Topic: 1. Real Numbers Days: 15 Know: Understand: Do: Absolute value Number Sets Vocabulary: integers rational numbers irrational numbers simplify evaluate There are laws for performing mathematical operations to ensure that the values obtained will be consistent. Numbers can be used to count, label, order, identify, measure, and describe things and experiences. A1.1.1.3.1 -- Essential Simplify/evaluate expressions involving properties/ laws of exponents, roots, and/or absolute values to solve problems. Note: Exponents should be integers from 10 to 10. A1.1.1.4.1 -- Important Use estimation to solve problems. Concepts: Order of Operations -perfect squares -basic exponents Comparing and Ordering -irrational and rational numbers Combining Like Terms Page 1 of 2
Topic: 1. Real Numbers Days: 15 Which standards are students learning in this unit? A1.1.1.1.1 -- Essential Compare and/or order any real numbers. Note: Rational and irrational may be mixed. A1.1.1.3.1 -- Essential Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems. Note: Exponents should be integers from 10 to 10. A1.1.1.4.1 -- Important Use estimation to solve problems. Page 2 of 2
Topic: 2. Solving Linear Equations Days: 15 Know: Understand: Do: Distributive property Combining like terms Absolute value Vocabulary: like terms absolute value distributive property inverse operations let statement A variable represents an unknown that will change in different settings. A1.1.2.1.1 -- Essential Write, solve, and/or apply a linear equation (including problem situations). A1.1.2.1.2 -- Essential Use and/or identify an algebraic property to justify any step in an equationsolving process. Note: Linear equations only. A1.1.2.1.3 -- Essential Interpret solutions to problems in the context of the problem situation. Note: Linear equations only. A1.2.1.1.1 -- Essential Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically. Concepts: Solving Linear Equations Solving Word Problems Under the Word Problem Concept, teach representing patterns algebraically. Include absolute value Page 1 of 2
Topic: 2. Solving Linear Equations Days: 15 Which standards are students learning in this unit? A1.1.2.1.1 -- Essential Write, solve, and/or apply a linear equation (including problem situations). A1.1.2.1.2 -- Essential Use and/or identify an algebraic property to justify any step in an equationsolving process. Note: Linear equations only. A1.1.2.1.3 -- Essential Interpret solutions to problems in the context of the problem situation. Note: Linear equations only. A1.2.1.1.1 -- Essential Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically. Page 2 of 2
Topic: 3. Solving Inequalities Days: 15 Know: Understand: Do: Vocabulary: Page 1 of 2
Topic: 3. Solving Inequalities Days: 15 Which standards are students learning in this unit? A1.1.3.1.1 -- Essential Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities). A1.1.3.1.2 -- Essential Identify or graph the solution set to a linear inequality on a number line. A1.1.3.1.3 -- Essential Interpret solutions to problems in the context of the problem situation. Note: Limit to linear inequalities. Page 2 of 2
Topic: 4. Functions and their Graphs Days: 20 Know: Understand: Do: domain and range vertical line test Vocabulary: independent variable dependent variable function domain range origin axis Mathematical models simplify reality to enable useful solutions. Mathematical ideas can be represented numerically, graphically, or symbolically. A1.2.1.1.1 -- Essential Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically. A1.2.1.1.2 -- Essential Determine whether a relation is a function, given a set of points or a graph. A1.2.1.1.3 -- Essential Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table). A1.2.1.2.1 -- Essential Create, interpret, and/or use the equation, graph, or table of a linear function. A1.2.1.2.2 -- Essential Translate from one representation of a linear function to another (i.e., graph, table, and equation). Page 1 of 2
Topic: 4. Functions and their Graphs Days: 20 Which standards are students learning in this unit? A1.1.3.1.1 -- Essential Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities). A1.1.3.1.2 -- Essential Identify or graph the solution set to a linear inequality on a number line. A1.2.1.1.1 -- Essential Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically. A1.2.1.1.2 -- Essential Determine whether a relation is a function, given a set of points or a graph. A1.2.1.1.3 -- Essential Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table). A1.2.1.2.1 -- Essential Create, interpret, and/or use the equation, graph, or table of a linear function. A1.2.1.2.2 -- Essential Translate from one representation of a linear function to another (i.e., graph, table, and equation). Page 2 of 2
