Middle School Math Course 2. Correlation of the ALEKS course Middle School Math Course 2 to the Common Core State Standards for Grade 7 (2010)

Transcription

1 Middle School Math Course 2 Correlation of the ALEKS course Middle School Math Course 2 to the Common Core State Standards for Grade 7 (2010) 7.RP: Ratios & Proportional Relationships 7.RP.A.1: 7.RP.A.2: Recognize and represent proportional relationships between quantities. 7.RP.A.2.A: 7.RP.A.2.B: 7.RP.A.2.C: = ALEKS course topic that addresses the standard Analyze proportional relationships and use them to solve real-world and mathematical problems. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 / 1/4 miles per hour, equivalently 2 miles per hour. Word problem on unit rates associated with ratios of fractions Word problem on unit rates associated with ratios of mixed numbers Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Identifying proportional relationships in tables by calculating unit rates: Whole numbers Identifying proportional relationships in tables by calculating unit rates: Fractions Identifying proportional relationships in graphs: Basic Identifying proportional relationships in graphs: Advanced Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Word problem on unit rates associated with ratios of whole numbers: Whole number answers Finding a unit price Using tables to compare ratios Computing unit prices to find the better buy Word problem on unit rates associated with ratios of whole numbers: Decimal answers Word problem on unit rates associated with ratios of fractions Word problem on unit rates associated with ratios of mixed numbers Identifying proportional relationships in tables by calculating unit rates: Whole numbers Identifying proportional relationships in tables by calculating unit rates: Fractions Identifying proportional relationships in graphs: Basic Identifying proportional relationships in graphs: Advanced Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Writing an equation to represent a proportional relationship ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/19

2 7.RP.A.2.D: 7.RP.A.3: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Finding outputs and rate of increase given the graph of a line that models a real-world situation Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Solving a word problem on proportions using a unit rate Word problem on proportions: Problem type 1 Finding a percentage of a whole number Finding a percentage of a whole number without a calculator: Basic Finding a percentage of a whole number without a calculator: Advanced Applying the percent equation: Problem type 1 Applying the percent equation: Problem type 2 Finding a percentage of a total amount: Real-world situations Finding a percentage of a total amount without a calculator: Sales tax, commission, discount Estimating a tip without a calculator Writing a ratio as a percentage without a calculator Finding the rate of a tax or commission Finding the total amount given the percentage of a partial amount Finding a percentage of a total amount in a circle graph Computations from a circle graph Finding the final amount given the original amount and a percentage increase or decrease Finding the sale price given the original price and percent discount Finding the sale price without a calculator given the original price and percent discount Finding the total cost including tax or markup Finding the original amount given the result of a percentage increase or decrease Finding the original price given the sale price and percent discount Finding the percentage increase or decrease: Basic Finding the percentage increase or decrease: Advanced Finding the absolute error and percent error of a measurement Finding simple interest without a calculator Comparing discounts Computing percentages for categories of a budget Computing a percentage from a table of values 7.NS: The Number System 7.NS.A.1: 7.NS.A.1.A: = ALEKS course topic that addresses the standard Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/19

3 7.NS.A.1.B: 7.NS.A.1.C: 7.NS.A.1.D: Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.A.2: 7.NS.A.2.A: 7.NS.A.2.B: Identifying relative change when combining two quantities Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Identifying a sum as a point located a given distance from another point Word problem with addition or subtraction of integers Properties of addition Understand subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. Computing the distance between two integers on a number line Computing and understanding distances between integers on a number line Word problem with addition or subtraction of integers Computing distances between decimals on the number line 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 Addition and subtraction with 3 integers Addition and subtraction with 4 or 5 integers Signed fraction addition or subtraction: Basic Signed fraction subtraction involving double negation Signed fraction addition or subtraction: Advanced Addition and subtraction of 3 fractions involving signs Signed decimal addition and subtraction Signed decimal addition and subtraction with 3 numbers Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as ( 1)( 1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Integer multiplication and division Multiplication of 3 or 4 integers Word problem with multiplication or division of integers Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then (p/q) = ( p)/q = p/( q). Interpret quotients of rational numbers by describing real-world contexts. Division involving zero Integer multiplication and division Word problem with multiplication or division of integers Identifying equivalent signed fractions Identifying numbers as integers or non-integers ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 3/19

