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1 1 of 7 8/11/ :27 AM Units: Teacher: PacedAlgebraPartA, CORE Course: PacedAlgebraPartA Year: The Language of Algebra What is the difference between an algebraic expression and an algebraic equation? What does it mean to "evaluate " an expression? Writing Expressions and Translate words into algebraic expession. Translate words into algebraic algebraic expression variable numerical expression factor product quotient equation Write an algebraic expression for each verbal expression. Write a verbal expression for each algebraic expression. Write an equation for a given sentence. Write a sentence for a given Target specific for the lesson. Evaluating Expressions 9/30/2013 In what order should operations be done? Order of Operations Use the order of operations to evaluate expressions. Recognize and identify the properties of equality. order of operations properties evaluate Find the value of an expression using order of operations. Order of Operations Bingo For which operations does the Commutative Property hold? For which operations does the Associative Property hold? Commutative and Associative Properties use and identify commutative and associative properties to expressions. commutative property associative property whole numbers closure property counterexample Name the property shown by a statement. Simplify an expression and identify the properties used to do so. Communitive & Associative Properties use the Distributive Property to expressions? B - Use Distributive symbols, Property terminology, standard notation, rules, graphing and other types of representations to communicate observations, predictions, concepts, procedures, generalizations, ideas, and results. use the distributive property to evaluate & expressions. to recognize and combine like terms. distributive property term coefficient like terms equivalent expressions simpliest form Use the distributive property to expressions. Distributive Property How can you use a problem solving plan to solve a problem? How do everyday expressions translate into expressions? A - Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts. A Plan for Problem use a 4-step plan to solve problems. use and recognize formulas. formula problems by looking for a pattern or drawing a diagram. problems by making a table or working backwards. problems by using an equation or a formula. problems guess & check method or making a graph. 4-Step Problem Method What are the three criteria for a good sample? A - Design and Collecting conduct an experiment Data using random sampling. to collect data using good sampling criteria. organize data in frequency charts & tables. data experiments observational studies sampling population sample frequency table tally marks cumulative frequency table Determine whether a set of data is a good sample. Make a frequency table to organize data. Gathering and Displaying Data Which type of graph or chart is most appropriate for a given set of data? A - Design and conduct an experiment using random sampling. Displaying and Interpreting Data construct and interpret line graphs. construct and interpret histograms. construct and interpret stem-and-leaf plots. line graph histogram cumulative frequency histogram stem-and-leaf plot Make a line graph to organize data. Make a frequency table to organize data. Make a histogram to organize and display data. Make a stem-and-leaf plot to organize and display data.

2 2 of 7 8/11/ :27 AM Where are the positive and negative numbers located on the number line? A - and compare values of irrational and complex on a Number Line compare and order graph integers on a number line. determine the absolute values of number line negative number integer Venn diagram natural number graph coordinate absolute value Name the coordinates of a point on the number line. Graph a set of numbers on a number line. Evaluate expressions involving absolute value. Order integers from least to greatest. Target specific for the lesson. on the Number Line 10/31/2013 Where can the origin, x-axis, and y-axis be located on a coordinate plane? graph ordered pairs? Where are the quadrants located? B - Use symbols, terminology, standard notation, rules, graphing and other types of representations to communicate observations, predictions, concepts, procedures, generalizations, ideas, and results. The Coordinate Plane graph points on a coordinate identify the quadrant. identify origin, x-axis, and y-axis. coordinate system y-axis x-axis origin coordinate plane ordered pair x-coordinate y-coordinate quadrant Identify the x-axis, the y-axis and the origin on a coordinate Write the ordered pair that names a point on a graph. Graph points on a coordinate Name the quadrant in which a point is located. Points on a Coordinate Plane add positive and negative Adding add zero pair opposites additive inverse expessions with variables. Add integers with like signs. Add integers with opposite signs. Adding subtract positive and negative integers? subtract expressions with varibles. Subtract an integer by adding its additive inverse. Evaluate expressions involving subtraction of multiply positive and negative integers? multiplying apply the rules for determining signs of products. Multiply itwo integers with like signs. Multiply integers with different signs. Evaluate and expresssions involving multiplication of divide positive and negative integers? divide apply the rules for determining signs of quotients. Find the quotient of two integers with like signs. Find the quotient of two integers with different signs. Evaluate and expressions involving division of Addition and Subtraction compare and order rational M11.A Compare and/or order any real numbers (rational and irrational may be mixed). Rational Numbers to rational number compare and inequality order rational cross products unit cost recognize & use inequality symbols. use cross products to compare fractions. use unit cost to compare prices. Express a fraction as a decimal. Use inequality symbols to compare rational Order rational numbers from least to greatest. Use Unit Cost to compare and determine the best buy. Target specific for the lesson. Converting Between Fractions and Decimals Comparing and Ordering Rational Numbers 11/30/2013

