HTS Math Curriculum Map

Curriculum Map for 8th Grade Algebra at HTS

	Topic & Content	Skills	Assessment
September	Language of Algebra Variables and Constants, Grouping and Operation Symbols, Expressions and Equations, Bases and Exponents ********** Properties of Real Numbers Commutative, Associative & Distributive Properties Consecutive Integers Reciprocals	Translating words into symbols, expressions and equations Simplifying expressions following the proper order of operations Converting story problems into equations using variables and appropriate symbols ********** Using the Number Line to demonstrate the rules for adding and subtracting integers	Create story problems and then build expressions and equations to solve them. Challenge fellow students with your problems, then verify how they solved yours. Demonstrate proficiency on chapter test ********** Represent properties by using concrete models and algebra tiles
October	Solving Equations & Problems Using One Variable Inverse Operations Equations with variables on both sides Story problems involving cost, value and income	Using inverse operations to solve one & two step equations Combining like terms within an expression or equation Set up charts to help organize information to solve problems. Use substitution to represent additional variables in terms of the first variable.	Convert story problems into equations involving the use of one variables. Represent any other variables in terms of the first variable Substitute these variables into a "Master Equation". Solve these equations. Chapter tests on all related skills
November	Linear Equations Equations in two variables Slope and rate of change Constant - y-intercept Representing relationships between two sets of numeric data with a symbolic rule (function) Representing same relationship using a plot on the coordinate plane ********** Solving Systems of Equations Using Two Variables Systems of linear equations	Create equations in two variables Given numeric data, plot these points on a coordinate plane. Find the slope and y-intercept of a line Given a pair of points, find the equation of the line that encompasses these points Convert the linear equation from slope-intercept form to standard form. ********** Solving systems of equations by graphing, substitution and linear combination (AKA elimination)	Plot points on the coordinate plane to represent a linear relationship. ********** Given 4 different systems of equations, determine which method of solving the sytem is most appropriate. Solve those systems using four different methods: graphing by hand on graph paper including a clearly labelled set of axes and scale, graphing on a graphing calculator, combining the two linear equations to eliminate one of the variables first, substituting one variable with an expression involving the second variable, then solving as a one-variable equation. Given story problems involving two variables, represent these using a system of equations. Chapter tests on all related skills
December	Polynomials and Factoring Exponents Polynomials Story problems involving polynomial expressions including rate-time-distance, area of rectangles & problems without solutions. ********** Factoring polynomial expressions Using patterns to assist in factoring Solving equations using factoring	Adding and subtracting polynomials Multiplying and dividing polynomials Raising polynomial expressions to powers Transforming formulas & Solving for one variable in terms of another ******** Factoring integers and expressions Factoring using GCF Factoring by grouping Factoring by Difference of Squares Factoring patterns for ax^2 + bx + c** Factoring using several methods on the same polynomial expression Solving equations by factoring Using factoring to solve problems.	Build polynomial expressions by multiplying monomials and binomials. Demonstrate the F.O.I.L. method using the standard multiplication algorithm. ********** Challenge your partner by multiplying binomials to create a trinomial or other polynomial and then swap polynomials for factoring them back down into simplest factored form. Convert story problems into charts and master equations, then solve these equations by factoring. Chapter tests on all related skills
January	Rational Expressions Fractions and rational expressions Restrictions on variables in rational expressions Common denominators Polynomial long division ********** Applications of Rational Expressions Ratio and proportion Equations with fractional coefficients Story problems involving percent, wet and dry mixtures, and rate of work Negative exponents & scientific notation	Simplifying, multiplying and dividing rational expressions Adding and subtracting rational expressions with like and unlike denominators Long division of polynomials Synthetic division of polynomials ********** Solving equations involving rational expressions Creating equations involving ratios and proportions, and solving them Simplifying problems with negative exponents into standard form Converting numbers from standard form to scientific notation to expanded notation and back again	Chapter tests on all related skills Demonstrate how synthetic division mirrors the important steps in polynomial long division ********** Convert story problems involving mixtures and rate of work into equations with rational expressions, then solve them Chapter tests on all related skills
February	Functions and Relations Functions defined by tables, graphs and equations Graphing of linear functions Quadratic functions Direct and inverse variation	Determining whether or not a given relation is a function Graphing quadratic functions, listing the axis of symmetry, the vertex, the roots and the y-intercept	Use the vertical line test to determine if the plot of a given relation defines a function. If so, what kind of function? Show the effects of a change in each of the coefficients or constants in this equation (*ax^2 + bx + c*) on the graph of the function. Chapter tests on all related skills
March	Inequalties in One Variable Order of real numbers One variable inequalities ******** Inequalities in Two Variables Two variable inequalities ******** Absolute Value Absolute Value inequalities in one and two variables	Solving inequalities and graphing the solution on a number line Solving conjunctions and disjunctions of combined inequalities ******** Solving two variable inequalities and graphing their solution on the coordinate plane Graphing systems of inequalities on the coordinate plane ******** Solving equations and inequalities involving absolute value and graphing their solutions appropriately	Given number lines and graphs of coordinate planes, write up problems to match each situations. Match graphs and number lines to given inequalities Chapter tests on all related skills
April	Rational and Irrational Numbers Properties of rational numbers Perfect squares Simplified form of irrational numbers Pythagorean Theorem	Converting repeating and terminating decimals into rational numbers Simplifying rational square roots and irrational square roots Simplifying square roots of variable expressions Multiplying and dividing radicals Adding and subtracting radicals Multiplication of binomials containing radicals Solving simple radical equations	Create right triangles representing Pythagorean triples on graph paper Chapter test on all related skills
May	Quadratic Functions Quadratic equations with perfect squares Completing the square Quadratic formula Discriminant and graphing ********** Tying It All Together	Solving quadratic equations by the following methods: perfect squares completing the square quadratic formula graphing on the coordinate plane Solving and graphing direct and inverse variation problems involving squares (optional - do not always have time to cover these) Solving problems involving joint and combined variation (optional - do not always have time to cover these) ********** Analyzing equations and determining best method for solving them. Using multiple methods to solve same equations	Given 4 quadratic equations, determine the best method for solving them; then solve them Retrace derivation of the quadratic formula Given a quadratic equation in the form y = ax^2 + bx + c, determine how many solutions there will be, and if they are real solutions ********** Given a group of equations of different degrees, determining the best method for solving each of them. Use multiple methods to solve the same equation or system of equations

Additional Topics Covered	Probability & Discrete Math Zip code, counting principle, systematic lists, tree diagrams ********** Line of best fit Geometry Integrations Coordinate graphing of parallel and perpendicular lines	Solving puzzle problems from the real world Deciphering bar codes ********** Finding line of best fit using graphing calculator	Create spiral and rectangular spiral representing golden ratio on graph paper Decipher the bar code in the US zip code and the UPC ********** Finding line of best fit with real world data - Slinky problem

Gaps in Current Curriculum	Matrices	Creating a matrix given sets of tabular data Use scalar multiplication to multiply a matrix by a constant

Superfluous Topics	None (possible candidates are the review topics in the first two chapters of the book. However, to make sure all students are up to speed with necessary skills to start Algebra I)	.	.

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