Correlation of the ALEKS courses Algebra 1 and High School Geometry to the Wyoming Mathematics Content Standards for Grade 11

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1 Correlation of the ALEKS courses Algebra 1 and High School Geometry to the Wyoming Mathematics Content Standards for Grade 11 1: Number Operations and Concepts Students use numbers, number sense, and number relationships in a problem-solving situation. MA11.1.1: Students represent and apply real numbers in a variety of forms. Order of operations: Problem type 1 Order of operations: Problem type 2 Equivalent fractions Simplifying a fraction Ordering fractions Fractional position on a number line Addition or subtraction of fractions with the same denominator Addition or subtraction of fractions with different denominators Unit fraction multiplication Product of a fraction and a whole number Fraction multiplication Fraction division Writing an improper fraction as a mixed number Writing a mixed number as an improper fraction Addition of mixed numbers with same denominator and carry Subtraction of mixed numbers with same denominator and borrowing Mixed number multiplication: Problem type 1 Mixed number division Ordering decimals Ordering fractions and decimals Converting a decimal to a fraction: Advanced Converting a fraction to a terminating decimal Addition of aligned decimals Subtraction of aligned decimals Multiplication of a decimal by a power of ten Multiplication of a decimal by a whole number Converting between percentages and decimals Converting a percentage to a fraction Converting a fraction to a percentage Writing a ratio as a percentage Percentage of a whole number Plotting integers on a number line Plotting rational numbers on a number line Absolute value of a number Integer addition: Problem type 1 Integer addition: Problem type 2 Integer subtraction: Problem type 1 Integer subtraction: Problem type 2 ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/9

2 Integer subtraction: Problem type 3 Integer subtraction Operations with absolute value Integer multiplication and division Signed fraction addition: Advanced Signed fraction multiplication: Advanced Signed decimal addition with three numbers Evaluating expressions with exponents: Problem type 1 Evaluating expressions with exponents: Problem type 2 Exponents and order of operations Scientific notation with positive exponent Scientific notation with negative exponent MA11.1.2: Students apply the structure and properties of the real number system. Integers and rational numbers Rational and irrational numbers Properties of addition Properties of real numbers MA11.1.3: Students explain their choice of estimation and problem solving strategies and justify results of solutions in problem-solving situations involving real numbers. Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Word problem with multiple decimal operations: Problem type 1 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 Computing a percentage from a table of values MA11.1.4: Students use proportional reasoning to solve problems. Solving a word problem involving rates and time conversion Solving a proportion of the form x/a = b/c Solving a proportion of the form (x+a)/b = x/c Simple word problem on proportions Word problem on proportions: Problem type 1 Word problem on proportions: Problem type 2 2: Geometry Students apply geometric concepts, properties, and relationships in a problem-solving situation. TD = Teacher Directed MA11.2.1: Students use transformations, congruency, symmetry, similarity, perpendicularity, parallelism, and the Pythagorean Theorem to solve problems. Identifying parallel and perpendicular lines Identifying and naming congruent triangles Pythagorean Theorem ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/9

3 MA a: MA b: MA c: Computing an area using the Pythagorean Theorem Identifying congruent shapes on a grid Identifying similar or congruent shapes on a grid Identifying transformations 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 Drawing lines of symmetry Rotation of a figure about the origin Dilation Finding an angle of rotation Rotational and point symmetries MA11.2.2: Students communicate, using mathematical language, to: Interpret, represent, or create geometric figures; Finding coordinates of vertices of polygons Drawing an angle with the protractor Naming segments, rays, and lines Finding the coordinates of a point to make a parallelogram Vertices, edges, and faces of a solid Nets of solids Side views of a solid made of cubes Draw or build figures from a mathematical description; Finding the coordinates of a point to make a parallelogram Side views of a solid made of cubes Analyze properties and determine attributes of 2- and 3-dimensional objects. Acute, obtuse, and right triangles Scalene, isosceles, and equilateral triangles Triangle inequality: Problem type 1 Triangle inequality: Problem type 2 Relationship between angle measures and side lengths in a triangle: Problem type 1 Relationship between angle measures and side lengths in a triangle: Problem type 2 Classifying quadrilaterals Classifying parallelograms Classifying quadrilaterals: Advanced problem Properties of parallelograms: Problem type 1 Properties of parallelograms: Problem type 2 Properties of rectangles Properties of rhombi Vertices, edges, and faces of a solid Side views of a solid made of cubes MA11.2.3: Students communicate the reasoning used in identifying geometric relationships in problem-solving situations. TD MA11.2.4: Students solve problems involving the coordinate plane such as the distance between two points, the midpoint, and slope. Finding slope given the graph of a line on a grid Finding slope given two points on the line Determining the slope of a line given its graph ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 3/9

