GRAPHING LINEAR EQUATIONS Or What’s My Line? …math.buffalostate.edu/~it/projects/weaver.pdfGRAPHING LINEAR EQUATIONS Or ... Algebraic Stained Glass Window Overview of Unit

GRAPHING LINEAR EQUATIONSOr

What’s My Line?By: Cathy Weaver

Course/Grade Level: Course I (Algebra), Grade 9

Time Span: Three 82-minute classes(6 classes under regular scheduling)

Technology and Manipulatives: TI-83 or 84 Plus Calculator Alpha Shapes

Geoboards CBR Measuring Tapes

Cathy Weaver Graphing Linear Equations12/16/04 I2T2 Final Project

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Overall Objectives for the Unit Ovrall Objctives for the UnitThe students will be able to:• Plot points in a coordinate plane• Use data to create a scatter plot and determine a reasonable interpretation of

the data• Graph linear equations using tables or lists, including horizontal and vertical

lines.• Identify x and y intercepts.• Create quick graphs using x and y intercepts.• Find slope given two points on a line.• Apply slope to real-life situations.• Determine slopes and y-intercepts by investigating linear equations and their

graphs.• Graph lines using equations in slope-intercept form.• Use various technologies and resources to expand their knowledge of

graphing linear equations.• Work efficiently with calculators and computers.

NYS Standards Covered NYSandards

• Standard 3: OPERATIONS• Standard 4: MODELING AND MULTIPLE REPRESENTATION• Standard 5: MEASUREMENT• Standard 6: UNCERTAINTY• Standard 7: PATTERNS AND FUNCTIONS

NCTM Standards Covered Ns Covered• Algebra• Geometry• Problem Solving• Communication• Connections• Representation

® Description of Resources Used Description ofResources Used

McDougal Littell, Algebra 1, by Larson, Boswell, Kanold, Stiff, Chapter 4, pages202-249, copyright 2001.


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McDougall Littell, Algebra 1: Test and Practice Generator CD-ROM.

http://gildersleeve.nn.k12.va.us/SOL_Math7.html, 7th Grade Math SOLResources.

http://www.bonita.k12.ca.us/schools/ramona/teachers/carlton/tutorialinteractives/inF-L/graphing/01graphingorderedpairs.html, Graphing Ordered Pairs , DeniseCarlton

http://www.bonita.k12.ca.us/schools/ramona/teachers/carlton/tutorialinteractives/inF-L/graphing/graphing2.html, Graphing a Line y = mx + b , Denise Carlton

http://www.themathlab.com/Algebra/lines%20and%20distances/stained%20glass%20window.htm, Algebraic Stained Glass Window, Copyright 1999-2003themathlab.com .

I2T2 Project 5 2004 Notebook, Algebra & Functions, A5 HS Introduction to CBR& Graphs.

® Description of Materials and Equipment Needed E® quipment Needed

Day One: (2 days if not block schedule)• Notes and overhead – 4.1• Cheerios


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• Plastic Gloves• Tape measures• How much is a handful? Activity• TI-83 or 84 Calculators with link cables and overhead screen• Homework Assignment – created using McDougall Littell Algebra 1: Test and

Practice Generator CD-ROM.

Day Two: (2 days if not block schedule)• Notes and overheads• Masking Tape – Create Coordinate plane on classroom floor using tiles as

grid.• Measuring tapes or string• Coordinate Cards• Geoboards and worksheet• Alpha Shapes and worksheet• Classroom computers• TI-83 or 84 Calculators• Homework Assignment - created using McDougall Littell Algebra 1: Test and

Practice Generator CD-ROM.

Day Three: (2 days if not block schedule)• Notes and overheads• Geoboards• CBR• I2T2 Project 5 Algebra and Functions Pg 53-61• Guess My Coefficient• TI-83 or 84 Calculators and overhead screen• Homework Assignment – Algebraic Stained Glass Window

Overview of UnitThe following schedule is based on block scheduling. The unit can easily beconverted to a 45 minute class by splitting each lesson into two sections.

Day One: Coordinates and Scatter Plots• Do Now Activity – review of past material• Students complete notes for this section and receive instruction for activity.• Students complete “How Much is a Handful?” Activity and discuss results and

problems encountered.


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• Students use TI-83 or 84 Plus to create scatter plot and find regressionequation and discuss how to use this information.

• Assign coordinate/scatter plot homework assignment.

