Algebra 1 Seamless Curriculum Guide

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Mabel Robinson
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1 QUALITY STANDARD #1: REAL NUMBERS AND THEIR PROPERTIES 1.1 The student will understand the properties of real numbers. o Identify the subsets of real numbers o Addition- commutative, associative, identity, inverse o Multiplication - commutative, associative, identity, property of zero, inverse o Distributive Property o Identify and apply properties 1.2 The student will understand the basic laws of exponents. o a n X a m = a n+m o a n / a m = a n-m o (a n ) m = a nm o a 0 = 1, for a not equal to zero o a 1 = a o Perform operations with scientific notation o Perform basic operations with exponents 1.3 The student will understand how to simplify and evaluate expressions. o Identify and perform operations on integers and rational numbers o Substitute in for a variable and evaluate the expressions o Write expressions in simplified form o Combine like terms to simplify an expression o Express radicals in simplified form o Simplify numerical absolute values o Order of operations (PEMDAS) o Write a variable expression given a verbal or written phrase and vice versa Vocabulary: commutative, associative, distributive, inverse, identity, like terms, variable, numerical expression, algebraic expression, PEMDAS, radical, exponent, coefficient, evaluate, natural number, whole number, integer, rational number, irrational number, real number, equation, power, base, square root, term Unit 1 Suggested Timeline: 25 days 1

2 QUALITY STANDARD #2: SOLVING EQUATIONS AND INEQUALITIES 2.1 The student will understand how to solve equations. o 1- step equations o 2- step equations o Multi-step equations o Equations with variables on both sides o Solve equation for a given variable o Understand there will be a unique solution o Write and solve equations from verbal or written directions 2.2 The student will understand how to solve inequalities. o Know the properties of greater than and less than o 1- step inequalities o 2- step inequalities o Multi-step inequalities o Graph solutions on a number line o Inequality rules for multiplying and dividing by a negative number o Recognize the similarities and differences between solving equations and inequalities o Write and solve inequalities from verbal or written directions 2.3 The student will understand how to evaluate formulas. o Be able to evaluate a multi-variable expression o Select, manipulate, and use an appropriate formula for problem solving o Solve formulas for a given variable o Write and solve an equation based on a real life model (ratio, proportion, percent, integers, distance, mixture, and work problems) Vocabulary: inequality, formula, <, >, number line, reciprocal, solution, simplest form, addition property of equality, multiplication property of equality, solution set Unit 2 Suggested Timeline: 20 days 2

3 QUALITY STANDARD #3: LINEAR EQUATIONS AND INEQUALITIES 3.1 The student will understand how to work in the coordinate plane. o Plot points o Identify coordinates o Correctly label points o Identify the axes and quadrants, label appropriately 3.2 The student will understand how to graph linear equations and inequalities o Find slope as rise over run o Find slope given 2 points o Find the x- and y-intercept o Find slope looking at a graph of a line o Identify positive, negative, zero, and undefined slope o Understand the relationship of parallel and perpendicular lines and their slopes o Graph horizontal and vertical lines o Graph a line given the y-intercept and slope o Graph a line using a table of values o Graph a line using the intercept-intercept method o Graph a line using the point-slope method o From observation identify the slope and y-intercept given a linear graph o Discuss slope as a rate of change o Differentiate when a solid or dotted line is needed for an inequality o Shading on a linear inequality 3.3 The student will understand how to find and write the equation of a line. o Standard form of a linear equation o Slope intercept form o Point slope form o Given a graph of a line o Given the slope and y-intercept o Given the slope and a point o Given 2 points 3

4 Vocabulary: ordered pair, x-axis, y-axis, quadrant, x-intercept, y-intercept, slope, rate of change, table of values, horizontal line, vertical line, standard form, slope intercept form, point slope form, perpendicular, parallel, coordinate plane, origin, rise, run, undefined slope, zero slope Unit 3 Suggested Timeline: 30 days QUALITY STANDARD #4: Polynomials 4.1 The student will understand polynomials and perform operations with them. o Find the degree of a polynomial o Classify polynomials by their terms and degree o Add and subtract polynomials o Multiply polynomials using the distributive property and the FOIL process o Arrange a polynomial in ascending or descending order o Factoring polynomials Factor out common factor Difference of two squares Perfect trinomial squares Factor trinomials that have 1 as a leading coefficient Factor trinomials with a leading coefficient other than The student will understand how to solve quadratic equations. o Solve by factoring and using zero product property o Solve by the quadratic formula o Represent real world problems in quadratic form and solve Vocabulary: monomial, binomial, trinomial, difference of squares, FOIL, linear, constant, quadratic, cubic, quartic, polynomial, perfect trinomial square, degree, factor, square root, leading coefficient, linear term, quadratic equation, ascending/descending, zero, root Unit 4 Suggested Timeline: 40 days 4

5 QUALITY STANDARD #5: SYSTEMS OF EQUATIONS AND INEQUALITIES 5.1 The student will understand different methods of solving linear systems of equations. o Solve by graphing o Solve by substitution o Solve by elimination o Recognize when there will be zero, one, or infinite solutions 5.2 The students will understand how to solve systems of linear inequalities. o Solve by graphing o Use dotted and solid lines correctly o Use shading appropriately to identify solution set Vocabulary: System of equations, coinciding lines, empty set, null set, infinite, elimination Unit 5 Suggested Timeline: 15 days QUALITY STANDARD #6: Functions 6.1 The student will understand the language and notation of function. o Definition of relation o Definition of function o Domain, x value, input o Range, y value, output o Evaluate a function given a rule and a replacement set Vocabulary: relation, function, domain, range, f(x), input, output Unit 6 Suggested Timeline: 10 days 5

6 Nice to Know: o Elementary Probability and Statistics o Graphing quadratics o Line of best fit o Absolute value equations o Writing equations of parallel and perpendicular lines o Operations with radicals o Systems of inequalities o Differentiate between a relation and a function o Know that y is equivalent to f(x) when graphing o Identify a function using a table of values o Vertical line test o System of equations/inequalities Consistent Inconsistent Dependent Feasibility region 6

Algebra I Unit Report Summary

Algebra I Unit Report Summary No. Objective Code NCTM Standards Objective Title Real Numbers and Variables Unit - ( Ascend Default unit) 1. A01_01_01 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02