Middle School Math Course 3. Correlation of the ALEKS course Middle School Math Course 3 to the Common Core State Standards for Grade 8 (2010)

Transcription

1 Middle School Math Course 3 Correlation of the ALEKS course Middle School Math Course 3 to the Common Core State Standards for Grade 8 (2010) 8.NS: The Number System 8.NS.A.1: 8.NS.A.2: = ALEKS course topic that addresses the standard Know that there are numbers that are not rational, and approximate them by rational numbers. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Converting a fraction to a terminating decimal: Basic Converting a fraction to a terminating decimal: Advanced Converting a fraction to a repeating decimal: Basic Converting a fraction to a repeating decimal: Advanced Converting a mixed number to a terminating decimal: Basic Converting a mixed number to a terminating decimal: Advanced Identifying rational decimal numbers Converting a repeating decimal to a fraction Identifying true statements about rational and irrational numbers Identifying numbers as rational or irrational Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π 2 ). For example, by truncating the decimal expansion of 2, show that 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Estimating a square root Using numerical methods to approximate a square root to the nearest tenth Using numerical methods to approximate a square root to the nearest hundredth Approximating the location of irrational numbers on a number line Ordering real numbers 8.EE: Expressions & Equations = ALEKS course topic that addresses the standard Work with radicals and integer exponents. 8.EE.A.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, = 3-3 = 1/3 3 = 1/27. Introduction to the product rule with positive exponents: Whole number base ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/15

2 Introduction to the power of a power rule with positive exponents: Whole number base Introduction to the quotient rule with positive exponents: Whole number base Power of 10: Negative exponent Evaluating an expression with a negative exponent: Whole number base Evaluating an expression with a negative exponent: Positive fraction base Evaluating an expression with a negative exponent: Negative integer base Introduction to the product rule with negative exponents: Whole number base Introduction to the quotient rule with negative exponents: Whole number base Introduction to the power of a power rule with negative exponents: Whole number base 8.EE.A.2: 8.EE.A.3: 8.EE.A.4: Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. Square root of a perfect square Identifying true statements about rational and irrational numbers Solving an equation of the form x 2 = a using the square root property Cube root of an integer Solving an equation of the form x 3 = a using integers Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times10 8 and the population of the world as 7 times 10 9, and determine that the world population is more than 20 times larger. Introduction to scientific notation with positive exponents Scientific notation with positive exponent Introduction to scientific notation with negative exponents Scientific notation with negative exponent Converting between scientific notation and standard form in a real-world situation Estimating numbers using scientific notation Finding the scale factor between numbers given in scientific notation in a real-world situation Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Choosing metric units and converting to the base unit in scientific notation Expressing calculator notation as scientific notation Multiplying numbers written in scientific notation: Basic Multiplying numbers written in scientific notation: Advanced Multiplying numbers written in decimal form or scientific notation in a real-world situation Dividing numbers written in scientific notation: Basic Dividing numbers written in scientific notation: Advanced Adding or subtracting numbers written in scientific notation: Same exponents, basic Adding or subtracting numbers written in scientific notation: Same exponents, advanced Adding or subtracting numbers written in scientific notation: Different exponents Estimating the sum or difference of two numbers written in scientific notation Understand the connections between proportional relationships, lines, and linear equations. ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/15

3 8.EE.B.5: 8.EE.B.6: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Making a table and plotting points given a unit rate Comparing proportional relationships given in different forms Finding slope given the graph of a line in quadrant 1 that models a real-world situation Interpreting direct variation from a graph Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Using right triangles to find the slope of a line Writing an equation of a line given the y-intercept and another point Analyze and solve linear equations and pairs of simultaneous linear equations. 8.EE.C.7: 8.EE.C.7.A: 8.EE.C.7.B: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solving equations with zero, one, or infinitely many solutions Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Additive property of equality with integers Multiplicative property of equality with integers Additive property of equality with fractions and mixed numbers Multiplicative property of equality with fractions Multiplicative property of equality with signed fractions Additive property of equality with decimals Multiplicative property of equality with decimals Using two steps to solve an equation with whole numbers Additive property of equality with a negative coefficient Solving a two-step equation with integers Introduction to solving an equation with parentheses Solving a multi-step equation given in fractional form Solving a two-step equation with signed decimals Introduction to solving an equation with variables on the same side Solving a linear equation with several occurrences of the variable: Variables on the same side Introduction to solving a linear equation with a variable on each side Solving a linear equation with several occurrences of the variable: Variables on the same side and distribution and distribution and two distributions Solving a two-step equation with signed fractions ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 3/15