4 Midpoint of a line segment in the plane Distance between two points in the plane Finding coordinates of vertices of polygons Area of quadrilaterals in the coordinate plane Finding the coordinates of a point to make a parallelogram MA11.2.5: Students connect geometry with other mathematical topics. Solving equations involving vertical angles Vertical angles and linear pairs Angles and parallel lines Angle measures of right or isosceles triangles with variables Finding a side length given the perimeter and side lengths with variables Finding the perimeter or area of a rectangle given one of these values Similar polygons Area as probability 3: Measurement Students use a variety of tools and techniques of measurement in a problem-solving situation. MA11.3.1: Students apply estimation and measurement using the appropriate methods and units to solve problems involving length, weight/mass, area, surface area, volume, and angle measure. Area of a triangle Computing an area using the Pythagorean Theorem Perimeter of a square or a rectangle Perimeter of a square or a rectangle Perimeter of a polygon Sides of polygons having the same perimeter Perimeter of a piecewise rectangular figure Finding a side length given the perimeter and side lengths with variables Distinguishing between area and perimeter Area of a square or a rectangle Finding the side length of a rectangle given its perimeter or area Areas of rectangles with the same perimeter Finding the perimeter or area of a rectangle given one of these values Area of a piecewise rectangular figure Area of a parallelogram Area of a trapezoid Area between two rectangles Area of a regular polygon Area involving rectangles and triangles Finding the radius or the diameter of a circle given its circumference Circumference and area of a circle Perimeter involving rectangles and circles Circumference ratios Arc length and area of a sector of a circle Area between two concentric circles ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 4/9

5 Area involving rectangles and circles Area involving rectangles and circles: Advanced problem 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 pyramid Volume of a cylinder Volume of a cone Volume of a sphere 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 Counting the cubes in a solid made of cubes Surface area of a sphere MA11.3.2: Students demonstrate an understanding of both metric and U. S. customary systems. Students are able to convert within each system. Customary unit conversion with whole number values Metric distance conversion with whole number values Converting between compound units: Basic Converting between compound units: Advanced MA11.3.3: Students identify and apply scale, ratios, and proportions in solving measurement problems. Circumference ratios Rate of filling of a solid Ratio of volumes Similar polygons Triangles and parallel lines Similar right triangles Similar solids: Problem type 1 Similar solids: Problem type 2 MA11.3.4: Students solve problems of angle measure including those involving polygons or parallel lines cut by a transversal. Supplementary and complementary angles Solving equations involving vertical angles Vertical angles and linear pairs Angles and parallel lines Introduction to angle addition Angle addition and angle bisectors Sum of the angle measures of a triangle Finding angle measures in extended triangles Angle measures with triangles and parallel lines 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 Properties of parallelograms: Problem type 1 Properties of rectangles Properties of rhombi The sum of interior angle measures in a convex polygon ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/9

6 Interior and exterior angle measures in a regular polygon MA11.3.5: Students solve indirect measurement problems. Indirect measurement 4: Algebra Students use algebraic methods to investigate, model, and interpret patterns and functions involving numbers, shapes, data, and graphs in a problem-solving situation. MA11.4.1: Students use algebraic concepts, symbols, and skills to represent and solve real-world problems. Solving a fraction word problem using a linear equation of the form Ax = B Writing a one-step variable expression for a real-world situation Translating a sentence into a one-step equation Solving a word problem with two unknowns using a linear equation Solving a decimal word problem using a linear equation with the variable on both sides 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 a multi-step inequality for a real-world situation Word problem with linear inequalities Writing an equation and drawing its graph to model a real-world situation Application problem with a linear function: Problem type 1 Application problem with a linear function: Problem type 2 Solving a word problem using a system of linear inequalities Solving a word problem involving a sum and another simple relationship using a system of linear equations Solving a value mixture problem using a system of linear equations Solving a distance, rate, time problem using a system of linear equations Solving a percent mixture problem using a system of linear equations Solving a tax rate or interest rate problem using a system of linear equations Solving a word problem using a quadratic equation with rational roots Word problem on direct variation Word problem on inverse variation Solving a word problem using a quadratic equation with irrational roots Solving a word problem using an exponential equation: Problem type 1 MA11.4.2: Students write, model, and evaluate expressions, functions, equations, and inequalities. Introduction to evaluating an algebraic expression Solving a proportion of the form x/a = b/c Solving a proportion of the form (x+a)/b = x/c Evaluating a linear expression in two variables Evaluating a quadratic expression in one variable Additive property of equality with whole numbers Additive property of equality with decimals Additive property of equality with integers ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 6/9

