Middle School Math Course 3 Correlation of the ALEKS course Middle School Math 3 to the Illinois Assessment Framework for Grade 8

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1 Middle School Math Course 3 Correlation of the ALEKS course Middle School Math 3 to the Illinois Assessment Framework for Grade 8 State Goal 6: Number Sense : : : : : = ALEKS course topic that addresses the standard TD = Teacher Directed Standard 6A : Representations and Ordering Read, write, and recognize equivalent representations of integer powers of 10. Powers of 10: Positive exponent Powers of 10: Negative exponent Read, write, recognize, model, and interpret integers, including translating numerical expressions. Reading the temperature from a thermometer Plotting integers on a number line Integers and rational numbers Recognize, translate between, and apply multiple representations of rational numbers (decimals, fractions, mixed numbers, percents, and roots). Square root of a rational perfect square Converting a decimal to a fraction: Advanced Converting a fraction to a terminating decimal Converting a fraction to a repeating decimal Converting a mixed number to a decimal Converting between percentages and decimals Converting a percentage to a fraction Converting a fraction to a percentage Writing a ratio as a percentage Interpreting circle graphs or pie charts Square root of a perfect square Estimating a square root Use scientific notation to represent numbers and solve problems. Scientific notation with positive exponent Scientific notation with negative exponent Multiplying and dividing numbers written in scientific notation Represent repeated factors using exponents. TD : : Order and compare rational numbers. Ordering fractions with same denominator Ordering fractions with same numerator Ordering fractions Ordering decimals Ordering fractions and decimals Ordering numbers with positive exponents Identify and locate rational and irrational numbers (e.g., square root 2, square root 5) on a number line. ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/11

2 6.8.08: Plotting rational numbers on a number line Rational and irrational numbers Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., exponents, roots, prime/composite, prime factorization, greatest common factor, least common multiple). Factors Prime numbers Prime factorization Greatest common factor Least common multiple Word problem with common multiples Integers and rational numbers Rational and irrational numbers Standards 6B, 6C : Computation, Operations, Estimation, and Properties : Solve problems and number sentences involving addition, subtraction, multiplication, and division using rational numbers, exponents, and roots. Integer addition: Problem type 1 Integer addition: Problem type 2 Integer subtraction: Problem type 1 Integer subtraction: Problem type 2 Integer subtraction: Problem type 3 Integer multiplication and division Addition or subtraction of fractions with the same denominator Addition or subtraction of fractions with different denominators Fractional part of a circle The reciprocal of a number Product of a unit fraction and a whole number Unit fraction multiplication Product of a fraction and a whole number Fraction multiplication Word problem with fractions Fraction division Addition or subtraction of mixed numbers with same denominator Addition of mixed numbers with same denominator and carry Subtraction of mixed numbers with same denominator and borrowing Addition or subtraction of mixed numbers with different denominators Mixed number multiplication: Problem type 1 Mixed number multiplication: Problem type 2 Mixed number division Addition of aligned decimals Subtraction of aligned decimals Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Multiplication of a decimal by a power of ten Multiplication of a decimal by a whole number Decimal multiplication: Problem type 1 Word problem with powers of ten Word problem with multiple decimal operations: Problem type 1 Division of a decimal by a power of ten Division of a decimal by a whole number Decimal division Signed fraction addition: Advanced Signed fraction multiplication: Advanced Signed decimal addition with three numbers ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/11

3 6.8.10: : Computing distances on the number line Evaluating expressions with exponents: Problem type 1 Evaluating expressions with exponents: Problem type 2 Identify and apply order of operations to simplify numeric expressions involving integers (including exponents and roots), fractions, and decimals. Order of operations: Problem type 1 Order of operations: Problem type 2 Operations with absolute value Exponents and order of operations Identify and apply the following properties of operations with rational numbers: the commutative and associative properties for addition and multiplication; the distributive property; the additive and multiplicative identity properties; the additive and multiplicative inverse properties; and the multiplicative property of zero : Introduction to properties of addition Introduction to properties of multiplication Understanding the distributive property Distributive property: Whole number coefficients Distributive property: Integer coefficients Properties of addition Properties of real numbers Describe the effect of multiplying and dividing by numbers, including the effect of multiplying or dividing a rational number by: : : a number less than zero; zero; a number between zero and one; and a number greater than one. Integer multiplication and division Product of a unit fraction and a whole number Product of a fraction and a whole number Fraction multiplication Fraction division Mixed number multiplication: Problem type 1 Mixed number division Signed fraction multiplication: Advanced Properties of real numbers Select, use, and justify appropriate operations, methods, and tools to compute or estimate with rational numbers. Verify solutions and determine the reasonableness of results. Estimating a sum Estimating a difference Estimating a product Estimating a quotient Interpreting circle graphs or pie charts Estimate the square or cube root of a number less than 1,000 between two whole numbers (e.g., cube root 200 is between 5 and 6). Estimating a square root Standard 6D : Ratios, Proportions, and Percents ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 3/11

