Unit Title: Algebra

Unit Title: Algebra Subject: Mathematics Timeframe Needed for Completion: 15 weeks Grade Level: 8th Grading Period: 2nd and 3rd Nine Weeks Unit Title: Algebra Big Idea/Theme: What’s your Function? Understandings:  Solve Equations (one-step, two-step, variables on both sides, distributive prop., square, square roots, cube and cube roots)  Formulas (Solve for a specific variable)  Functions and Relations  Linear or Nonlinear  Slope  Intercepts  Linear Equations  Linear Inequalities Essential Questions: Curriculum Goals/Objectives (to be assessed at the end of the The Golden Rule: Love it, Live it or Laugh at it? unit/quarter) How do you use patterns to help you make decisions? COMPETENCY The learner will understand and use linear How can you use Algebra outside of class? GOAL 5: relations and functions. How has equality or inequality shaped your life? Objectives Equality or inequality? Explain. 5.01 Develop an understanding of function.

What distinguishes one line from another? a. Translate among verbal, tabular, graphic, and algebraic representations of functions. Guiding Questions: b. Identify relations and functions as linear or nonlinear. Why solve equations? c. Find, identify, and interpret the slope (rate How do you determine what steps to use when solving an of change) and intercepts of a linear equation/inequality? relation. d. Interpret and compare properties of linear How do you know when you have solved an equation correctly? functions from tables, graphs, or equations. What are opposite operations? What operation is opposite of square root? How do you know? 5.02 Write an equation of a linear relationship What operation is opposite of cubing a number? How do you given: two points, the slope and one point on the line, know? or the slope and y-intercept. What is the difference between a function and a relation? 5.03 Solve problems using linear equations and Are all functions relations? inequalities; justify symbolically and graphically. Are all relations functions? 5.04 Solve equations using the inverse relationships How can you determine when a relation is not a function? of addition and subtraction, multiplication and What are the different ways you can model/represent a function division, squares and square roots, and cubes and cube or relation? roots. What are the advantages/disadvantages to looking at a table as . opposed to the graphic representation? What are the advantages/disadvantages to looking at a graph as Unit Title: Algebra opposed to the algebraic representation? Is there any representation that is more beneficial than the others? (verbal, tabular, graphic and algebraic) Explain. Explain how you can create the other three representations given one representation to start with. What is the difference between linear and nonlinear? How can you determine if a situation represents a linear or nonlinear relation? What is slope? How can slope be represented? Is it possible to have no slope? Is zero slope and no slope the same? Is undefined slope and no slope the same? How can you determine when lines have the same slope? How can you determine which line is steeper? What is the x and y intercept? What is the significance of the x- and y- intercept in problem situations? If the x-intercept stays the same but the slope changes how is the line affected line? If the slope stays the same but the x-intercept or y-intercept changes, how does that affect the line? What determines if a line moves along the vertical axis? What determines if a line moves along the vertical axis? Why do most linear equations have two variables? What kinds of lines only have one variable? How would you graph linear equations given: the slope and a point, two points, the equation in standard form, the equation in slope-intercept form? How would you write the equation of a line in slope-intercept form given: the slope and a point or two points. How can you take an equation in standard form and put it in slope-intercept form? Compare and contrast equations and inequalities? How is the graph of an inequality different from an equation? Looking at the graph of an equation how can you determine a solution for the inequality? How do you determine when an inequality has a solid line or a broken line? Unit Title: Algebra What is the significance of the broken line or solid line?

Essential Skills/Vocabulary: Assessment Tasks:

Vocabulary: Essential Skills: Class Discussions/Philosophical Chairs/Socratic Seminar input  Translate among verbal, Learning Logs output tabular, graphic and relation algebraic representations. Cornell Notes function table  Determine if relations or Think-Pair-Share function rule functions are linear or Concept Maps function notation nonlinear from any of the Graphic Organizers variable given representations. (Listed Interactive Notebook independent above) Groupwork dependent  Understand slope as the coefficient constant rate of change in a Projects equation line. Quickwrites slope-intercept form  Find the slope of a line Foldables f(x) = ax + b (rise/run) given a set of RAFTS point-slope form ordered pairs, a table of Journals y - y1 = a(x - x1) values, the graph of a line, or standard form the equation of a line. Ax + By = C  Distinguish between lines properties of equality with undefined/no slope commutative property (vertical) and lines with zero associative property slope (horizontal). distributive property  Identify where a line crosses identities the x-axis (x-intercept) and slope (rate of change) the y-axis (y-intercept). y-intercept  Use slope to identify parallel x-intercept lines (same slope). vertical line test  Determine if the graph of two linear function linear functions has no points non-linear function in common (parallel lines), intercepts has one point in common slope (intersecting lines), or has all parallel lines points in common intersecting lines (same line). perpendicular lines  Use knowledge about linear Unit Title: Algebra collinear points relationships to solve real equation world problems. slope-intercept form  Write an equation of a linear f(x) = ax + b relationship given: two points, point-slope form the slope and one point on the y - y1 = a(x - x1) line, or the slope and y- standard form intercept. Ax + By = C  Interpret situations compound inequality mathematically and write a < x < b appropriate algebraic radical expression expressions to represent them.  Solve, graph and interpret single-variable equations/inequalities on a number line and two-variable equations/inequalities using the coordinate plane.  Solve one-step, two-step, variables on both sides, distributive property, square, square root, cube, cube roots and formula (isolate one variable of the formula) equations and inequalities.

Problem Solving Strategies  guess and test  make a table/chart/  graph  make a diagram/picture  make an organized list  work backwards  work a simpler problem  extraneous information Unit Title: Algebra Materials Suggestions:

NCDPI Resources: http://www.ncpublicschools.org/curriculum/mathematics/middlegrades/grade08/ http://mathlearnnc.sharpschool.com/cms/One.aspx?portalId=4507283&pageId=5149151 National Library of Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html NCTM Illuminations http://illuminations.nctm.org/ Lesson Plan sites and Activities: http://www.lessonplanspage.com/Math.htm http://www.ilovemath.org Math Graphic Organizers http://www.enchantedlearning.com/graphicorganizers/math/

Problem Solving/Problem Websites http://library.thinkquest.org/25459/learning/problem/ http://www.geom.uiuc.edu/~lori/mathed/problems/problist.html http://www.rhlschool.com/math.htm http://nces.ed.gov/nationsreportcard/itmrlsx/search.aspx

AVID Library/Mathematics Write Path Books I and II