4 7.NS.A.2.C: Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.A.2.D: Integer multiplication and division Multiplication of 3 or 4 integers Signed fraction multiplication: Basic Signed fraction multiplication: Advanced Signed fraction division Signed decimal multiplication Signed decimal division Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. 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 Converting a fraction or mixed number to a rounded decimal Identifying rational decimal numbers 7.NS.A.3: Solve real-world and mathematical problems involving the four operations with rational numbers. Operations with absolute value: Problem type 1 Operations with absolute value: Problem type 2 Word problem with addition or subtraction of integers Word problem with multiplication or division of integers Order of operations with integers Word problem involving fractions and multiplication Multi-step word problem involving fractions and multiplication Word problem involving fractions and division Word problem involving addition or subtraction of fractions with different denominators Fractional part of a circle Word problem involving addition or subtraction of mixed numbers with different denominators Word problem involving multiplication or division with mixed numbers Computing distances between decimals on the number line Word problem with addition or subtraction of 2 decimals Word problem with addition of 3 or 4 decimals and whole numbers Word problem with subtraction of a whole number and a decimal: Regrouping with zeros Word problem with multiplication of a decimal and a whole number Word problem with multiplication of two decimals Word problem with multiple decimal operations: Problem type 1 Word problem with division of a decimal and a whole number Word problem with division of two decimals Word problem with multiple decimal operations: Problem type 2 7.EE: Expressions & Equations = ALEKS course topic that addresses the standard Use properties of operations to generate equivalent expressions. ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 4/19

5 7.EE.A.1: 7.EE.A.2: 7.EE.B.3: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Combining like terms: Whole number coefficients Combining like terms: Integer coefficients Introduction to properties of addition Properties of addition Combining like terms: Fractional coefficients Combining like terms: Decimal coefficients Multiplying a constant and a linear monomial Distributive property: Whole number coefficients Distributive property: Integer coefficients Distributive property: Fractional coefficients Factoring a linear binomial Introduction to properties of multiplication Properties of real numbers Using distribution and combining like terms to simplify: Univariate Identifying properties used to simplify an algebraic expression Using distribution with double negation and combining like terms to simplify: Multivariate Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05." Finding the multiplier to give a final amount after a percentage increase or decrease Clearing fractions in an equation Writing algebraic expressions for the perimeter of a figure Writing algebraic expressions for the area of a figure Writing equivalent expressions for the volume of a rectangular prism Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $ If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Multi-step word problem involving fractions and multiplication Fractional part of a circle Word problem with multiple decimal operations: Problem type 1 Word problem with multiple decimal operations: Problem type 2 Solving a word problem on proportions using a unit rate Word problem on proportions: Problem type 1 Applying the percent equation: Problem type 1 Applying the percent equation: Problem type 2 Writing a ratio as a percentage without a calculator Finding the rate of a tax or commission Finding the total amount given the percentage of a partial amount ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/19

6 7.EE.B.4: 7.EE.B.4.A: 7.EE.B.4.B: Finding a percentage of a total amount in a circle graph Computations from a circle graph Finding the final amount given the original amount and a percentage increase or decrease Finding the sale price given the original price and percent discount Finding the sale price without a calculator given the original price and percent discount Finding the total cost including tax or markup Finding the original amount given the result of a percentage increase or decrease Finding the original price given the sale price and percent discount Finding the percentage increase or decrease: Basic Finding the percentage increase or decrease: Advanced Finding simple interest without a calculator Comparing discounts Computing a percentage from a table of values Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? 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 Identifying properties used to solve a linear equation Solving a two-step equation with signed decimals Solving a two-step equation with signed fractions Translating a sentence into a multi-step equation Writing an equation of the form Ax + B = C to solve a word problem Comparing arithmetic and algebraic solutions to a word problem Solving a decimal word problem using a linear equation of the form Ax + B = C Writing an equation of the form A(x + B) = C to solve a word problem Finding the side length of a rectangle given its perimeter or area Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Graphing a linear inequality on the number line Solving a two-step linear inequality with whole numbers Solving a two-step linear inequality: Problem type 1 Solving a two-step linear inequality: Problem type 2 Solving a two-step linear inequality with a fractional coefficient Translating a sentence into a multi-step inequality Solving a word problem using a two-step linear inequality and describing the solution Solving a word problem using a two-step linear inequality Solving a decimal word problem using a two-step linear inequality ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 6/19