4 6.8.15: : : : Use ratios to describe problem situations. Introduction to ratios Use proportional reasoning to model and solve problems. Finding unit rates Solving a word problem involving rates and time conversion Simple word problem on proportions Word problem on proportions: Problem type 1 Making reasonable inferences based on proportion statistics Similar polygons Similar right triangles Indirect measurement Read, write, recognize, model, and interpret percents, including those less than 1% and greater than 100%. Finding the percent of a grid that is shaded Interpreting circle graphs or pie charts Solve number sentences and problems involving fractions, decimals, and percents (e.g., percent increase and decrease, interest rates, tax discounts, tips). Fractional part of a circle Word problem with fractions Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Word problem with powers of ten Word problem with multiple decimal operations: Problem type 1 Percentage of a whole number Finding the sale price given the original price and percent discount Finding the original price given the sale price and percent discount Finding the percentage increase or decrease Simple interest Computations from circle graphs Computing a percentage from a table of values State Goal 7: Measurement : : = ALEKS course topic that addresses the standard TD = Teacher Directed Standards 7A, 7B, 7C : Units, Tools, Estimation, and Applications Select and use appropriate standard units and tools to solve measurement problems, including measurements of polygons and circles. Measuring length to the nearest quarter or half inch Measuring an angle with the protractor Solve problems involving perimeter/circumference and area of polygons, circles, and composite figures using diagrams, models, and grids or by measuring or using given formulas (may include sketching a figure from its description). Perimeter of a piecewise rectangular figure Area as probability Area of a triangle Sides of polygons having the same perimeter Perimeter of a square or a rectangle Perimeter of a polygon Area of a square or a rectangle ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 4/11

5 7.8.03: : : : Distinguishing between area and perimeter Areas of rectangles with the same perimeter Finding the side length of a rectangle given its perimeter or area Area of a piecewise rectangular figure Area of a parallelogram Area of a trapezoid Area between two rectangles Area involving rectangles and triangles Finding the perimeter or area of a rectangle given one of these values Circumference of a circle Finding the radius or the diameter of a circle given its circumference Circumference and area of a circle Perimeter involving rectangles and circles Area between two concentric circles Area involving rectangles and circles Area involving inscribed figures Circumference ratios Compare and estimate length (including perimeter/circumference), area, volume, weight/mass, and angles (0 to 360 ) using referents. TD Solve problems involving the volume or surface area of a right rectangular prism, right circular cylinder, or composite shape using an appropriate formula or strategy. Ratio of volumes Volume of a rectangular prism Volume of a piecewise rectangular prism Volume of a cylinder Rate of filling of a solid Surface area of a cube or a rectangular prism Surface area of a solid made of unit cubes Surface area of a cylinder Surface area involving prisms or cylinders Solve problems involving unit conversions within the same measurement system for length, weight/mass, capacity, square units, and measures expressed as rates (e.g., converting feet/second to yards/minute). Customary unit conversion with whole number values Customary unit conversion with whole number values, two-step conversion Customary unit conversion with mixed number values Customary unit conversion with mixed number values, two-step conversion Customary area unit conversion with whole number values Metric distance conversion with whole number values Metric mass or capacity conversion with whole number values Metric distance conversion with decimal values Metric conversion with decimal values, two-step conversion Metric area unit conversion with decimal number values Solve problems involving scale drawings, maps, and indirect measurement (e.g., determining the height of a building by comparing its known shadow length to the known height and shadow of another object). Indirect measurement State Goal 8: Algebra = ALEKS course topic that addresses the standard ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/11