Topic: 5. Writing and Graphing Linear Relationships Days: 15 Know: Understand: Do: graph linear inequalities graph linear equations finding slope Vocabulary: slope slop-intercept form standard form point-slope form x-intercept y-intercept rate of change Mathematical models simplify reality to enable useful solutions. Mathematical ideas can be represented numerically, graphically or symbolically. Slope is a number that represents a rate of change and can be graphically represented. A1.2.1.1.1 -- Essential Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically. A1.2.1.2.1 -- Essential Create, interpret, and/or use the equation, graph, or table of a linear function. A1.2.1.2.2 -- Essential Translate from one representation of a linear function to another (i.e., graph, table, and equation). Concepts: A1.2.2.1.1 - Identify, describe, and/or use constant rates of change. A1.2.2.1.2 - Apply the concept of linear rate of change (slope) to solve problems. A1.2.2.1.3a - Write or identify a linear equation when given: the graph of the line. A1.2.2.1.3b - Write or identify a linear equation when given: two points on the line. A1.2.2.1.3c - Write or identify a linear equation when given: the slope and a point on the line. A1.2.2.1.4 - Determine the slope and/or yintercept represented by a linear equation or graph. A1.1.3.1.1 - Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities). A1.1.3.1.2 - Identify or graph the solution set to a linear inequality on a number line. Page 1 of 2
Topic: 5. Writing and Graphing Linear Relationships Days: 15 Which standards are students learning in this unit? A1.2.2.1.1 -- Essential Identify, describe, and/or use constant rates of change. A1.2.2.1.2 -- Essential Apply the concept of linear rate of change (slope) to solve problems. A1.2.2.1.3a -- Essential Write or identify a linear equation when given: the graph of the line. A1.2.2.1.3b -- Essential Write or identify a linear equation when given: two points on the line. A1.2.2.1.3c -- Essential Write or identify a linear equation when given: the slope and a point on the line. A1.2.2.1.4 -- Essential Determine the slope and/or yintercept represented by a linear equation or graph. A1.2.1.1.1 -- Essential Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically. A1.2.1.2.1 -- Essential Create, interpret, and/or use the equation, graph, or table of a linear function. A1.2.1.2.2 -- Essential Translate from one representation of a linear function to another (i.e., graph, table, and equation). A1.1.3.1.1 -- Essential Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities). A1.1.3.1.2 -- Essential Identify or graph the solution set to a linear inequality on a number line. Page 2 of 2
Topic: 6. Systems of Equations and Inequalities Days: 20 Know: Understand: Do: Substitution method Elimination method Interpret intersections in graphs Vocabulary: systems elimination How to solve for a common solution(s) between two equations or inequalities. A1.1.2.2.1 -- Essential Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination. Note: Limit systems to two linear equations. A1.1.2.2.2 -- Essential Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear equations. A1.1.3.2.1 -- Essential Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities. A1.1.3.2.2 -- Essential Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear inequalities. Graphing Substitution Elimination Page 1 of 2
Topic: 6. Systems of Equations and Inequalities Days: 20 Which standards are students learning in this unit? A1.1.2.2.1 -- Essential Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination. Note: Limit systems to two linear equations. A1.1.2.2.2 -- Essential Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear equations. A1.1.3.2.1 -- Essential Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities. A1.1.3.2.2 -- Essential Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear inequalities. Page 2 of 2
Topic: 7. Exponents and Radicals Days: 12 Know: Understand: Do: Vocabulary: multiplication property power of a power distributive property over multiplication and division (power of a product, power of a quotient) division property zero exponent negative exponents rational exponents There are laws for performing mathematical operations to ensure that the volues obtained will be consistent. A1.1.1.1.2 -- Essential Simplify square roots (e.g., 24 = 26). A1.1.1.3.1 -- Essential Simplify/evaluate expressions involving properties/ laws of exponents, roots, and/or absolute values to solve problems. Note: Exponents should be integers from 10 to 10. Page 1 of 2