3 3 of 7 8/11/ :27 AM add and subtract rational M11.A Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, Adding and add & subtract rational find least common denominator. Add and subtract rational numbers with like signs. Add and subtract rational numbers with unlike signs. Adding & Rationals find mean, median, mode and range for a set of data? M11.E Use measures of central tendency to describe a set of data. (Reference: A, A) Mean, Median, Mode, and Range find measure of central mean, tendency median, mean mode, and median range of a set mode of data. measure of variation range univariate bivariate categorical measurement Find the mean of a set of data. Find the median of a set of data. Find the mode of a set of data. Find the range of a set of data. Determining Measures of Central Tendency & Dispersion test a repalcement set to determine which elements are soultions? determine whether a statement open sentences given number replacement set is a solution of an solving solution pick solutions from a replacement set. Find the solution of an equation from a replacement set. Use order of operations to find the solution of an open ended sentence containing an equal sign. Soultion Set solve one-step equations using addition and subtraction? Addition and Subtraction equivalent equations by equations using addition and subtraction properties. Use the addition property of equality to solve a one step Use the subtraction property of equality to solve a one step One Step Addition/Subtraction How does the presence of an absolute value in an equation change the way it is solved? Involving Absolute Value solve equations involving absolute value. empty set equations involving absolute value. Recognize absolute value equations with no solution (empty set). Absolute Value Multiplication and Division What are the rules and methods of multiplying rational Multiply rational numbers multiplicative property of -1 Multiply rational numbers with like signs. Multiply rational numbers with different signs. Simplify expressions involving multiplication of rational word problems involving multiplication of rational Target specific for the lesson. Multiplyiong 12/31/2013 What is an event, M11.E outcome, and sample Determine the number space? of permutations and/or How is the combinations or apply Fundamental the fundamental Counting Principle counting principle. used to determine (Formula provided on the number of the reference sheet). outcomes for a given event? M11.E Use probability to predict outcomes. Counting Outcomes Use tree diagrams and the Fundamental Counting Principle to count outcomes. tree diagram outcomes sample space event Fundamental Counting Principle permutation combination Make a tree diagram to show the possible outcomes of an experiment. Use the Fundamental Counting Principal to determine the number of outcomes. Counting Outcomes What are the rules and methods of dividing rational Divide rational multiplicative inverse reciprocal division property of equality multiplication property of equality Divide rational numbers with like signs. Divide rational numbers with different signs. Simplify expressions involving division of rational word problems involving division of rational

4 4 of 7 8/11/ :27 AM Multiplication and Division, part 2 solve one-step equations using multiplication and/or division? Multiplication and Division multiplication and division equations by properties of equality. consecutive integers Use the Division Property of Equality to solve one step Use the Multiplication Property of Equality to solve one step Target specific for the lesson. One Step Multiplication/ Division 1/31/2014 determine the order in which operations should be used to solve a multi-step equation? Multi-Step equations involving more than one operation. identity multi-step equations involving consecutive Multi-step How does solving multi-step equations differ when there are variables on both sides? Variables on Both Sides equations with variables on both sides. equations with variable on both sides. equations by combining like terms. with Variables on both sides. How does solving multi-step equations differ when there are grouping symbols? Grouping Symbols equations with grouping symbols. (Parentheses, brackets & fraction bars) equations containing grouping symbols. and recognize equations with no solution. and recognize equations with all real numbers as a solution (Identity). with Grouping Symbols Proportional Reasoning and Probability What's the difference between a ratio and a proportion? solve a proportion? M11.A Apply ratio and/or proportion in problem-solving situations. (Reference: A, P) Proportions proportions using cross products. ratio proportion rate unit rate dimensional analysis Use cross products to solve simple proportions. proportions by cross multiplying. Target specific for the lesson. Proportions 2/28/2014 How can solving proportions help to solve percent problems? M11.A The Percent problems using Proportion operations with rational numbers including rates and percents (single and multi-step and multiple procedure operations) (e.g., distance, work and mixture problems, etc.). problems by percent proportion and cross products. percent percentage base percent propportion circle graph Express a fraction or ratio as a percent. Use the percent proportion to find the base, percent, or percentage Construct and interpret a circle graph. Using the Percent proportions What does P = RB represent and how is it used to solve percent problems? M11.A The Percent problems using operations with rational numbers including rates and percents (single and multi-step and multiple procedure operations) (e.g., distance, work and mixture problems, etc.). problems by percent percent equation rate simple interest mixture problem a proportion percent Use the simple interest formula (I = prt) to solve problems involving interest. mixture problems. Using the Percent Equation. How does percent of change help us find percent of increase or decrease? M11.A Percent of problems using Change operations with rational numbers including rates and percents (single and multi-step and multiple problems involving percent of increase or decrease. percent of increase percent of decrease sales tax discount Find the percent of increase. Find the percent of decrease. problems involving sales tax. Determining Percent Increase & Decrease