7 7.G: Geometry 7.G.A.1: 7.G.A.2: 7.G.A.3: 7.G.B.4: 7.G.B.5: = ALEKS course topic that addresses the standard Draw, construct, and describe geometrical figures and describe the relationships between them. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Finding lengths using scale models Finding a scale factor: Same units Using a scale drawing to find actual area Reproducing a scale drawing at a different scale Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Drawing a circle with a given radius or diameter Creating triangles from given side lengths: Problem type 1 Creating triangles from given side lengths: Problem type 2 Using triangle inequality to determine if side lengths form a triangle Determining if a triangle is possible based on given angle measures Determining if given measurements define a unique triangle, more than one triangle, or no triangle Drawing triangles with given conditions: Angle measures Drawing triangles with given conditions: Side lengths and angle measures Drawing triangles with given side lengths using a compass Drawing and identifying a polygon in the coordinate plane Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Identifying horizontal and vertical cross sections of solids Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Circumference of a circle Finding the radius or the diameter of a circle given its circumference Circumference ratios Perimeter involving rectangles and circles Area of a circle Circumference and area of a circle Distinguishing between the area and circumference of a circle Area involving rectangles and circles Area between two concentric circles Word problem involving the area between two concentric circles Area involving inscribed figures Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 7/19

8 7.G.B.6: Finding the complement or supplement of an angle given a figure Solving an equation involving complementary or supplementary angles Finding angle measures given two intersecting lines Solving equations involving vertical angles Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Area of a square or a rectangle Volume of a rectangular prism Finding the side length of a rectangle given its perimeter or area Area of a rectangle involving fractions Area of a rectangle involving mixed numbers and fractions Distinguishing between the area and perimeter of a rectangle Areas of rectangles with the same perimeter Word problem involving the area of a square or a rectangle Finding the perimeter or area of a rectangle given one of these values Area of a piecewise rectangular figure Area between two rectangles Word problem involving the area between two rectangles Area of a triangle Finding the area of a trapezoid on a grid by using triangles and rectangles Area involving rectangles and triangles Area of a parallelogram Area of a trapezoid Finding the perimeter or area of a rectangle in the coordinate plane Area of quadrilaterals in the coordinate plane Volume of a rectangular prism made of unit cubes Volume of a solid made of cubes with unit fraction edge lengths Volume of a rectangular prism with fractional edge lengths Word problem involving the volume of a rectangular prism Word problem involving the rate of filling or emptying a rectangular prism Volume of a piecewise rectangular prism Volume of a triangular prism Word problem involving the volume of a triangular prism Surface area of a cube or a rectangular prism Surface area of a rectangular prism made of unit cubes Distinguishing between surface area and volume Using a net to find the surface area of a rectangular prism Word problem involving the surface area of a rectangular prism Surface area of a piecewise rectangular prism made of unit cubes Surface area of a triangular prism 7.SP: Statistics & Probability 7.SP.A.1: = ALEKS course topic that addresses the standard Use random sampling to draw inferences about a population. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 8/19

9 7.SP.A.2: 7.SP.B.3: 7.SP.B.4: 7.SP.C.5: 7.SP.C.6: 7.SP.C.7: representative samples and support valid inferences. Choosing an appropriate method for gathering data: Problem type 1 Choosing an appropriate method for gathering data: Problem type 2 Finding sample size and comparing samples for estimating the mean Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Comparing sample means Introduction to expectation Draw informal comparative inferences about two populations. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. Assessing the degree of overlap of two distributions Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. Comparing measures of center and variation Using back-to-back stem-and-leaf plots to compare data sets Using box-and-whisker plots to compare data sets Investigate chance processes and develop, use, and evaluate probability models. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Classifying likelihood Introduction to the probability of an event Probability of an event Understanding likelihood Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Experimental and theoretical probability Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. 7.SP.C.7.A: Develop a uniform probability model by assigning equal probability to all outcomes, and use ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 9/19