Topic: 7. Exponents and Radicals Days: 12 Which standards are students learning in this unit? A1.1.1.1.2 -- Essential Simplify square roots (e.g., 24 = 26). A1.1.1.3.1 -- Essential Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems. Note: Exponents should be integers from 10 to 10. Page 2 of 2
Topic: 8. Polynomials Days: 20 Know: Understand: Do: Combining like terms Distributive property Operations of polynomials (add, subtract, multiply) Factoring Simplifying rational expressions Undefined values difference of squares Greatest common factors of polynomials Degree of a polynomial Vocabulary: undefined values monomial binomial trinomial polynomial There are multiple ways to write the same expression, and seeing the expression written in a different way might help a person think about the situation in a new way. How to add, subtract, and multiply polynomials. A1.1.1.5.1 -- Essential Add, subtract, and/or multiply polynomial expressions (express answers in simplest form). Note: Nothing larger than a binomial multiplied by a trinomial. A1.1.1.5.2 -- Essential Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials are limited to the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors. A1.1.1.5.3 -- Essential Simplify/reduce a rational algebraic expression. A1.1.1.2.1 -- Essential Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials. Concepts: Adding and Subtracting Multiplying Factoring LCM and GCF Factoring algebraic expressions where a is greater than 1 Solving quadratics Determining undefined values Page 1 of 2
Topic: 8. Polynomials Days: 20 Which standards are students learning in this unit? A1.1.1.5.1 -- Essential Add, subtract, and/or multiply polynomial expressions (express answers in simplest form). Note: Nothing larger than a binomial multiplied by a trinomial. A1.1.1.5.2 -- Essential Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials are limited to the form ax 2 +bx+c where a is equal to 1 after factoring out all monomial factors. A1.1.1.5.3 -- Essential Simplify/reduce a rational algebraic expression. A1.1.1.2.1 -- Essential Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials. Page 2 of 2
Topic: 9. Probablility and Statistics Days: 10 Know: Understand: Do: Constructing box and whisker plots Constructing stem and leaf plot Compound events Testing for outliers Vocabulary: outliers quartile interquartile range measure of central tendency dependent events independent events box and whisker plots stem and leaf plots favorable outcome scatter plot line of best fit How to choose the best form of graphical representation to display data effectively. Probability describes the likelihood of an event occurring in a population. A1.2.2.2.1 -- Essential Draw, identify, find, and/or write an equation for a line of best fit for a scatter plot. A1.2.3.1.1 -- Essential Calculate and/or interpret the range, quartiles, and interquartile range of data. A1.2.3.2.1 -- Essential Estimate or calculate to make predictions based on a circle, line, bar graph, measures of central tendency, or other representations. A1.2.3.2.2 -- Essential Analyze data, make predictions, and/or answer questions based on displayed data (boxandwhisker plots, stemandleaf plots, scatter plots, measures of central tendency, or other representations). A1.2.3.2.3 -- Essential Make predictions using the equations or graphs of bestfit lines of scatter plots. A1.2.3.3.1 -- Essential Find probabilities for compound events (e.g., find probability of red and blue, find probability of red or blue) and represent as a fraction, decimal, or percent. Graphical Representation of Data Measures of Central Tendencies Probability Page 1 of 2
Topic: 9. Probablility and Statistics Days: 10 Which standards are students learning in this unit? A1.2.2.2.1 -- Essential Draw, identify, find, and/or write an equation for a line of best fit for a scatter plot. A1.2.3.1.1 -- Essential Calculate and/or interpret the range, quartiles, and interquartile range of data. A1.2.3.2.1 -- Essential Estimate or calculate to make predictions based on a circle, line, bar graph, measures of central tendency, or other representations. A1.2.3.2.2 -- Essential Analyze data, make predictions, and/or answer questions based on displayed data (boxandwhisker plots, stemand leaf plots, scatter plots, measures of central tendency, or other representations). A1.2.3.2.3 -- Essential Make predictions using the equations or graphs of bestfit lines of scatter plots. A1.2.3.3.1 -- Essential Find probabilities for compound events (e.g., find probability of red and blue, find probability of red or blue) and represent as a fraction, decimal, or percent. Page 2 of 2
Topic: New Unit 10 Days: 10 Know: Understand: Do: Page 1 of 2
Topic: New Unit 10 Days: 10 Which standards are students learning in this unit? Page 2 of 2