Linear FunctionsLinear Functions

CTSE 5040CTSE 5040Jennifer MillerJennifer Miller

Alabama Course of Study Objectives

2. Analyze linear functions from their equations, slopes, and intercepts.a. Finding the slope of a line from its equation or by applying the slope formulab. Determining the equations of linear functions given two points, a point and the slope, tables of values, graphs, or ordered pairs.

TEAM-Math ObjectivesTEAM-Math Objectives

c. Analyze linear functions from their slopes, equations, and intercepts: Find slope of a line form equation or using slope formula. Determine the equations of linear functions given 2 points, a point and slope, tables of values, graphs, and ordered pairs.

Technology Technology

““Technology is not a panacea. As with Technology is not a panacea. As with any teaching tool, it can be used well or any teaching tool, it can be used well or poorly. Teachers should use technology poorly. Teachers should use technology to enhance their students’ learning to enhance their students’ learning opportunities by selecting, or creating opportunities by selecting, or creating mathematical tasks that takes advantage mathematical tasks that takes advantage of what technology can do efficiently and of what technology can do efficiently and well” (NCTM, 2000, p. 25-26). well” (NCTM, 2000, p. 25-26).

Technological Resources

Geometer’s SketchPadGeometer’s SketchPadGraphing CalculatorGraphing CalculatorOnline ResourcesOnline Resources

Geometer’s SketchPadGeometer’s SketchPadNot just GeometryNot just GeometryGrid FormGrid Form– Labeled axesLabeled axes

Plot pointsPlot pointsPlot functionsPlot functionsMeasure slopeMeasure slopeFormulate equation Formulate equation Great VisualsGreat VisualsVariety of colorsVariety of colorsInteractive Interactive Animate objectsAnimate objectsTrace objectsTrace objects

The Slope gameThe Slope gameIntroduction to linear functionsIntroduction to linear functionsPair studentsPair studentsStudent 1Student 1– Construct 5 linesConstruct 5 lines– Measure slopeMeasure slope– Hide labelHide label

Student 2Student 2– Match slope to lineMatch slope to line

Students switchStudents switchRepeatRepeat

Competition Student interactionConstruct knowledgeClass discussion

Graphing CalculatorGraphing CalculatorY= Y= – Multiple equationsMultiple equations– Compare Compare

GraphGraphTableTableWindowWindow– Min, Max, SclMin, Max, Scl

Trace/ZoomTrace/ZoomTable SetTable Set

22ndnd + CALC + CALC– ValueValue– ZerosZeros– IntersectionIntersection– Etc. Etc.

Linear Functions ActivityLinear Functions ActivityGiven y = 3x+2Given y = 3x+2Find y-intercept Find y-intercept – GraphGraph

TRACE(ZOOM)TRACE(ZOOM)– TableTable– 22ndnd+CALC +CALC

Value x=0Value x=0– Pencil & paperPencil & paper

X=0 solveX=0 solve

More examplesMore examplesy=mx+by=mx+b

Linear Functions ActivityLinear Functions Activity

Use: IntroductionUse: IntroductionVariety of methodsVariety of methodsMore familiar with the graphing calculatorMore familiar with the graphing calculator– Explore features, capabilitiesExplore features, capabilities

Promotes explorationPromotes exploration

Online ResourcesOnline ResourcesEndless resourcesEndless resources– Java appletsJava applets– VideosVideos– Interactive gamesInteractive games– Many moreMany more

InteractiveInteractiveGood visualsGood visualsChose selectively Chose selectively – Confusion Confusion

Activity: Slope of a Line Activity: Slope of a Line

http://http://www.mathopenref.com/coordslope.htmlwww.mathopenref.com/coordslope.html

ReferencesReferences

National Council of Teachers of Mathematics. National Council of Teachers of Mathematics. (2000). (2000). Principles and Standards for School Principles and Standards for School MathematicsMathematics.  Reston, VA: Author..  Reston, VA: Author.Page, John. (2009). Slope of a Line. Retrieved Page, John. (2009). Slope of a Line. Retrieved on December 11, 2009. on December 11, 2009. http://www.mathopenref.com/coordslope.htmlhttp://www.mathopenref.com/coordslope.htmlThe Slope Game. (2006). Key Curriculum The Slope Game. (2006). Key Curriculum Press.com. Retrieved on December 11, 2009. Press.com. Retrieved on December 11, 2009. http://www.keypress.com/x5575.xmlhttp://www.keypress.com/x5575.xml