6 Standard 8A : Representations, Patterns, and Expressions : : : : : : : : Analyze, extend, and create sequences or linear functions, and determine algebraic expressions to describe the n th term of a sequence. Finding a specified term of a geometric sequence given the common ratio and first term Writing a function rule given a table of ordered pairs: One-step rules Function tables with two-step rules Function tables Writing a function rule given a table of ordered pairs: Two-step rules Graphing integer functions Finding the next terms of a simple sequence Finding a specified term of an arithmetic sequence given the common difference and first term Write an expression using variables to represent unknown quantities. Writing a one-step variable expression for a real-world situation 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 Simplify algebraic expressions. Distributive property: Whole number coefficients Distributive property: Integer coefficients Combining like terms: Integer coefficients Combining like terms: Advanced Simplifying a sum or difference of three univariate polynomials Recognize and generate equivalent forms of algebraic expressions. Properties of addition Properties of real numbers Introduction to algebraic symbol manipulation Algebraic symbol manipulation Evaluate or simplify algebraic expressions with one or more rational variable values (e.g., 3a² - b for a = 3 and b = 7). Evaluating a linear expression in two variables Evaluating a quadratic expression in one variable Standard 8B : Connections Using Tables, Graphs, and Symbols Recognize, describe, and extend patterns using rate of change. Writing a function rule given a table of ordered pairs: One-step rules Function tables Writing a function rule given a table of ordered pairs: Two-step rules Writing an equation and drawing its graph to model a real-world situation Interpreting the graphs of two functions Represent linear equations and quantitive relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph. Graphing a line given its equation in slope-intercept form Graphing a line given its equation in standard form Graphing a line given the x- and y-intercepts Graphing a line through a given point with a given slope Graphing a vertical or horizontal line Interpreting the graphs of two functions Translate between different representations (table, written, graphical, or pictorial) of whole number relationships and linear expressions. Writing a function rule given a table of ordered pairs: One-step rules ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 6/11

7 8.8.09: : Function tables with two-step rules Function tables Writing a function rule given a table of ordered pairs: Two-step rules Graphing integer functions Graphing a line given its equation in slope-intercept form Graphing a line given its equation in standard form Graphing a line given the x- and y-intercepts Graphing a line through a given point with a given slope Graphing a vertical or horizontal line Writing an equation of a line given the y-intercept and another point Writing an equation and drawing its graph to model a real-world situation Interpret the meaning of slope and intercepts in linear situations. Graphing a line given the x- and y-intercepts Graphing a line through a given point with a given slope Finding slope given the graph of a line on a grid Finding slope given two points on the line Finding x- and y-intercepts of a line given the equation: Advanced Identify, graph, and interpret up to two inequalitites with a single variable (including the intersection or union of these inequalities) on a number line. Graphing a linear inequality on the number line Graphing a compound linear inequality on the number line Standards 8C, 8D : Writing, Interpreting, and Solving Equations : : : Represent and analyze problems with linear equations and inequalities. Solving a word problem with two unknowns using a linear equation Solving a decimal word problem using a linear equation of the form Ax + B = C Solving a fraction word problem using a linear equation with the variable on both sides Writing an equation and drawing its graph to model a real-world situation Solve linear equations and inequalities in one variable over the rational numbers (e.g., 5x+7= -13, 4x-3= -7x+8, -2x+3>-5). Additive property of equality with whole numbers Additive property of equality with decimals Additive property of equality with fractions and mixed numbers Additive property of equality with integers Additive property of equality with a negative coefficient Multiplicative property of equality with whole numbers Multiplicative property of equality with signed fractions Solving a two-step equation with integers Solving a two-step equation with signed fractions Solving a linear equation with several occurrences of the variable: Variables on the same side and distribution Solving a linear equation with several occurrences of the variable: Variables on both sides and distribution Solving a linear inequality: Problem type 1 Solving a linear inequality: Problem type 2 Solving a linear inequality: Problem type 3 Solve word problems involving unknown quantities. Word problem with powers of ten Word problem with multiple decimal operations: Problem type 1 Solving a word problem involving rates and time conversion Simple word problem on proportions Word problem on proportions: Problem type 1 ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 7/11

8 Finding the sale price given the original price and percent discount Finding the original price given the sale price and percent discount Finding the percentage increase or decrease Simple interest Solving a fraction word problem using a linear equation of the form Ax = B Solving a word problem with two unknowns using a linear equation Solving a decimal word problem using a linear equation of the form Ax + B = C Solving a fraction word problem using a linear equation with the variable on both sides State Goal 9: Geometry : = ALEKS course topic that addresses the standard Standard 9A : Properties of Single Figures and Coordinate Geometry Solve problems involving two- and three- dimensional shapes. Acute, obtuse, and right angles Area of a triangle Sum of the angle measures of a triangle Pythagorean Theorem Sides of polygons having the same perimeter Perimeter of a square or a rectangle Perimeter of a polygon Area of a square or a rectangle Distinguishing between area and perimeter Areas of rectangles with the same perimeter Finding the side length of a rectangle given its perimeter or area Area of a piecewise rectangular figure Area of a parallelogram Area of a trapezoid Area involving rectangles and triangles Introduction to circle: diameter, radius, and chord Circumference of a circle Finding the radius or the diameter of a circle given its circumference Circumference and area of a circle Perimeter involving rectangles and circles Area between two concentric circles Area involving rectangles and circles Area involving inscribed figures Ratio of volumes Circumference ratios Volume of a solid made of unit cubes Volume of a rectangular prism Volume of a piecewise rectangular prism Volume of a triangular prism Volume of a cylinder Rate of filling of a solid Vertices, edges, and faces of a solid Surface area of a cube or a rectangular prism Surface area of a solid made of unit cubes Surface area of a triangular prism Surface area of a cylinder Surface area involving prisms or cylinders Nets of solids ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 8/11