Day Two: Quick Graphs, Intercepts, and Slope• Do Now Activity – review previous class material• Students complete notes and receive directions for stations.• Students rotate between 4 stations

- Floor Graph- Geoboards- Computer Activity- Alpha Shapes

• Assign quick graphs/intercepts/slope homework assignment.

Day Three: Slope as a Rate of Change and Quick Graphs UsingSlope-Intercept Form

• Do Now Activity – review previous class material• Students complete notes and receive directions for stations.• Students rotate between 5 stations

- Floor Graph- Geoboards- Guess My Coefficient- CBR- Match It- Algebraic Stained Glass Window

• Algebraic Stained Glass Window Project - students to work on through out ifthey have completed work at station before it is time to switch.

• Assign homework assignment – complete stained glass window project

Day One: Coordinates and Scatter PlotsOBJECTIVES:

1. Students will be able to successfully identify the components of thecoordinate plane.

2. Students will be able to successfully plot points in the coordinate plane.3. Students will be able to successfully collect data and use data to create a

scatter plot.


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4. Students will be able to successfully make predictions based on grapheddata.

5. Students will be able to successfully determine appropriate trend line andrelate trend line to real-life situations.

6. Students will be able to successfully use the graphing calculator as a toolto enter, graph and interpret data.

MATERIALS/EQUIPMENT/TEXTBOOK PAGES:Materials –Chapter 4.1 Notes, How Much is a Handful Activity, Scatter plot

Homework

Equipment – Overhead projector, Calculator, Link Cables, Cheerios,Gloves, Tape measures

Textbook Pages – 4.1 Coordinates and Scatter Plots 203-209

PRIOR KNOWLEDGE ASSESSMENT:Do Now Activity – Review of previous lessons including graph to determine slopeand y intercept.Notes – Initial examples allow students to display prior knowledge of coordinate

plane and scatter plots.

ANTICIPATORY SET:Students will notice several examples of scatter plots displayed in classroom.This will start them thinking about scatter plots and their meaning.

TEACHER INPUT:Introduce and discuss coordinate plane and scatter plot as described inobjectives. Encourage students to provide definitions and explanations asneeded through out lesson. Allow students to provide information from prior andcurrent learning necessary for completing notes. Guide students towardsbecoming confident in their abilities.

STUDENT ACTIVITIES:- Complete Do Now Activity- Active participation in classroom discussion.- Complete Handful activity.- Ask questions as needed.

GUIDED PRACTICE:Students and teacher will complete notes for lesson. As a group there willopportunity to practice targeted objectives.

INDEPENDENT PRACTICE:Through out the lessons students will practice individual problems as indicated innotes. Every student will participate in the activity with opportunity for drawing


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his or her own conclusions. Homework assignment will provide additionalindividual practice.

ALTERNATIVE ASSIGNEMNTS:As lesson progresses teacher will alter examples or practice problems if studentsexhibit comprehension or difficulties. Additional items will come from textbook orteacher created examples.

CLOSURE:Teacher will ask:

1. “Why is it important to understand scatter plots?”The expectation is that students will be able to give real-lifeexamples that are appropriate for the material covered.

2. “ What information can you get from a scatter plot?”Students should recognize that scatter plots show trends. In real-life these are used to provide easily understood displays of data.

ASSESSMENT:1. Immediate assessment - student responses verbal and written2. Continued assessment – student success on homework assignment.3. Final assessment – student success on quiz of material covered.

HOMEWORK:Worksheet 6 problems including the coordinate plane and various scatterplots that allow for individual interpretation and use of graphing claculator.Assignment created on McDougall Littell, Algebra 1: Test and PracticeGenerator CD-ROM.

NOTES: Coordinates and Scatter Plots(4.1)

A. Plotting Points on the Coordinate Plane1. Identify the following – x-axis, y-axis, Quadrant I, II, III, IV, and

origin.2. Plot the following points by hand (0,-2), (3,9), (-3,-3), and (-6, 5)


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Scatter Plots- an organization of data on a coordinate axis that shows therelationship between two quantities.

1. Plot data2. Describe the pattern if there is one.3. Make a prediction based on the pattern.

Vocabulary1. Independent variable

2. Dependent variable

Example 1 – Discuss scatter plots displayed in classroom.