10 7.SP.C.7.B: 7.SP.C.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 7.SP.C.8.A: 7.SP.C.8.B: 7.SP.C.8.C: the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Introduction to the probability of an event Probability of an event Outcomes and event probability Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? Experimental and theoretical probability Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Outcomes and event probability Probability of independent events Probability of dependent events Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event. Interpreting a tree diagram Determining a sample space and outcomes for a compound event Outcomes and event probability Probabilities involving two dice Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? Identifying outcomes in a random number table used to simulate a compound event Using a random number table to simulate a compound event Standards for Mathematical Practices = ALEKS course topic that addresses the standard 1: Make sense of problems and persevere in solving them. Word problem on unit rates associated with ratios of whole numbers: Whole number answers Word problem with division of whole numbers and rounding Least common multiple of 2 numbers Identifying a sum as a point located a given distance from another point Identifying relative change when combining two quantities Operations with absolute value: Problem type 1 Operations with absolute value: Problem type 2 ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 10/19

11 Computing the distance between two integers on a number line Computing and understanding distances between integers on a number line Word problem with addition or subtraction of integers Word problem with multiplication or division of integers Order of operations with integers Identifying equivalent signed fractions Word problem involving fractions and multiplication Multi-step word problem involving fractions and multiplication Word problem involving fractions and division Word problem involving addition or subtraction of fractions with different denominators Fractional part of a circle Word problem involving addition or subtraction of mixed numbers with different denominators Word problem involving multiplication or division with mixed numbers Computing distances between decimals on the number line Word problem with addition or subtraction of 2 decimals Word problem with addition of 3 or 4 decimals and whole numbers Word problem with subtraction of a whole number and a decimal: Regrouping with zeros Word problem with multiplication of a decimal and a whole number Word problem with multiplication of two decimals Word problem with multiple decimal operations: Problem type 1 Word problem with division of a decimal and a whole number Word problem with division of two decimals Word problem with multiple decimal operations: Problem type 2 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 Converting a fraction or mixed number to a rounded decimal Finding a unit price Using tables to compare ratios Computing unit prices to find the better buy Word problem on unit rates associated with ratios of whole numbers: Decimal answers Word problem on unit rates associated with ratios of fractions Word problem on unit rates associated with ratios of mixed numbers Solving a word problem on proportions using a unit rate Word problem on proportions: Problem type 1 Word problem with powers of ten Identifying proportional relationships in tables by calculating unit rates: Whole numbers Identifying proportional relationships in tables by calculating unit rates: Fractions Finding lengths using scale models Finding a scale factor: Same units Using a scale drawing to find actual area Reproducing a scale drawing at a different scale Finding a percentage of a whole number Finding a percentage of a whole number without a calculator: Basic Finding a percentage of a whole number without a calculator: Advanced Applying the percent equation: Problem type 1 Applying the percent equation: Problem type 2 Finding a percentage of a total amount: Real-world situations ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 11/19

12 Finding a percentage of a total amount without a calculator: Sales tax, commission, discount Estimating a tip without a calculator Writing a ratio as a percentage without a calculator Finding the rate of a tax or commission Finding the total amount given the percentage of a partial amount Finding a percentage of a total amount in a circle graph Computations from a circle graph Finding the multiplier to give a final amount after a percentage increase or decrease Finding the final amount given the original amount and a percentage increase or decrease Finding the sale price given the original price and percent discount Finding the sale price without a calculator given the original price and percent discount Finding the total cost including tax or markup Finding the original amount given the result of a percentage increase or decrease Finding the original price given the sale price and percent discount Finding the percentage increase or decrease: Basic Finding the percentage increase or decrease: Advanced Finding the absolute error and percent error of a measurement Finding simple interest without a calculator Comparing discounts Computing percentages for categories of a budget Combining like terms: Whole number coefficients Combining like terms: Fractional coefficients Combining like terms: Decimal coefficients Factoring a linear binomial Introduction to solving an equation with parentheses Identifying properties used to solve a linear equation Clearing fractions in an equation Solving a fraction word problem using a linear equation of the form Ax = B Writing an equation of the form Ax + B = C to solve a word problem Comparing arithmetic and algebraic solutions to a word problem Solving a decimal word problem using a linear equation of the form Ax + B = C Writing an equation of the form A(x + B) = C to solve a word problem Solving a word problem with two unknowns using a linear equation Graphing a linear inequality on the number line Solving a word problem using a two-step linear inequality and describing the solution Solving a word problem using a two-step linear inequality Solving a decimal word problem using a two-step linear inequality Identifying proportional relationships in graphs: Basic Identifying proportional relationships in graphs: Advanced Finding outputs and rate of increase given the graph of a line that models a real-world situation Finding the complement or supplement of an angle given a figure Solving an equation involving complementary or supplementary angles Finding angle measures given two intersecting lines Solving equations involving vertical angles Creating triangles from given side lengths: Problem type 1 Creating triangles from given side lengths: Problem type 2 Determining if a triangle is possible based on given angle measures Determining if given measurements define a unique triangle, more than one triangle, or no triangle ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 12/19