9 9.8.02: : : : : : : Solve problems that require knowledge of triangle and quadrilateral properties (e.g., triangle inequality). Acute, obtuse, and right triangles Scalene, isosceles, and equilateral triangles Identifying and naming congruent triangles Sum of the angle measures of a triangle Angle measures of right or isosceles triangles with variables Finding an angle measure for a triangle with an extended side Finding an angle measure for a triangle sharing a side with another triangle Classifying quadrilaterals Classifying parallelograms Sides of polygons having the same perimeter Areas of rectangles with the same perimeter Finding the side length of a rectangle given its perimeter or area Find the length of any side of a right triangle using the Pythagorean theorem (whole number solutions). Pythagorean Theorem Identify, describe, and determine the radius, diameter, and circumference of a circle and their relationship to each other and to pi. Introduction to circle: diameter, radius, and chord Circumference of a circle Finding the radius or the diameter of a circle given its circumference Graph points, and identify coordinates of points on the Cartesian coordinate plane (all four quadrants). Reading a point in the coordinate plane Plotting a point in the coordinate plane Analyze the results of a combination of transformations, and determine a different transformation that could produce the same result. Translation of a polygon Coordinates of translated points Reflection of a polygon over a vertical or horizontal line Coordinates of points reflected over an axis Rotation of a figure about the origin Dilation Identify or analyze relationships of angles formed by intersecting lines (including parallel lines cut by a transversal) and angles formed by radii of a circle. Corresponding and alternate angles Supplementary and vertical angles Solving equations involving vertical angles Solving equations involving angles and parallel lines Solve problems involving vertical, complementary, and supplementary angles. Supplementary and complementary angles Supplementary and vertical angles Solving equations involving vertical angles Standard 9B : Relationships Between and Among Multiple Figures : : Identify front, side, and top views of a three-dimensional solid built with cubes. Side views of a solid made of cubes Counting the cubes in a solid made of cubes Solve problems involving congruent and similar figures. Constructing congruent angles Identifying and naming congruent triangles ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 9/11

10 9.8.12: Similar polygons Similar right triangles Indirect measurement Relate absolute value to distance on the number line. Absolute value of a number State Goal 10: Data Analysis, Statistics, and Probability : : : : : : = ALEKS course topic that addresses the standard TD = Teacher Directed Standards 10A, 10B: Data Analysis and Statistics Read, interpret (including possible misleading characteristics), and make predictions from data represented in a bar graph, line (dot) plot, Venn diagram (with two or three circles), chart/table, line graph, scatterplot, circle graph, stem-and-leaf plot, or histogram. Computations from circle graphs Interpreting circle graphs or pie charts Computing a percentage from a table of values Interpreting bar graphs Double bar graphs Interpreting line graphs Interpreting a stem-and-leaf plot Using back-to-back stem-and-leaf plots to compare data sets Venn diagrams with three sets Interpreting the graphs of two functions Compare and contrast the effectiveness of different representations of the same data. TD Create a bar graph, chart/table, line graph, or circle graph and solve a problem using the data in the graph for a given set of data. Histograms for numerical data Bar graphs for non-numerical data Identify or draw a reasonable approximation of the line of best fit from a set of data or a scatter plot, and use the line to make predictions. Sketching the line of best fit Scatter plots and correlation Analyze and apply measures of central tendency (mode, range, median, and mean) in problem-solving situations. Mode of a data set Mean and median of a data set Finding the value for a new score that will yield a given mean How changing a value affects the mean and median Rejecting unreasonable claims based on average statistics Choosing the best measure to describe data Standard 10C: Probability Solve problems involving the probability of an event composed of repeated trials, compound events (including independent events), or future events with or without replacement. Outcomes and event probability Introduction to probability of an event ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 10/11

11 : : Probability of an event Area as probability Probability of independent events Probability of dependent events Die rolling Represent all possible outcomes (sample space) for simple or compound events (e.g., tables, grids, tree diagrams). Tree diagrams Outcomes and event probability Die rolling Solve simple problems involving the number of ways objects can be arranged (permutations and combinations). Word problem involving permutations Word problem involving combinations ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 11/11