How Much is a Handful?Investigating Trends (Linear Regression) with the TI-83 or TI-84

BACKGROUND: The manufacturers of Crispy Oat Rounds cereal want the cereal to beconsidered a snack as well as a breakfast food. Their goal is to make a cereal so thatwhen a child or an adult takes a handful they will get enough cereal to be a satisfyingsnack. Members of the department conducted thousands of random tests, on consumersof all ages, to determine how many pieces of cereal make a handful. They claim to have


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found a direct relationship between the size a person’s hand and the number of pieces ofcereal. From the data they determined an equation that can be used to predict how manypieces of cereal are in a handful.

YOUR TASK: As a class we will create a sampling to determine how much is a handful.

PROCEDURE:1. With a partner measure your hand. Measure from the base of your palm to

the tip of your middle finger. Record your measure to the nearest _ inch.

Hand measure

2. Take a handful of cereal, count the number of pieces, and record the amount.

Cereal pieces____________________

3. Record you groups data

Hand Size

Pieces of Cereal

Identify the independent variable.

Identify the dependent variable.

Describe any relationship you see developing.

4. Based on your group’s measurements make a hypothesis about therelationship between hand size and the number of cereal pieces.


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5. One member of your group will not enter your data in the overhead calculator.Put hand size in L1 and cereal count in L2. If other data is already there addyours to the list.

****Remember to push enter after putting in each number.

6. When the entire class has entered their data, one member of you groupshould link with the teacher to transfer the lists. This group member will thenlink with the other group members to transfer the lists to them.

Linking TI-83+ Calculators Using the Send/Receive Options1. Insert the link cable into the I/O ports at the bottom edge of the sending

and receiving calculators. Be sure that the connections are firmly made.This is the primary cause for transmission failure. Turn on bothcalculators.

2. On the receiving calculator, select LINK. Select RECEIVE and press

ENTER. "Waiting..." will appear on the screen.

3. On the sending calculator, select LINK. Select SEND.

o To send lists (data) select 4: List... Press ENTER


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n Place the cursor beside the name of the list to be sent. PressENTER. You may select as many lists as you wish. Be sure thateach selected list has a solid square marker to the left of theprogram name. Move the arrow up or down to reveal the solidsquares.

n Use the right-cursor key to highlight TRANSMIT. Press ENTER.n Since there is probably data in the list, you will be asked to

overwrite or rename. Select overwrite unless the current data mustbe preserved.

"Done" will appear on both calculators when the process is complete.

7. Using the list just transferred to your calculator, create a scatter plot of thedata on a sheet of graph paper.

8. Draw in what you consider to be the line of best fit (AKA, trend line orregression line.)

9. Determine the equation of this line.

a. Find the y-intercept (b)

Find the slope (m)

b. Write the equation of the line in slope-intercept form (y = mx + b). Use thevalues you found for m and b above. This is your regression equation.

y =

c. Label your line on your scatter plot.

10. Using your regression equation answer the following questions.

a. What type of trend appears?


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b. Does the research and developments claim that there is a directrelationship between hand size and number of pieces of cereal in ahandful appear to be correct? Why or why not?

c. Make a predictionHow many pieces of cereal will a child with a 3-inch hand grab?

How many pieces of cereal will an adult with a 10-inch hand grab?

11. Write a brief description of your findings. Be sure to indicate if you proved ordisproved your hypothesis.


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12. As a class we will continue on the calculator.

CREATING A SCATTER PLOT ON THE TI-83 or 84 PLUS

1. Choose STAT PLOT (2nd Y=),select Plot 1 and set it up asshown.

2. Press ZOOM 9: ZoomStat


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3. Set the calculator so that it will round decimalsto the nearest whole number.Press MODE then use the down arrow key tothe second row. Highlight 0 press ENTER.

4. Press STAT -> CALC -> 4: LinReg(ax+b)press ENTER

5. Your screen will look like this

Now press VARS select Y-VARS : 1:Function press ENTER . Select 1: Y1 pressENTER.

6. The home screen should look like this:


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Press ENTER to see the regression equation.The calculator uses a instead of m for slope.Record the equation here

7. Press GRAPH, the regression line is drawn over the data.Uses the table function to see how close you were in predicting thecereal amounts for 3 and 10-inch hands.

There is no answer key for this activity because results will vary. Be sure toprovide plastic gloves for your class because they will want to eat the Cheerios.Through out the activity there are many opportunities to discuss what thestudents are discovering. This part of the lesson is not scripted because it isdifferent every time. Listen and watch your class the learning possibilities areamazing.