5 5 of 7 8/11/ :27 AM How does probability differ from odds? procedure operations) (e.g., distance, work and mixture problems, etc.). M11.E Find, convert, and/or compare the probability and/or odds of a simple event. Probability and Odds Find the probability and odds of a simple event. probability random theoretical probability experimental probability odds complement problems involving discount. Find simple probability. Find odds in favor or odds against a given outcome. Finding Probability and Odds How do mutually exclusive and inclusive events differ? M11.E Find, Compound convert, and/or Events compare the probability and/or odds of a simple event. Find the probability of mutually exclusive and inclusive events. compound events independent events mutually exclusive inclusive events Find the probability of compound events. Find the probability of independent events. Determine the difference between mutually exclusive and inclusive events. Finding Probability of Compound Events Functions and Graphs What is the domain and the range of a relation? M11.D Analyze and/or use patterns or relations. (Reference: Q; A; ) Relations Show relations as sets of x-coordinate y-coordinate relation ordered pairs, domain as tables, and range as graphs. State the domain of a relation. State the range of a relation. Express a relation as a set of ordered pairs. Express a relation in the form of a table. Express a relation as a graph. Target specific for the lesson. Domain & Range of a Relation 3/31/2014 determine if an ordered pair is a solution of a given equation? M11.D Analyze and/or use patterns or relations. (Reference: Q; A; ) as Relations equations for a given domain. solution set equation in two variables Determine whether a given ordered pair is a solution to a given an equation for a given domain. Determining if an Ordered Pair is a Solution of an Equation. an equation for a given range. How can you determine if an equation is? M11.D Identify or graph functions, equations or inequalities on a coordinate Linear Relations Graph relations by setting up a table of ordered pairs and graphing on the coordinate equation Determine whether an equation is by looking at its graph. Determine whether an equation is by looking at the Graph equations by selecting your own domain values. Linear determine if a realation is a function? M11.D Identify or graph functions, equations or inequalities on a coordinate Functions Determine whether a given relation is a function function rule or the vertical line test. function function zero vertical line test functional notation functional value Determine whether a relation is a function the function rule. Use the vertical line test to determine whether a relation is a function. Write equations in functional notation. Functions Find f(x) for a given value of x. Linear How does slope M11.D Compute relate to rise (change and/or use the slope in y) and run (change of a line. (Reference: in x)? J, L) How is the slope formula used when you are given two ordered pairs? Slope Find the slope slope of a line rate of change given the coordinates of two points on the line. Calculate slope using rise divided by run. Calculate slope slope formula (change in y divided by change in x) Determine if a graph has positive or negative slope. Determine if a graph has zero slope (horizontal). Target specific for the lesson. Finding Slope 4/30/2014 Determine if a graph has undefined slope (vertical).