4 8.EE.C.8: 8.EE.C.8.A: 8.EE.C.8.B: 8.EE.C.8.C: and fractional coefficients Solving a proportion of the form (x+a)/b = c/d Solving a proportion of the form a/(x+b) = c/x Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Identifying solutions to a system of linear equations Graphically solving a system of linear equations Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. Graphically solving a system of linear equations Introduction to using substitution to solve a linear equation Solving a system of linear equations of the form y = mx + b Solving a system of linear equations using substitution Solving a system of linear equations using elimination with addition Solving a system of linear equations using elimination with multiplication and addition Solving systems of linear equations with 0, 1, or infinitely many solutions Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Solving a word problem involving a sum and another basic relationship using a system of linear equations Solving a word problem using a system of linear equations of the form Ax + By = C Solving a word problem using a system of linear equations of the form y = mx + b Solving a value mixture problem using a system of linear equations 8.F: Functions 8.F.A.1: = ALEKS course topic that addresses the standard Define, evaluate, and compare functions. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function tables with two-step rules Table for a linear equation Graphing a linear equation of the form y = mx Graphing a line given its equation in slope-intercept form: Integer slope Graphing a line given its equation in slope-intercept form: Fractional slope Identifying functions from relations Vertical line test Table for a linear function Graphing a function of the form f(x) = ax + b: Integer slope Graphing a function of the form f(x) = ax + b: Fractional slope ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 4/15

5 8.F.A.2: 8.F.A.3: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. Comparing proportional relationships given in different forms Comparing properties of linear functions given in different forms Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s 2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4), and (3,9), which are not on a straight line. Identifying linear equations: Basic Use functions to model relationships between quantities. 8.F.B.4: 8.F.B.5: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Writing an equation to represent a proportional relationship Writing a function rule given a table of ordered pairs: One-step rules Writing a function rule given a table of ordered pairs: Two-step rules Finding slope given the graph of a line on a grid Finding slope given two points on the line Finding the slope of horizontal and vertical lines Writing an equation of a line given its slope and y-intercept Writing an equation in slope-intercept form given the slope and a point Writing an equation of a line given the y-intercept and another point Writing the equation of the line through two given points Writing and evaluating a function that models a real-world situation: Basic Writing and evaluating a function that models a real-world situation: Advanced Graphing ordered pairs and writing an equation from a table of values in context Writing an equation and drawing its graph to model a real-world situation: Basic Writing an equation and drawing its graph to model a real-world situation: Advanced Finding the initial amount and rate of change given a table for a linear function Finding the initial amount and rate of change given a graph of a linear function Interpreting the parameters of a linear function that models a real-world situation Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Finding where a function is increasing, decreasing, or constant given the graph Choosing a graph to fit a narrative: Basic Choosing a graph to fit a narrative: Advanced 8.G: Geometry = ALEKS course topic that addresses the standard ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/15

