and evaluation. Journal entry following student work. / Small group instruction
Students worked in small groups to complete flash cards given in order to determine the input and output of a graph
Individualized instruction
Students who chose to work individually worked on flash cards using white boards and showed the answer on the answer key
Peer tutoring
Students who worked on input and out and showed advanced skills can be teamed with another student in order to perform peer tutoring with flash cards
Use of manipulatives
Smart board activity created by teacher
Chunking information
Create worksheets and activities showing each input and output of a function separated by charts
Oral questioning
Oral question students who do not understand questions or have IEPs / Exit ticket
What is the output?
What is the input of a function?
Journal entry
Create a real world scenario using an input and output of ordered pairs (x and y) detailing something that occurs in everyday life
Do now
POD of LOTI
Quiz
What is a function quiz?
One-sentence summary
Journal entry one sentence summaries of vocabulary words
Homework
See textbook for homework samples / Vertical line test:
http://www.coolmath.com/algebra/15-functions/03-vertical-line-test-01.htm
function notation game:
http://www.coolmath.com/crunchers/algebra-problems-function-notation-1.htm
function notation two player game:
http://www.quia.com/cb/79591.html
Represent functions in different ways and compare them.
Recognize and describe the difference between linear and exponential growth, using tables, graphs, and equations. / Functions can be represented in equation forms and using function tables.
Day 2:
Students worked with smart notebook activity where they were given various representations of any function. Students needed to graph the function and determine if it was a function or not.
If completed, students will graph the function using the coordinates found using either their function table or their equation of a line.
This is a review of what is learned previously in the beginning of the unit. / Individualized instruction
Complete smart notebook activity with all independent problems given
Peer tutoring
Team up students with higher and lower functions in this activity for peer tutoring
Use of manipulatives
White boards for systematic equations
Computer activities for remediation
See above websites for review
Video tutorials from textbook
See my.hrw.com for video tutorials from textbook / Exit ticket
Journal entry
Do now
POD from LOTI
Quiz
Function table and linear equations quiz
Transfer and apply
Use reference sheet created for transferring and applying what students learned previously in the beginning of the our unit
Homework
Handout or textbook activity / Function machine:
http://www.shodor.org/interactivate/activities/LinearFunctMachine/
Figure out the function to stop the machine:
http://pbskids.org/cyberchase/games/functions/functions.html/
Simple linear functions:
http://www.onlinemathlearning.com/cgi-bin/counter.pl?url=http%3A%2F%2Fwww%2Eshodor%2Eorg%2Finteractivate%2Factivities%2FNumberCruncher%2F&referrer=http%3A%2F%2Fwww%2Eonlinemathlearning%2Ecom%2Fmath-games-collection%2Ehtml
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. / Day 1:
Slope of a line lesson introduction:
http://www.mathwarehouse.com/algebra/linear_equation/slope-of-a-line.php
Guided Practice:
Students will practice problems using Smart board and white boards or graph paper in order to interpret the equation y = mx + b
·  Students will complete various equations
·  Graph each equation
·  State the m (slope)
·  State the b (intercept)
Independent practice:
Practice problems are given on a power point presentation using a jeporady game or a regular power point .
More activities
Sing a song to “pop goes the weasel”:
“y = mx + b where m is the slope….Y = mx + b where b is the y-intercept….”
For extra credit points, students must sing the song to the teacher one on one while solving an equation as an exit passes.
Textbook video introduction with power point on interpreting equations in the slope intercept form of an equation.
Definitions and variables defined in notebooks with examples.
Students create reference sheet where m is in red and b is in blue in order to depict the y-intercept and slope of a line. Identify horizontal and vertical slopes with integers. Students will note the difference in each.
Students given slope equation formula. Work out examples through practice problems provided.
Matching game: students must identify functions that are not linear through a matching game with functions on a card. Out of 20 cards, they must find the nonlinear functions with the vertical line test.
They will identify the functions on a worksheet provided by the teacher
Slope Intercept Line Art Project:
·  Students will complete a project on slope intercept form of an equation
·  Students wll design a picture of their very own (trace it from an image on Google)
·  They will create five positive slopes with equations, 5 negative slopes with equations, 5 zero slopes with equations, and 5 undefined slopes with equations
·  All work must be shown on a separate sheet of paper with correct coordinate points
For modified work, reduce the number of equations to solve or allow students to just find the slope
Various LOTI activities
Bungee Jumping and Linear equations mini activity from LOTI
Loticlassroom.com. In this lesson plan, students will be participating in a bungee jumping simulation using metal Arnold Schwarzenegger can openers as the bungee jumpers. Students will collect
data, chart the data on a grid, and then write linear equations using the slope intercept format (y = mx + b).
Materials/Resources:
Website – YouTube: Nevis Bungee Jump - SCARED
http://www.youtube.com/watch?v=kJ-slNvmFYA&feature=related
Website – Line of Best Fit
http://illuminations.nctm.org/ActivityDetail.aspx?ID=146
Who Wants to Be a Millionaire PowerPoint
Bungee Jumping & Equations PowerPoint
Record lesson mini activity from LOTI:
In this lesson plan, students will investigate mathematical relationships involving different athletic events and attempt to predict athletic performance 40 years from now using algebraic concepts and processes.
Materials:
• Website: Usain Bolt
http://www.youtube.com/watch?v=By1JQFxfLMM&feature=channel
• Website: Online 100 Meter Sprint
http://www.playagame.ws/games/Sport+games/100+Meter.html
• Website: Jason Lezak
http://www.youtube.com/watch?v=Rg9lCvAvBdg
• Website: Online 100 Meter Sprint
http://www.playagame.ws/games/Sport+games/Sprint+Game.html
• Website: Swim Race
http://thegamerstop.com/43043-Swim-Race.html
• Website: Long Jump
http://www.officegamespot.com/free-games/long_jump.php
• Website: High Jump
http://www.kongregate.com/games/SwifterTS/high-jump
• World Records & Equations PowerPoint
FOR MORE ADVANCED STUDENTS: Identifying slope form of the equation given either with a partner or by yourself: equations must be solved in the form of y = mx + b
http://www.math-play.com/slope-intercept-game.html
Follow instructions with the given linear function in the form of y = mx + b: http://www.ltcconline.net/greenl/java/BasicAlgebra/Linegraph/LineGraph.htm
Save the Zogs Interactive website identifying linear equations in the form of y = mx + b:
This game begins with equations of y = x…students must complete each level in order to advance to equations in the form of y = mx + b