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Day Two: Quick Graphs, Intercepts, and SlopeOBJECTIVES:1. Students will be able to plot points in the coordinate plane.2. Students will be able to graph a linear equation using a table or a list of

values.3. Students will be able to successfully graph horizontal and vertical lines.4. Students will be able to successfully identify x and y intercepts on a graph.5. Students will be able to successfully make a quick graph using the intercepts.6. Students will be able to successfully determine the slope of a line using two

points on the line.7. Students will be able to determine facts about various geometric shapes

based on the slope of their sides.

MATERIALS/EQUIPMENT/TEXTBOOK PAGES:Materials –Chapter 4.2, 3, 4 Notes, Coordinate Cards, Geoboard

Equations and Paper, Alpha Shapes Worksheet

Equipment – Overhead projector, Floor graph, Geoboards, Alpha Shapes,Classroom Computers Calculator, Graph paper

Textbook Pages – 4.2 Graphing Linear Equations 210-2174.3 Quick Graphs Using Intercepts 218-2254.4 The Slope of a Line 226 -228

PRIOR KNOWLEDGE ASSESSMENT:Do Now Activity – Review of previous lessonNotes – Initial examples allow students to display prior knowledge of coordinate

plane, intercepts, and graphing lines.


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ANTICIPATORY SET:Students will notice several examples of graphed lines. This will start themthinking about scatter plots and their meaning.

TEACHER INPUT:Introduce and discuss graphing linear equations using tables and intercepts. Anddetermining slope. Encourage students to provide definitions and explanationsas needed through out lesson. Allow students to provide information from priorand current learning necessary for completing notes. Guide students towardsbecoming confident in their abilities.

STUDENT ACTIVITIES:- Complete Do Now Activity- Active participation in classroom discussion.- Complete all stations.- Ask questions as needed.

GUIDED PRACTICE:Students and teacher will complete notes for lesson. As a group there willopportunity to practice targeted objectives.

INDEPENDENT PRACTICE:Through out the lessons students will practice individual problems as indicated innotes. Every student will participate in the activities with opportunity for drawinghis or her own conclusions. Homework assignment will provide additionalindividual practice.



1. “How are intercepts important to graphing lines?”The expectation is that students will be able to discuss usingintercept to draw a line.

2. “ What does slope mean?”Students should recognize that slope is used to determine how toget from one point on a line to another.

3. “ What did you discover about the shapes you were working with?”


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Students should be able to discuss the results the discovered aboutthe relationship between the slopes of the sides of the variousshapes.


HOMEWORK:Worksheet: 10 problems including the graphing lines from a list, graphinglines using the intercepts, and determining the slope of a line. Assignmentcreated on McDougall Littell, Algebra 1: Test and Practice Generator CD-ROM.

NOTES: Graphing Linear Equations (4.2)OBJECTIVE 1: Graphing a linear equation

Example 1: Graphing an EquationUse a table of values to graph the followinga. 5x = y - 2

Is (0, 2) on the line?Is (2, 0) on the line?

Example 2: Use a table of values to graph the equation 3x - 2y = 6


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Example 3: Graphing y = b and y= a

a. Graph the equation y = -1b. Graph the equation x = 2


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Quick Graphs Using INTERCEPTS (4.3)

OBJECTIVE 1: Finding the Intercepts of a lineA. The x – intercept : This is the x-coordinate of a point that crosses the x-axis.

When a point is on the x-axis the y-coordinate is always .

Example1. : Find the x-intercept of the graph of the following equations a. 4x + 3y = 12.

b. y = 2x -4

c. 2y = 4x + 6

B. The y – intercept : This is the x-coordinate of a point that crosses the y-axis.When a point is on the y-axis the x-coordinate is always .


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Example2. : Find the y-intercept of the graph of the following equations

a. 4x + 3y = 12.

b. y = 2x -4

c. 2y = 4x + 6

OBJECTIVE 2: Using Intercepts to Make a Quick Graphs of a Linear EquationExample 3.

a. Graph the equations x – 2 = 4y

x-intercept:

y-intercept:


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The Slope of a Line(4.4)

GOAL 1: Finding the Slope of A Line

FORMULA: Slope = run

rise=

sxinchange

syinchange

'

' =

12

12

xx

yy

-

-

Ex. A line contains the points (5, 7) and (3, 4), what is its slope?

Find the slope of the following lines that contain the given points and graph theline on graph paper to check your calculation.