13 Drawing triangles with given conditions: Angle measures Drawing triangles with given conditions: Side lengths and angle measures Drawing triangles with given side lengths using a compass Drawing and identifying a polygon in the coordinate plane Finding the missing length in a figure Writing algebraic expressions for the perimeter of a figure Finding the side length of a rectangle given its perimeter or area Areas of rectangles with the same perimeter Writing algebraic expressions for the area of a figure Word problem involving the area of a square or a rectangle Finding the perimeter or area of a rectangle given one of these values Area of a piecewise rectangular figure Area between two rectangles Word problem involving the area between two rectangles Finding the area of a trapezoid on a grid by using triangles and rectangles Area involving rectangles and triangles Finding the perimeter or area of a rectangle in the coordinate plane Finding the radius or the diameter of a circle given its circumference Circumference ratios Perimeter involving rectangles and circles Area involving rectangles and circles Area between two concentric circles Word problem involving the area between two concentric circles Area involving inscribed figures Identifying horizontal and vertical cross sections of solids Volume of a solid made of cubes with unit fraction edge lengths Volume of a rectangular prism with fractional edge lengths Writing equivalent expressions for the volume of a rectangular prism Word problem involving the volume of a rectangular prism Word problem involving the rate of filling or emptying a rectangular prism Volume of a piecewise rectangular prism Word problem involving the volume of a triangular prism Surface area of a cube or a rectangular prism Using a net to find the surface area of a rectangular prism Word problem involving the surface area of a rectangular prism Surface area of a piecewise rectangular prism made of unit cubes Surface area of a triangular prism Choosing an appropriate method for gathering data: Problem type 1 Choosing an appropriate method for gathering data: Problem type 2 Computing a percentage from a table of values Finding sample size and comparing samples for estimating the mean Comparing measures of center and variation Using back-to-back stem-and-leaf plots to compare data sets Using box-and-whisker plots to compare data sets Comparing sample means Assessing the degree of overlap of two distributions Determining a sample space and outcomes for a compound event Probability of an event Understanding likelihood Outcomes and event probability Probabilities involving two dice Experimental and theoretical probability ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 13/19

14 Introduction to expectation Identifying outcomes in a random number table used to simulate a compound event Using a random number table to simulate a compound event 2: Reason abstractly and quantitatively. Additive property of equality with whole numbers Fractional part of a circle Plotting rational numbers on a number line Additive property of equality with fractions and mixed numbers Additive property of equality with decimals Word problem on unit rates associated with ratios of whole numbers: Decimal answers Solving a word problem on proportions using a unit rate Writing an equation to represent a proportional relationship Word problem on proportions: Problem type 1 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 Identifying properties used to solve a linear equation Solving a two-step equation with signed decimals Solving a two-step equation with signed fractions Solving a fraction word problem using a linear equation of the form Ax = B Translating a sentence into a one-step equation Translating a sentence into a multi-step equation Writing an equation of the form Ax + B = C to solve a word problem Comparing arithmetic and algebraic solutions to a word problem Solving a decimal word problem using a linear equation of the form Ax + B = C Writing an equation of the form A(x + B) = C to solve a word problem Translating a sentence by using an inequality symbol Graphing a linear inequality on the number line Solving a two-step linear inequality with whole numbers Solving a two-step linear inequality: Problem type 1 Solving a two-step linear inequality: Problem type 2 Solving a two-step linear inequality with a fractional coefficient Translating a sentence into a multi-step inequality Solving a word problem using a two-step linear inequality and describing the solution Solving a word problem using a two-step linear inequality Solving a decimal word problem using a two-step linear inequality Function tables with two-step rules Writing a function rule given a table of ordered pairs: One-step rules Solving an equation involving complementary or supplementary angles Solving equations involving vertical angles Writing algebraic expressions for the perimeter of a figure Finding the side length of a rectangle given its perimeter or area Writing algebraic expressions for the area of a figure Writing equivalent expressions for the volume of a rectangular prism Constructing a histogram for numerical data Assessing the degree of overlap of two distributions Interpreting a tree diagram Introduction to the probability of an event Probability of an event Outcomes and event probability ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 14/19