7 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 an equation to find the value of an expression 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 fractional coefficients Solving a linear equation with several occurrences of the variable: Variables on both sides and distribution Solving a linear equation with several occurrences of the variable: Variables on both sides and two distributions Solving a linear equation with several occurrences of the variable: Fractional forms with binomial numerators Translating a sentence into a simple inequality Writing a compound inequality Graphing a linear inequality on the number line Graphing a compound linear inequality on the number line Solving a linear inequality: Problem type 1 Solving a linear inequality: Problem type 2 Solving a linear inequality: Problem type 3 Solving a linear inequality: Problem type 4 Simple absolute value equation Solving an equation involving absolute value: Basic Solving an equation involving absolute value: Advanced Solving an inequality involving absolute value Solving an inequality involving absolute value: Basic Finding a solution to a linear equation in two variables Identifying solutions to linear equations in two variables Finding x- and y-intercepts of a line given the equation: Advanced Writing an equation of a line given the y-intercept and another point Writing the equation of a line given the slope and a point on the line Writing the equation of the line through two given points Writing the equations of vertical and horizontal lines through a given point Function tables with two-step rules Function tables 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 Solving equations written in factored form Finding the roots of a quadratic equation with leading coefficient 1 Finding the roots of a quadratic equation with leading coefficient greater than 1 Roots of a product of polynomials Solving a quadratic equation needing simplification Introduction to algebraic symbol manipulation Algebraic symbol manipulation Applying the quadratic formula: Exact answers Solving a word problem using a quadratic equation with irrational roots MA11.4.3: Students graph linear equations and interpret the results in solving algebraic problems. Graphing a line given its equation in slope-intercept form Graphing a line given its equation in standard form Graphing a vertical or horizontal line ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 7/9

8 Writing an equation and drawing its graph to model a real-world situation Interpreting the graphs of two functions MA11.4.4: Students solve, graph, or interpret systems of linear equations. Classifying systems of linear equations from graphs Graphically solving a system of linear equations Solving a system of linear equations using elimination with multiplication and addition Solving a word problem involving a sum and another simple relationship using a system of linear equations Solving a value mixture problem using a system of linear equations Solving a distance, rate, time problem using a system of linear equations Solving a percent mixture problem using a system of linear equations Solving a tax rate or interest rate problem using a system of linear equations MA11.4.5: Students connect algebra with other mathematical topics. Slopes of parallel and perpendicular lines: Problem type 1 Slopes of parallel and perpendicular lines: Problem type 2 Solving a word problem using a quadratic equation with rational roots Solving equations involving vertical angles Vertical angles and linear pairs Angles and parallel lines Introduction to angle addition Angle measures of right or isosceles triangles with variables Finding a side length given the perimeter and side lengths with variables Finding the perimeter or area of a rectangle given one of these values 5: Data Analysis and Probability Students use data analysis and probability to analyze given situations and the results of experiments. MA11.5.1: Students apply knowledge of mean, median, mode, and range to interpret and evaluate information and data. Mode of a data set Mean and median of a data set Choosing the best measure to describe data Using back-to-back stem-and-leaf plots to compare data sets How changing a value affects the mean and median Rejecting unreasonable claims based on average statistics Finding the value for a new score that will yield a given mean MA11.5.2: Students draw reasonable inferences from statistical data and/or correlation/best fit line to predict outcomes. Scatter plots and correlation Introduction to expectation Rejecting unreasonable claims based on average statistics Making reasonable inferences based on proportion statistics MA11.5.3: Students communicate about the likelihood of events using concepts from ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 8/9

9 probability. MA a: MA b: MA c: sample space Counting principle Word problem involving permutations Word problem involving combinations evaluate simple probabilities Introduction to probability of an event Probability of an event Outcomes and event probability Die rolling evaluate experimental vs. theoretical Experimental and theoretical probability MA11.5.4: Students determine, collect, organize, and analyze relevant data needed to make conclusions. Histograms for numerical data Interpreting bar graphs Interpreting line graphs Choosing a graph to fit a narrative Computations from circle graphs Interpreting circle graphs or pie charts Choosing the best measure to describe data Interpreting a stem-and-leaf plot Using back-to-back stem-and-leaf plots to compare data sets Computing a percentage from a table of values Finding if a question can be answered by the data Finding the value for a new score that will yield a given mean Venn diagrams with two sets Venn diagrams with three sets ALEKS - Copyright 2013 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 9/9

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

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 6.8.01: 6.8.02: 6.8.03: 6.8.04: 6.8.05: = ALEKS