1. (-3, 0) and (-1,6)

2. (-1, -3) and (5, -3)


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3. (-2, 1) and (1, -3)

4. (0, -1) and (0,4)


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HUMAN FLOOR GRAPH ACTIVITY

SET UP: Prior to class teacher should use masking tape to create a coordinateplane on the floor. This works best if the class has floor tiles because they canbe used to create the grid.

MATAERIALS: String or measuring tapes and note cards with coordinates,intercepts, and equations. Graph paper to have students create what they aredoing by hand.

THE ACTIVITY: Have groups of six or more students work through this activity.Use index cards to give them instructions. Students or teacher can take turnsreading the cards.

INTERCEPTS: Have two students be the intercepts others will connect them tocreate a line. Discuss what points will be on the line.

INDEX CARDS: x-intercepts y-intercepts5 7-5 -22 -30 4-1 0

HORIZONTAL AND VERTICAL LINES: Read equation from index card.Students all find a place on the line.

INDEX CARDS: horizontal verticaly= 7 x=-7y= -1 x=8y= 0 x=1y= -3 x=0

USING A TABLE: Students will stand at given coordinates. They will create aline using string or measuring tape to connect the points. Others in group willidentify slope and y-intercept to discover the equation of the line. They will beasked if a certain point is on the line.

INDEX CARDS: Line 1: (0, 1), (1, 2), (-1, -1), (-2,-3) and Is (-4, 5) onthis line?

Solution: y = 2x + 1, no

Line 2: (0, 1), (2, 0), (-2, 2), (4,-1) and Is (-4, 3) on thisline?

Solution: y = -1/2x + 1, yes


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GEOBOARD ACTIVITYSET UP: Prior to class teacher should set up a group of desks with enoughgeoboards and rubber bands to accommodate group size.

MATAERIALS: Geoboards, rubber bands, geopaper with and without linesdrawn in.

THE ACTIVITY: Have group of students work through this activity. The firstexamples will have students place rubber bands where instructed and thendetermine the slope of the line. Then students will place rubber bands based ongiven instructions and draw answer on geopaper.

GEOPAPER ON NEXT PAGES


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GEODOTS AND LINES

Directions: Create the following lines on your geoboard. Determine theslope and record your answer in the space provided.

m = m = m =

m = m = m =


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Directions: Create a line on the geoboard using the given intercepts.Draw the line on the geopaper. Determine the slope of each line andrecord your results.

x-intercept: 4 x-intercept: 3 x-intercept: 1y-intercept: 2 y-intercept: 1 y-intercept: 4

m= m= m=

Do you see any pattern developing with thesegraphs?

x-intercept: 2y-intercept: 3

m=


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Directions: Create a line on the geoboard using the given slopes. Drawthe line on the geopaper.

m = 4 m = _ m = -3/2

m = -4 m = -1/2 m = 3/2

Do you notice anything about the slopes?

Undefined m = 0


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GEODOTS AND LINES(ANWER KEY)

Directions: Create the following lines on your geoboard. Determine theslope and record your answer in the space provided.

m = 3 m = no slope m = -2/3

m = undefined m = 1/3 m = -2


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Directions: Create a line on the geoboard using the given intercepts.Draw the line on the geopaper. Determine the slope of each line andrecord your results.

x-intercept: 4 x-intercept: 3 x-intercept: 1y-intercept: 2 y-intercept: 1 y-intercept: 4

m= -1/2 m= -1/3 m= -4

Do you see any pattern developing with thesegraphs? SLOPE IS –y intercept/x intercept.

x-intercept: 2y-intercept: 3

m= -3/2


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ALPHA SHAPES ACTIVITY

SET UP: Prior to class teacher should set up a group of desks with AlphaShapes and graph paper.

MATAERIALS: Alpha Shapes – use H, I, R, U, V, and W for this activity andgraph paper. I used _ inch paper for this. If you use another scale, you will haveto modify the activity to fit correctly.

THE ACTIVITY: Have group of students work through this activity. They shouldplace the given shape on graph paper using the shapes described above. Asthey graph each shape, they should find the slopes of each line and record theiranswers in the table provided. Discussion can come up about the relationships ofthe slopes they find in the various shapes.

Activity on next pages.


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SLOPES IN ALPHA SHAPES

Directions: Trace the Alpha Shapes on graph paper using the coordinates you are given.Be sure that you have placed the Alpha Shape so that you can read the numbers andletter correctly, they should not be backwards. Determine the slope of each line in theshape. Record your results in the table. Record any observations you discover aboutthe slopes of the sides of the shapes.