6 6 of 7 8/11/ :27 AM What is the Point-Slope form of a equation? M11.D Given the graph of the line, 2 points on the line or the slope and a point on a line, write or identify the equation in pointslope, standard and/or slope-intercept form. Writing in Point-Slope Form Write a equation in Point-Slope Form given the coordinates of a point on the line and the slope of the line. point-slope form Write a equation in point-slope form. Write the point-slope form of an equation given two ordered pairs. Writing Linear in Point-Slope Form What if the Slope-intercept form of a equation? M11.D Given the graph of the line, 2 points on the line or the slope and a point on a line, write or identify the equation in pointslope, standard and/or slope-intercept form. Writing in Slope-Intercept Form Write a equation in Slope- Intercept Form given the slope and y-intercept of the line. y-intercept x-intercept slope-intercept form Write a equation in slope-intercept form. Write the equation of a line in slope-intercept form, given two ordered pairs. Writing Linear in Slope-Intercept Form How does a scatter plot differ when there is a positive slope as opposed to a negative slope? What does it mean if there is no obvious pattern or relationship on a scatter plot? M11.E Draw, find, and/or write an equation for a line of best fit for a scatter plot. Scatter Plots Graph and interpret points on Scatter Plots. scatter plot Determine whether a scatteplot has a positve, negative or no relationship. Make a scatterplot to represent a set of data. Analyzing Scatter Plots graph a equation when given the x and y-intercepts? M11.D Interpret and/or use, quadratic and/or exponential functions and their equations, graphs or tables. (Reference: K, Q,) Linear Graph equations by X and Y- intercepts or the slope and y-intercept. Determine the x-intercept of an equation, and graph it.. Determine the y-intercept of an equation, and graph it. Determine the slope and y-intercept of an equation, and graph it. Using X and Y-Intercepts to Grapg Linear How is slope used to determine if lines are parallel or perpendicular? M11.C Relate slope to perpendicularity and/or parallelism (limit to algebraic expressions; slope formula provided on the reference sheet). Parallel and Perpendicular Lines Write an equation of a line that is parallel to the graph of a given equation and that passes through a given point. Write an equation of a line that is perpendicular to the graph of a given equation and that passes through a given point. parallel lines perpendicular lines Determine whether two lines have the same slope and are thus parallel. Determine whether two lines have opposite reciprocal slopes and are thus perpendicular. Write the equation of line through a given point and either parallel or perpendicular to a given line. Using Slopes of Parallel & Perpendicular Lines Powers and Roots write expressions using exponents? Powers and Exponents Write expressions using Write powers as a multiplication expression. perfect squares exponent base powers Write expressions using Evaluate expressions involving Target specific for the lesson. Exponent Expressions 5/31/2014 What is done with exponents when multiplying like bases? What is done with exponents when dividing like bases? and Powers Use exponent rules to multiply and divide powers. Use the Product of Powers rule to expressions. Use the Quotient of Powers rule to expressions. Evaluate expressions containing zero Using Exponent Rules Waht are the rules for eliminating negative exponents in expressions? Negative Exponents Simplify expressions containing negative Simplify expressions containing negative Write expressions using only positive exponents, and evaluate. Simplifying Expression With Negative Exponents

7 7 of 7 8/11/ :27 AM M11.A express very large or Express numbers very small numbers and/or using scientific expressions using notation? scientific notation (including numbers less than 1). Scientific Notation Express numbers in Scientific Notation. Multiply and Divide numbers expressed in Scientific Notation. scientific notation Express number s in Scientific Notation. Convert numbers written in Scientific Notation into standard form. Multiply two numbers written in Scientific Notation. Divide two numbers written in Scientific Notation. Expressing Numbers in Scientific Notation find the square root of a perfect square? Square Roots Simplify radicals by product and quotient properties of square roots. square root radical sign radical expression prime number composite number prime factorization Find the square root of perfect squares wriiten as whole Find the square root of perfect squares wriiten as fractions or decimals. Simplifying Square roots of Perfect Squares. estimate the square root of a number that is not a perfect square? M11.A Find the square root of an integer to the nearest tenth using either a calculator or estimation. Estimating Square Roots Estimate square roots to nearest whole number. irrational numbers Estimate square roots to the nearest whole number. Estimating Square Roots find the missing side of a right triangle when given two of the sides? M11.C problems involving right triangles using the Pythagorean Theorem. (Reference: B) M11.C Find distinguish between the measure of a side the legs and the of a right triangle using hypotenuse of a right the Pythagorean triangle? Theorem (Pythagorean Theorem included on the reference sheet). The Pythagorean Theorem Use the Pythagorean Theorem to solve a variety of problems involving right triangles. legs hypotenuse Pythagorean Theorem converse Identify the legs and the hypotenuse of a right triangle. Find the length of the hypotenuse of a right triangle, Pythagorean Theorem. Find the length of one leg of a right triangle, Pythagorean Theorem. Use Pythagorean Theorem to determine if three given lengths could be the sides of a right triangle. Using Pythagorean Theorem

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