6 Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.A.1: 8.G.A.1.A: 8.G.A.1.B: 8.G.A.1.C: 8.G.A.2: 8.G.A.3: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Properties of translated figures Properties of reflected figures Properties of rotated figures Angles are taken to angles of the same measure. Properties of translated figures Properties of reflected figures Properties of rotated figures Parallel lines are taken to parallel lines. Properties of translated figures Properties of reflected figures Properties of rotated figures Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Identifying congruent shapes on a grid Identifying transformations Determining if figures are related by a translation Determining if figures are related by a reflection Determining if figures are related by a rotation Determining if figures are congruent and related by a transformation Determining if figures are congruent and related by a sequence of transformations Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Translating a point and giving its coordinates: One step Translating a point and giving its coordinates: Two steps Translating a polygon Using a translated point to find coordinates of other translated points Reflecting a point across an axis Reflecting a point across both coordinate axes Reflecting a point across an axis and giving its coordinates Finding the coordinates of a point reflected across an axis Finding the coordinates of a point reflected across both axes Reflecting a polygon across the x-axis or y-axis Reflecting a polygon over a vertical or horizontal line Finding the coordinates of three points reflected over an axis Finding the coordinates of a point reflected across an axis and translated Rotating a point and giving its coordinates Rotating a figure about the origin Dilating a segment and giving the coordinates of its endpoints The effect of dilation on side length Determining if figures are related by a dilation The effect of dilation on area Dilating a figure ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 6/15

7 8.G.A.4: 8.G.A.5: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. Identifying similar or congruent shapes on a grid Determining if figures are similar and related by a sequence of transformations Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Finding angle measures given two parallel lines cut by a transversal Establishing facts about the angles created when parallel lines are cut by a transversal Finding an angle measure of a triangle given two angles Finding an angle measure for a triangle with an extended side Establishing facts about the interior angles of a triangle Establishing facts about the interior and exterior angles of a triangle Finding angle measures of a triangle given two angles of a similar triangle Finding angle measures and side ratios to determine if two triangles are similar Understand and apply the Pythagorean Theorem. 8.G.B.6: 8.G.B.7: 8.G.B.8: 8.G.C.9: Explain a proof of the Pythagorean Theorem and its converse. Demonstrating the converse of the Pythagorean Theorem Informal proof of the Pythagorean Theorem Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Introduction to the Pythagorean Theorem Pythagorean Theorem Word problem involving the Pythagorean Theorem Using the Pythagorean Theorem repeatedly Identifying side lengths that give right triangles Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Using the Pythagorean Theorem to find distance on a grid Distance between two points in the plane: Exact answers Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Volume of a cylinder Word problem involving the volume of a cylinder Word problem involving the rate of filling or emptying a cylinder Volume of a cone Volume of a cone: Exact answers in terms of pi Word problem involving the volume of a cone Volume of a sphere Word problem involving the volume of a sphere ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 7/15

8 8.SP: Statistics & Probability 8.SP.A.1: 8.SP.A.2: 8.SP.A.3: 8.SP.A.4: = ALEKS course topic that addresses the standard Investigate patterns of association in bivariate data. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Constructing a scatter plot Scatter plots and correlation Classifying linear and nonlinear relationships from scatter plots Identifying outliers and clustering in scatter plots Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Sketching the line of best fit Classifying linear and nonlinear relationships from scatter plots Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. Predictions from the line of best fit Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? Constructing a two-way frequency table: Basic Constructing a two-way frequency table: Advanced Making an inference using a two-way frequency table Calculating relative frequencies in a contingency table Standards for Mathematical Practices = ALEKS course topic that addresses the standard 1: Make sense of problems and persevere in solving them. Word problem with division of whole numbers and rounding Order of operations with integers and exponents Converting a fraction to a terminating decimal: Basic Converting a fraction to a terminating decimal: Advanced Converting a fraction to a repeating decimal: Basic Converting a fraction to a repeating decimal: Advanced ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 8/15

