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Catherine Inman Content Enhancement Final Project EDSP 404 Grade Level: Algebra 1 (9th – 12th grade) SOL: Remember to print: http://www.doe.virginia.gov/VDOE/Instruction/Math/curriculum_framework_2009/algebra1cf.pdf NAME The Unit Organizer 4 BIGGER PICTURE DATE Linear Functions 2 LAST UNIT /Experience 8 UNIT SCHEDULE CURRENT CURRENT UNIT UNIT 1 Graphing Relations and Functions 5 Analyzing Linear Equations 3 NEXT UNIT /Experience Solving Linear Inequalities UNIT MAP Slope Direct Variation Graphing and Writing Equations using formulas Quiz pp. 256 - 314 Slope-intercept Exploring Activity Slope Point-slope Exploring Activity By applying Quiz Parallel lines Parallel and Perpendicular Lines Slope-Intercept form Perpendicular lines Quiz Point-slope form Review •Describe what is slope? •How would you relate slope to climbing a mountain? •Compare and contrast point-slope and slope-intercept form. •Compare and contrast parallel and perpendicular lines? Solve Graph Manipulate UNIT 7 6 Identify RELATIONSHIPS UNIT SELF-TEST QUESTIONS Unit Test The Unit Organizer 9 Expanded Unit Map Rise over run Linear Functions Slope Graphing and Writing Equations using formulas pp. 256 - 314 y2 – y1 =m x2 – x1 By applying y = mx + b Slope-Intercept form Point-slope form y – y1 = m(x – x1) NEW UNIT SELF-TEST QUESTIONS 10 NAME DATE Parallel and Perpendicular Lines m=m m = -1/m The FRAME Routine Key Topic Slope-Intercept Form is about… A linear equation written in the form y = mx+b. Main idea Main idea Slope Essential details What Change in y’s over change in x’s. is it? Rise over run. Can find it by: Where in the equation Is it constant y2 – y1 y - intercept Variables Essential details Essential details Where the graph crosses the y-axis. Find y where x=0 =m x2 – x1 Represented by “m” in the equation y = mx+b. Slope is constant only in a linear equation Main idea Coordinate points These numbers will vary. Can find only one if given the other. Represented by “b” in the equation y = mx + b. Represented by “x” and “y” in the equation y = mx + b. Always one constant number in a linear equation The coordinate points will change So What? (What’s important to understand about this?) This will help make graphing and solving linear equations easier. Linear equations are used to model things over time such as distance over time or cost over time (speed and inflation). Slope Coordinate point Variables x, y Key Words Negative numbers Positive numbers Zero slope Undefined slope cubic (y-5)=6(x-2) y - intercept y = 5x+3 2x + 3y = 10 CONVEY CONCEPT Point – Slope Form OFFER OVERALL CONCEPT CONCEPT DIAGRAM Linear Equations NOTE KEY WORDS CLASSIFY CHARACTERISTICS Always Present Slope Sometimes Present Negative numbers (Known) Coordinate point Variables x, y Positive numbers Never Present Undefined slope cubic Zero slope y - intercept EXPLORE EXAMPLES 2x + 3y = 10 Examples: Nonexamples: (y-5)=6(x-2) y = 5x+3 (y-7)=2(x-3) 2x + 3y = 10 (y-7)=2(x-3) (y+4)=.5(x-2) (y+4)=.5(x-2) (y-2)=1(x+0) y=7 (y-2)=1(x+0) 13,000 y=7 13,000 PRACTICE WITH NEW EXAMPLE TIE DOWN A DEFINITION Point – Slope Form is a type of linear equation that uses a known coordinate, slope and variables x and y. LINCS Tables 1 Term Slope 3 4 Term Direct Variation 3 4 Reminding Word Term Constant of variation 3 4 Reminding Word Term Family of graphs 3 Reminding Word Famine List the parts 2 LINCing Picture 2 4 5 LINCing Story LINCing Picture The group of farmers had a severe famine that year. Identify a remaining word Definition Definition The number k in equations of the form y = kx. Cindy had to construct the letter k a number of times. Construct 1 LINCing Picture An equation of the form y = kx where k is a non-zero constant. 5 LINCing Story Definition Ratio of the change in y to the change in x. 5 LINCing Story 2 Sarah had to select the correct form for her paper. Select 1 LINCing Picture Timmy had hope that his grade would change. Reminding Word Hope 1 5 LINCing Story Note a LINCing story 2 Definition A group of graphs or equations of graphs with at least one characteristic in common. Create a LINCing picture Self-test