Alpha ShapeAnd

Coordinates

Slope Observation

H1: (-9, 0)2: (-2, 4)3: (-5, -8)

Point 1-2:

Point 2-3:

Point 3-1:

I1: (-2, -2)2: (10, 2)3: (1, -11)

Point 1-2:

Point 2-3:

Point 3-1:

R1: (1, -6)2: (8, 5)3: (10, -7)

Point 1-2:

Point 2-3:

Point 3-1:


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U1: (1, 11)2: (10, 9)3: (13, 0)4: (4, 2)

Point 1-2:

Point 2-3:

Point 3-4:

Point 4-1:

V1: (0, 5)2: (9, 3)3: (7, 6)

Point 1-2:

Point 2-3:

Point 3-1:

W1: (-8, 1)2: (-1, 7)3: (5, 0)4: (-2, -6)

Point 1-2:

Point 2-3:

Point 3-4:

Point 4-1:


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ANSWER KEYH: SLOPE: Points1-2: –4/11

Points 2-3: 4Points 3-1: -2

OBSERVATION: No slopes the same

I: SLOPE: Points1-2: 1/3Points 2-3: 13/9Points 3-1: 3

OBSERVATION: Right triangle slope of the legs are negativereciprocals.

R: SLOPE: Points1-2: 11/7Points 2-3: -6Points 3-1: -1/9

OBSERVATION: No slopes the same

U: SLOPE: Points1-2: -2/9Points 2-3: -3Points 3-4: -2/11Points 4-1: -3

OBSERVATION: One pair of parallel lines. This is a trapezoid.

V: SLOPE: Points1-2: -2/9Points 2-3: -3/2Points 3-1: 1/7

OBSERVATION: No slopes the same.

W: SLOPE: Points1-2: 6/7Points 2-3: -7/6Points 3-4: 6/7Points 4-1: -7/6

OBSERVATION: Two pairs of parallel lines. Slopes of adjacent sides arenegative reciprocals. This is a square.


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COMPUTER ACTIVITY

MATAERIALS: Computers with internet access. Students can work in pairs.

THE ACTIVITY: Have students log onto either of the following websites andcomplete the activities.

http://www.bonita.k12.ca.us/schools/ramona/teachers/carlton/tutorialinteractives/inF-L/graphing/01graphingorderedpairs.html

http://www.bonita.k12.ca.us/schools/ramona/teachers/carlton/tutorialinteractives/inF-L/graphing/graphing2.html


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Day Three: Quick Graphs Using Slope – Intercept Form andSlope As a Rate of Change (Intro)OBJECTIVES:1. Students will be able to graph a linear equation using the slope intercept form

of the equation.2. Students will be able to successfully identify slope of a line.3. Students will be able to successfully y intercept on a graph.4. Students will be able to successfully make a quick graph y = mx +b.5. Students will be able to recognize that slope is a rate of change.6. Students will be able to interpret the meaning of slope in real-life situations.

MATERIALS/EQUIPMENT/TEXTBOOK PAGES:Materials –Chapter 4.4, 6 Notes, Equation Cards, Geoboard Equations

and Paper, Calculators with Guess My Coefficient Game

Equipment – Overhead projector, Floor graph, Geoboards, Calculator andlink cables, CBR, Overhead, Graph paper, Rulers, Colored Pencils

Textbook Pages – 4.4 The Slope of a Line 228-233 4.6 Quick Graphs Using Slope-Intercept Form 241-249

PRIOR KNOWLEDGE ASSESSMENT:Do Now Activity – Review of previous lessonNotes – Initial examples allow students to display prior knowledge of slope,

intercepts and graphing lines.

ANTICIPATORY SET:Students will notice several examples of graphed lines with equations anddescriptions of rates of change. This will start them thinking about scatter plotsand their meaning.

TEACHER INPUT:Introduce and discuss lines as descriptions of speed or other rates of change anddiscuss how slope intercept equation is determined. Encourage students toprovide definitions and explanations as needed through out lesson. Allowstudents to provide information from prior and current learning necessary forcompleting notes. Guide students towards becoming confident in their abilities.

STUDENT ACTIVITIES:- Complete Do Now Activity- Active participation in classroom discussion.- Complete all stations.- Ask questions as needed.