9 Converting a mixed number to a terminating decimal: Basic Converting a mixed number to a terminating decimal: Advanced Solving a fraction word problem using a linear equation of the form Ax = B Solving a decimal word problem using a linear equation of the form Ax + B = C Making a table and plotting points given a unit rate Comparing proportional relationships given in different forms Finding slope given the graph of a line in quadrant 1 that models a real-world situation Finding slope given the graph of a line on a grid Finding slope given two points on the line Finding the slope of horizontal and vertical lines Interpreting direct variation from a graph Writing an equation of a line given its slope and y-intercept Writing an equation in slope-intercept form given the slope and a point Writing an equation of a line given the y-intercept and another point Writing the equation of the line through two given points Writing and evaluating a function that models a real-world situation: Basic Writing and evaluating a function that models a real-world situation: Advanced Writing an equation and drawing its graph to model a real-world situation: Basic Writing an equation and drawing its graph to model a real-world situation: Advanced Finding the initial amount and rate of change given a table for a linear function Finding the initial amount and rate of change given a graph of a linear function Comparing properties of linear functions given in different forms Interpreting the parameters of a linear function that models a real-world situation Finding where a function is increasing, decreasing, or constant given the graph Identifying solutions to a system of linear equations Solving a word problem involving a sum and another basic relationship using a system of linear equations Solving a word problem using a system of linear equations of the form Ax + By = C Solving a word problem using a system of linear equations of the form y = mx + b Solving a value mixture problem using a system of linear equations Introduction to scientific notation with positive exponents Scientific notation with positive exponent Introduction to scientific notation with negative exponents Scientific notation with negative exponent Converting between scientific notation and standard form in a real-world situation Estimating numbers using scientific notation Finding the scale factor between numbers given in scientific notation in a real-world situation Estimating a square root Using numerical methods to approximate a square root to the nearest tenth Using numerical methods to approximate a square root to the nearest hundredth Ordering real numbers Converting a repeating decimal to a fraction Solving an equation of the form x 2 = a using the square root property Solving an equation of the form x 3 = a using integers Introduction to the Pythagorean Theorem Pythagorean Theorem Word problem involving the Pythagorean Theorem Using the Pythagorean Theorem repeatedly Using the Pythagorean Theorem to find distance on a grid Distance between two points in the plane: Exact answers ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 9/15

10 Solving equations involving vertical angles Finding angle measures given two parallel lines cut by a transversal Finding an angle measure of a triangle given two angles Finding angle measures of a triangle given two angles of a similar triangle Finding angle measures and side ratios to determine if two triangles are similar Finding the coordinates of a point reflected across an axis Finding the coordinates of a point reflected across both axes Reflecting a polygon across the x-axis or y-axis Reflecting a polygon over a vertical or horizontal line Finding the coordinates of three points reflected over an axis Finding the coordinates of a point reflected across an axis and translated Rotating a point and giving its coordinates The effect of dilation on side length Determining if figures are related by a dilation The effect of dilation on area Volume of a cylinder Word problem involving the volume of a cylinder Word problem involving the rate of filling or emptying a cylinder Word problem involving the volume of a cone Word problem involving the volume of a sphere Making an inference using a two-way frequency table Calculating relative frequencies in a contingency table Constructing a scatter plot Scatter plots and correlation Predictions from the line of best fit Classifying linear and nonlinear relationships from scatter plots 2: Reason abstractly and quantitatively. Additive property of equality with integers Multiplicative property of equality with integers Additive property of equality with fractions and mixed numbers Multiplicative property of equality with fractions Multiplicative property of equality with signed fractions Additive property of equality with decimals Multiplicative property of equality with decimals Writing an equation to represent a proportional relationship Using two steps to solve an equation with whole numbers Additive property of equality with a negative coefficient Solving a two-step equation with integers Introduction to solving an equation with parentheses Solving a multi-step equation given in fractional form Solving a two-step equation with signed decimals Introduction to solving an equation with variables on the same side Solving a linear equation with several occurrences of the variable: Variables on the same side Introduction to solving a linear equation with a variable on each side Solving a linear equation with several occurrences of the variable: Variables on the same side and distribution and distribution ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 10/15