15 Probabilities involving two dice Experimental and theoretical probability 3: Construct viable arguments and critique the reasoning of others. 4: Model with mathematics. Identifying numbers as integers or non-integers Identifying rational decimal numbers Introduction to properties of addition Properties of addition Introduction to properties of multiplication Properties of real numbers Identifying properties used to solve a linear equation Writing a function rule given a table of ordered pairs: One-step rules Using triangle inequality to determine if side lengths form a triangle Determining if a triangle is possible based on given angle measures Determining if given measurements define a unique triangle, more than one triangle, or no triangle Classifying likelihood Understanding likelihood Word problem on unit rates associated with ratios of whole numbers: Whole number answers Plotting integers on a number line Identifying a sum as a point located a given distance from another point Computing and understanding distances between integers on a number line Word problem with addition or subtraction of integers Word problem with multiplication or division of integers Word problem involving fractions and multiplication Multi-step word problem involving fractions and multiplication Word problem involving fractions and division Word problem involving addition or subtraction of fractions with different denominators Fractional part of a circle Word problem involving addition or subtraction of mixed numbers with different denominators Word problem involving multiplication or division with mixed numbers Computing distances between decimals on the number line Word problem with addition or subtraction of 2 decimals Word problem with addition of 3 or 4 decimals and whole numbers Word problem with subtraction of a whole number and a decimal: Regrouping with zeros Word problem with multiplication of a decimal and a whole number Word problem with multiplication of two decimals Word problem with multiple decimal operations: Problem type 1 Word problem with division of a decimal and a whole number Word problem with division of two decimals Word problem with multiple decimal operations: Problem type 2 Finding a unit price Using tables to compare ratios Computing unit prices to find the better buy Word problem on unit rates associated with ratios of whole numbers: Decimal answers Word problem on unit rates associated with ratios of fractions Word problem on unit rates associated with ratios of mixed numbers ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 15/19

16 Solving a word problem on proportions using a unit rate Word problem on proportions: Problem type 1 Finding lengths using scale models Finding a scale factor: Same units Using a scale drawing to find actual area Reproducing a scale drawing at a different scale Finding the percentage of a grid that is shaded Finding a percentage of a whole number Finding a percentage of a total amount: Real-world situations Finding a percentage of a total amount without a calculator: Sales tax, commission, discount Estimating a tip without a calculator Writing a ratio as a percentage without a calculator Finding the rate of a tax or commission Finding the total amount given the percentage of a partial amount Finding a percentage of a total amount in a circle graph Computations from a circle graph Finding the final amount given the original amount and a percentage increase or decrease Finding the sale price given the original price and percent discount Finding the sale price without a calculator given the original price and percent discount Finding the total cost including tax or markup Finding the original amount given the result of a percentage increase or decrease Finding the original price given the sale price and percent discount Finding the percentage increase or decrease: Basic Finding the percentage increase or decrease: Advanced Finding the absolute error and percent error of a measurement Finding simple interest without a calculator Comparing discounts Computing percentages for categories of a budget Solving a fraction word problem using a linear equation of the form Ax = B Writing an equation of the form Ax + B = C to solve a word problem Comparing arithmetic and algebraic solutions to a word problem Solving a decimal word problem using a linear equation of the form Ax + B = C Writing an equation of the form A(x + B) = C to solve a word problem Solving a word problem with two unknowns using a linear equation Graphing a linear inequality on the number line Solving a word problem using a two-step linear inequality and describing the solution Solving a word problem using a two-step linear inequality Solving a decimal word problem using a two-step linear inequality Finding outputs and rate of increase given the graph of a line that models a real-world situation Drawing a circle with a given radius or diameter Creating triangles from given side lengths: Problem type 1 Creating triangles from given side lengths: Problem type 2 Drawing and identifying a polygon in the coordinate plane Finding the side length of a rectangle given its perimeter or area Word problem involving the area of a square or a rectangle Finding the perimeter or area of a rectangle given one of these values Area between two rectangles Word problem involving the area between two rectangles Finding the area of a trapezoid on a grid by using triangles and rectangles ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 16/19