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GUIDED PRACTICE:Students and teacher will complete notes for lesson. As a group there willopportunity to practice targeted objectives.INDEPENDENT PRACTICE:Through out the lessons students will practice individual problems as indicated innotes. Every student will participate in the activities with opportunity for drawinghis or her own conclusions. Homework assignment will provide additionalindividual practice.



1. “How are lines used to describe real-life situations?”The expectation is that students will be able to that a line canrepresent a rate of change.

2. “ How does the slope-intercept equation make it easy to graph a line?”Students should recognize that slope is used to determine how toget from one point on a line to another.


HOMEWORK:Students will complete stained glass window.


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NOTES: The Slope of a Line(4.4)Classification of Lines by Slope

1. A line with positive slope rises from left to right.m >0

2. A line with a negative slope falls from left to right.m < 0

3. A line with zero slope is horizontal.m = 0

4. A line with an undefined slope is vertical.m is undefined

Classify lines you graphed yesterday.

Goal 2: Interpreting Slope as a Rate of ChangeRate of change compares two different quantities that arechanging. An example is velocity, which compares the rate adistance is changing with time. Slope can be used to provide agraphical representation of a rate of change.

Example 2: Slope as rate of change.You are typing a paper. At 5:15 pm you have typed 275words. By 5:27 pm you have typed 660 words.a. Find the average rate of change in words per minutes.b. At this rate at what time will you have typed over 1012

words?


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NOTES: Quick Graphs Using Slope-Intercept Form(4.6)Goal 1: Graphing Using Slope-Intercept Form

SLOPE- INTERCEPT FORM OF THE EQUATION OF A LINEy mx b= + **MEMORIZE THIS EQUATION

m = the slope of the lineb = the y –intercept

Example 1: Writing Equations in slope intercept form

y = mx + b

EQUATIONSLOPE –

INTERCEPT FORM SLOPE y-INTERCEPT

y = -x +2 y = (-1)x + 2 -1 2

y = 3x –5

y = x + 3

2

y = -4y – x = -1

3x – 6 y = 12

Enter the equations on the calculator and check your answers.


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Example 2: Graphing using the Slope and y-interceptGraph the equation –2x + y = 5Slope y-intercept


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GOAL 2: Solving Real-Life Problems Example 4:

The equations below model the changing speeds of a car asit enters an expressway, travels on the expressway, and thenexits the expressway. Create a graph to represent the car’sdifferent speeds.s = speedt = time (in minutes)

Stage1: (first 2 minutes)s = 15t + 25Stage 2: ( next 10 minutes)s = 65Stage 3: ( next 2 minutes)s = -15t + 235


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HUMAN FLOOR GRAPH ACTIVITY (y = mx + b)

SET UP: Prior to class teacher should use masking tape to create a coordinateplane on the floor. This works best if the class has floor tiles because they canbe used to create the grid.

MATAERIALS: String or measuring tapes and note cards with coordinates,intercepts, and equations. Graph paper to have students create what they aredoing by hand.

THE ACTIVITY: Have groups of six or more students work through this activity.Use index cards to give them instructions. Students or teacher can take turnsreading the cards.

INTERCEPTS: Have two students determine slope and y- intercept havestudents direct other students to create line. Discuss the line.

INDEX CARDS: y = 2x + 1 y = -5/2x + 3y = -3x – 4 y = -4/3x - 2y = 2/3x + 4 2x + 4y = 8y = 0x + 5 -3x +2y = -6


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GEOBOARD ACTIVITY (y = mx + b)SET UP: Prior to class teacher should set up a group of desks with enoughgeoboards and rubber bands to accommodate group size.

MATAERIALS: Geoboards, rubber bands, geopaper with and without linesdrawn in.

THE ACTIVITY: Have group of students work through this activity. The firstexamples will have students place rubber bands where instructed and thendetermine the equation of the line. The bottom row and first column of pegsshould be used to represent the x and y axiz. Then students will place rubberbands based on given instructions and draw answer on geopaper.