11 and two distributions Solving a two-step equation with signed fractions and fractional coefficients Solving equations with zero, one, or infinitely many solutions Solving a proportion of the form (x+a)/b = c/d Solving a proportion of the form a/(x+b) = c/x Solving a fraction word problem using a linear equation of the form Ax = B Solving a decimal word problem using a linear equation of the form Ax + B = C Function tables with two-step rules Table for a linear equation Writing a function rule given a table of ordered pairs: One-step rules Writing a function rule given a table of ordered pairs: Two-step rules Graphing a linear equation of the form y = mx Graphing a line given its equation in slope-intercept form: Integer slope Graphing a line given its equation in slope-intercept form: Fractional slope Writing an equation of a line given its slope and y-intercept Writing an equation in slope-intercept form given the slope and a point Writing and evaluating a function that models a real-world situation: Basic Writing and evaluating a function that models a real-world situation: Advanced Graphing ordered pairs and writing an equation from a table of values in context Writing an equation and drawing its graph to model a real-world situation: Basic Writing an equation and drawing its graph to model a real-world situation: Advanced Interpreting the parameters of a linear function that models a real-world situation Table for a linear function Graphing a function of the form f(x) = ax + b: Integer slope Graphing a function of the form f(x) = ax + b: Fractional slope Choosing a graph to fit a narrative: Basic Choosing a graph to fit a narrative: Advanced Graphically solving a system of linear equations Introduction to using substitution to solve a linear equation Solving a system of linear equations of the form y = mx + b Solving a system of linear equations using substitution Solving a system of linear equations using elimination with addition Solving a system of linear equations using elimination with multiplication and addition Solving systems of linear equations with 0, 1, or infinitely many solutions Converting a repeating decimal to a fraction Solving an equation of the form x 2 = a using the square root property Solving an equation of the form x 3 = a using integers Introduction to the Pythagorean Theorem Pythagorean Theorem Word problem involving the Pythagorean Theorem Using the Pythagorean Theorem repeatedly Using the Pythagorean Theorem to find distance on a grid Distance between two points in the plane: Exact answers Solving equations involving vertical angles Finding an angle measure of a triangle given two angles Finding an angle measure for a triangle with an extended side Scatter plots and correlation 3: Construct viable arguments and critique the reasoning of others. ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 11/15

12 4: Model with mathematics. Identifying congruent shapes on a grid Identifying similar or congruent shapes on a grid Introduction to properties of addition Properties of addition Introduction to properties of multiplication Properties of real numbers Identifying linear equations: Basic Identifying functions from relations Vertical line test Estimating a square root Identifying rational decimal numbers Identifying true statements about rational and irrational numbers Identifying numbers as rational or irrational Establishing facts about the angles created when parallel lines are cut by a transversal Establishing facts about the interior angles of a triangle Establishing facts about the interior and exterior angles of a triangle Finding angle measures and side ratios to determine if two triangles are similar Identifying transformations Properties of translated figures Determining if figures are related by a translation Properties of reflected figures Determining if figures are related by a reflection Properties of rotated figures Determining if figures are related by a rotation Determining if figures are congruent and related by a transformation Determining if figures are congruent and related by a sequence of transformations The effect of dilation on side length Determining if figures are similar and related by a sequence of transformations Identifying side lengths that give right triangles Demonstrating the converse of the Pythagorean Theorem Informal proof of the Pythagorean Theorem Identifying congruent shapes on a grid Identifying similar or congruent shapes on a grid Solving a fraction word problem using a linear equation of the form Ax = B Solving a decimal word problem using a linear equation of the form Ax + B = C Making a table and plotting points given a unit rate Comparing proportional relationships given in different forms Using right triangles to find the slope of a line Interpreting direct variation from a graph Writing and evaluating a function that models a real-world situation: Basic Writing and evaluating a function that models a real-world situation: Advanced Writing an equation and drawing its graph to model a real-world situation: Basic Writing an equation and drawing its graph to model a real-world situation: Advanced Comparing properties of linear functions given in different forms Choosing a graph to fit a narrative: Basic Choosing a graph to fit a narrative: Advanced Solving a word problem involving a sum and another basic relationship using a system of linear equations Solving a word problem using a system of linear equations of the form Ax + By = C ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 12/15