17 Finding the perimeter or area of a rectangle in the coordinate plane Area of quadrilaterals in the coordinate plane Finding the radius or the diameter of a circle given its circumference Circumference ratios Perimeter involving rectangles and circles Area involving rectangles and circles Area between two concentric circles Word problem involving the area between two concentric circles Area involving inscribed figures Vertices, edges, and faces of a solid Volume of a rectangular prism made of unit cubes Volume of a solid made of cubes with unit fraction edge lengths Volume of a rectangular prism with fractional edge lengths Word problem involving the volume of a rectangular prism Word problem involving the rate of filling or emptying a rectangular prism Volume of a piecewise rectangular prism Word problem involving the volume of a triangular prism Nets of solids Surface area of a rectangular prism made of unit cubes Using a net to find the surface area of a rectangular prism Word problem involving the surface area of a rectangular prism Surface area of a piecewise rectangular prism made of unit cubes Computing a percentage from a table of values Comparing measures of center and variation Using box-and-whisker plots to compare data sets Comparing sample means Assessing the degree of overlap of two distributions Interpreting a tree diagram Introduction to the probability of an event Introduction to expectation Probability of independent events Probability of dependent events 5: Use appropriate tools strategically. 6: Attend to precision. Finding the percentage of a grid that is shaded Finding a percentage of a whole number Finding the sale price given the original price and percent discount Graphing a linear inequality on the number line Measuring an angle with the protractor Drawing an angle with the protractor Creating triangles from given side lengths: Problem type 1 Creating triangles from given side lengths: Problem type 2 Drawing triangles with given conditions: Angle measures Drawing triangles with given conditions: Side lengths and angle measures Drawing triangles with given side lengths using a compass Volume of a rectangular prism made of unit cubes Identifying outcomes in a random number table used to simulate a compound event Using a random number table to simulate a compound event Division involving zero ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 17/19

18 Word problem with division of whole numbers and rounding 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 Addition and subtraction with 3 integers Addition and subtraction with 4 or 5 integers Integer multiplication and division Multiplication of 3 or 4 integers Order of operations with integers Area of a square or a rectangle Volume of a rectangular prism Identifying equivalent signed fractions Signed fraction multiplication: Basic Signed fraction multiplication: Advanced Signed fraction division Signed fraction addition or subtraction: Basic Signed fraction subtraction involving double negation Signed fraction addition or subtraction: Advanced Addition and subtraction of 3 fractions involving signs Signed decimal addition and subtraction Signed decimal addition and subtraction with 3 numbers Signed decimal multiplication Signed decimal division 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 Converting a fraction or mixed number to a rounded decimal Word problem with powers of ten Finding a percentage of a whole number without a calculator: Basic Finding a percentage of a whole number without a calculator: Advanced Finding a percentage of a total amount without a calculator: Sales tax, commission, discount Estimating a tip without a calculator Writing a ratio as a percentage without a calculator Finding the sale price without a calculator given the original price and percent discount Finding simple interest without a calculator Multiplying a constant and a linear monomial Area of a rectangle involving fractions Area of a rectangle involving mixed numbers and fractions Distinguishing between the area and perimeter of a rectangle Area of a triangle Area of a parallelogram Area of a trapezoid Circumference of a circle Finding the radius or the diameter of a circle given its circumference Area of a circle Circumference and area of a circle ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 18/19