GEOPAPER ON NEXT PAGES


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GEODOTS AND LINES

Directions: Create the following lines on your geoboard. Determine theequation of the line in slope-intercept form and record your answer in thespace provided.

y = y = y =

y = y = y =


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Directions: Create a line on the geoboard using the given equaiton.Draw the line on the geopaper. Determine the slope and intercept ofeach line and record your results.

y = 3x +1 y = -x +4 y = -1/2x+3y-intercept: y-intercept: y-intercept:

m= m= m=

y= 2/3x +1 y = -3/2x + 2 -2y = -4x -6y-intercept: y-intercept: y-intercept:

m= m= m=


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GEODOTS AND LINES (ANSWER KEY)

Directions: Create the following lines on your geoboard. Determine theequation of the line in slope-intercept form and record your answer in thespace provided.

y = 2x y = undefined y = -x +4

y = no slope y = 1/2x y = -4/3x + 4


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Directions: Create a line on the geoboard using the given equaiton.Draw the line on the geopaper. Determine the slope and intercept ofeach line and record your results.

y = 3x +1 y = -x +4 y = -1/2x+3y-intercept: 1 y-intercept: 4 y-intercept: 3

m= 3 m= -1 m= -1/2

y= 2/3x +1 y = -3/2x + 3 -2y = -4x - 2y-intercept: 1 y-intercept: 2 y-intercept: 1

m= 2/3 m= -3/2 m= 2


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GUESS MY COEFFECIENT GAME

This game is on the TI-84 Plus and may be on some TI-83 Plus also. The gamecan be found in the applications menu. If it is not on all students’ calculatorsinstructed them to link and transfer the game. They can follow the previouslinking instructions. This game can be played alone or in competition ifcalculators are linked, you will need to determine which is best for yourclassroom. Have students play and record scores. Have them get their scoresverified and initialed by another student. Doing this will help you to be sure theyare participating.

SET UP: Prior to class teacher should set up a group of desks with link cablesand calculators. Score sheets can be provided or students can record on theirown paper.

MATAERIALS: TI-83 or 84 plus calculators, link cables

THE ACTIVITY: Have group of students play this game and record scores. Thisis a good way to introduce games on the calculator that students can play afterfinishing quizzes or tests.


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ALGEBRAIC STAINED GLASS WINDOW ACTIVITY

SET UP: Prior to class teacher should set up a group of desks with rulers,colored pencils, and graph paper.

MATAERIALS: Rulers, colored pencils, and graph paper. Follow the link belowto get the activity specifics and to create paper to be used.:

http://www.themathlab.com/Algebra/lines%20and%20distances/stained%20glass%20window.htm

THE ACTIVITY: Students will create stained glass windows using y = mx + b tocreate the lines the use to make their design. This will be started in class andcompleted as a homework assignment.


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ALGEBRAIC STAINED GLASS WINDOW

For this project, you will be using your graphing skills to design and create analgebraic stained glass window. Use colored markers, paint, colored paper,glitter, stickers, holiday designs, etc. to embellish your window. When you arefinished, you will have a nice piece of work that will show off your graphing skillsand be a great room decoration as well.

DIRECTIONS:Step 1:

Draw a coordinate plane in the center of your paper. The x and y axesshould extend to the edges of the paper. Lightly number your axes to theedges of the paper also.

Step 2:Create an ornate arrangement of at least six horizontal and vertical lines.These lines should be labeled with their respective equations. Also the "T-Chart paper" for horizontal and vertical lines should be completed.

Step 3:

Next you will need to write equations for six oblique, (diagonal), lines. Todo this, just be sure that your equation is in linear form and has both x andy variables.

Experiment with your equations. See if you can figure out how changingthe number in front of the "x" and changing the last number will changethe line.

Try to write an equation that will put a line where you want it to go.

Fill out a "T-Chart Paper" for these oblique lines equations and then graph thepoints from your chart.Be sure to LABEL your lines on the poster with their equations.

Step 4:

Now go in and color the sections of your paper that have been created bythe intersecting, oblique lines and diagonal segments.

These posters look great when held up against a window or light.

From: Algebraic Stained Glass Windowhttp://www.themathlab.com/Algebra/lines%20and%20distances/stained%20glass%20window.htm


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CBR – MATCH IT ACTIVITY

SET UP: Prior to class teacher should set up the CBR and overhead screen.

MATAERIALS: CBR, overhead screen, I2T2 Project 5 Notebook Section A5pages 53-60.

THE ACTIVITY: Students will work on worksheets and do the Match It activityusing the CBR. Depending on the time frame teacher can determine whichworksheets to use. Students can be working on these while waiting their turn atthe CBR.

Documents

GRAPHING LINEAR EQUATIONS Or What’s My Line? …math.buffalostate.edu/~it/projects/weaver.pdfGRAPHING LINEAR EQUATIONS Or ... Algebraic Stained Glass Window Overview of Unit