13 Solving a word problem using a system of linear equations of the form y = mx + b Solving a value mixture problem using a system of linear equations Approximating the location of irrational numbers on a number line Word problem involving the Pythagorean Theorem Identifying transformations Translating a polygon Using a translated point to find coordinates of other translated points Finding the coordinates of a point reflected across an axis Finding the coordinates of a point reflected across both axes Reflecting a polygon across the x-axis or y-axis Reflecting a polygon over a vertical or horizontal line Finding the coordinates of three points reflected over an axis Finding the coordinates of a point reflected across an axis and translated Rotating a figure about the origin Dilating a segment and giving the coordinates of its endpoints Determining if figures are related by a dilation Dilating a figure Volume of a rectangular prism made of unit cubes Volume of a cylinder Word problem involving the volume of a cylinder Word problem involving the rate of filling or emptying a cylinder Word problem involving the volume of a cone Word problem involving the volume of a sphere Constructing a two-way frequency table: Basic Constructing a two-way frequency table: Advanced Constructing a scatter plot Sketching the line of best fit 5: Use appropriate tools strategically. Graphically solving a system of linear equations Expressing calculator notation as scientific notation Using numerical methods to approximate a square root to the nearest tenth Using numerical methods to approximate a square root to the nearest hundredth Approximating the location of irrational numbers on a number line Measuring an angle with the protractor Drawing an angle with the protractor Finding angle measures and side ratios to determine if two triangles are similar Translating a point and giving its coordinates: One step Translating a point and giving its coordinates: Two steps Properties of translated figures Determining if figures are related by a translation Translating a polygon Reflecting a point across an axis Reflecting a point across both coordinate axes Reflecting a point across an axis and giving its coordinates Properties of reflected figures Determining if figures are related by a reflection Rotating a point and giving its coordinates Properties of rotated figures Determining if figures are related by a rotation Dilating a segment and giving the coordinates of its endpoints The effect of dilation on side length ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 13/15

14 6: Attend to precision. Determining if figures are related by a dilation The effect of dilation on area Determining if figures are similar and related by a sequence of transformations Word problem with division of whole numbers and rounding Converting a fraction to a terminating decimal: Basic Converting a fraction to a terminating decimal: Advanced Converting a fraction to a repeating decimal: Basic Converting a fraction to a repeating decimal: Advanced Converting a mixed number to a terminating decimal: Basic Converting a mixed number to a terminating decimal: Advanced Choosing metric units and converting to the base unit in scientific notation Multiplying numbers written in scientific notation: Basic Multiplying numbers written in scientific notation: Advanced Multiplying numbers written in decimal form or scientific notation in a real-world situation Dividing numbers written in scientific notation: Basic Dividing numbers written in scientific notation: Advanced Adding or subtracting numbers written in scientific notation: Same exponents, basic Adding or subtracting numbers written in scientific notation: Same exponents, advanced Adding or subtracting numbers written in scientific notation: Different exponents Estimating the sum or difference of two numbers written in scientific notation Square root of a perfect square Estimating a square root Cube root of an integer Volume of a cone Volume of a cone: Exact answers in terms of pi Volume of a sphere Identifying outliers and clustering in scatter plots 7: Look for and make use of structure. Understanding the distributive property Order of operations with integers and exponents Introduction to properties of addition Properties of addition Distributive property: Whole number coefficients Distributive property: Integer coefficients Distributive property: Fractional coefficients Introduction to properties of multiplication Properties of real numbers 8: Look for and express regularity in repeated reasoning. Converting a fraction to a repeating decimal: Basic Converting a fraction to a repeating decimal: Advanced Writing a function rule given a table of ordered pairs: One-step rules Writing a function rule given a table of ordered pairs: Two-step rules Finding the initial amount and rate of change given a table for a linear function Finding the initial amount and rate of change given a graph of a linear function Introduction to the product rule with positive exponents: Whole number base Introduction to the power of a power rule with positive exponents: Whole number base Introduction to the quotient rule with positive exponents: Whole number base ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 14/15

15 Power of 10: Negative exponent Evaluating an expression with a negative exponent: Whole number base Evaluating an expression with a negative exponent: Positive fraction base Evaluating an expression with a negative exponent: Negative integer base Introduction to the product rule with negative exponents: Whole number base Introduction to the quotient rule with negative exponents: Whole number base Introduction to the power of a power rule with negative exponents: Whole number base Introduction to scientific notation with positive exponents Scientific notation with positive exponent Introduction to scientific notation with negative exponents Scientific notation with negative exponent Converting between scientific notation and standard form in a real-world situation ALEKS - Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 15/15