Middle School Math Course 2

Transcription

1 Middle School Math Course 2 Correlation of the ALEKS course Middle School Math Course 2 to the Indiana Academic Standards for Mathematics Grade 7 (2014) 1: NUMBER SENSE = ALEKS course topic that addresses the standard 7.NS.1: Find the prime factorization of whole numbers and write the results using exponents. Writing expressions using exponents Prime factorization 7.NS.2: Understand the inverse relationship between squaring and finding the square root of a perfect square integer. Find square roots of perfect square integers. Square root of a perfect square Finding all square roots of a number 7.NS.3: Know there are rational and irrational numbers. Identify, compare, and order rational and common irrational numbers ( 2, 3, 5, π) and plot them on a number line. Plotting rational numbers on a number line Ordering real numbers Identifying true statements about rational and irrational numbers Identifying numbers as rational or irrational 2: COMPUTATION = ALEKS course topic that addresses the standard 7.C.1: 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 7.C.2: 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. Word problem with addition or subtraction of integers ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/17

2 Computing the distance between two integers on a number line Computing and understanding distances between integers on a number line Finding a point on a number line given the length of a segment and another point Computing distances between decimals on a number line 7.C.3: 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. Integer multiplication and division Multiplication of 3 or 4 integers 7.C.4: Understand that integers can be divided, provided that the divisor is not zero, and that every quotient of integers (with non-zero divisor) is a rational number. Understand that if p and q are integers, then -(p/q) = (-p)/q = p/(-q). Division involving zero Integer multiplication and division Identifying equivalent signed fractions Identifying numbers as integers or non-integers 7.C.5: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. Word problem on unit rates associated with ratios of fractions Word problem on unit rates associated with ratios of mixed numbers 7.C.6: Use proportional relationships to solve ratio and percent problems with multiple operations, such as the following: simple interest, tax, markups, markdowns, gratuities, commissions, fees, conversions within and across measurement systems, percent increase and decrease, and percent error. Solving a word problem on proportions using a unit rate Word problem on proportions: Problem type 1 Converting between metric and U.S. Customary unit systems Writing a ratio as a percentage without a calculator Finding the rate of a tax or commission 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 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 Finding a percentage of a total amount in a circle graph Applying the percent equation: Problem type 1 Applying the percent equation: Problem type 2 Finding the total amount given the percentage of a partial amount 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 ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/17

3 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.C.7: Compute with rational numbers fluently using a standard algorithmic approach. 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 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 fraction multiplication: Basic Signed fraction multiplication: Advanced Signed fraction division 7.C.8: Solve real-world problems with rational numbers by using one or two operations. Word problem with addition or subtraction of integers Word problem with multiplication or division of integers Word problem involving addition or subtraction of fractions with different denominators Word problem involving addition or subtraction of mixed numbers with different denominators Word problem involving fractions and multiplication Multi-step word problem involving fractions and multiplication Word problem involving fractions and division Word problem involving multiplication or division with mixed numbers Word problem with addition or subtraction of 2 decimals 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 multiple decimal operations: Problem type 1 Word problem with multiplication of two decimals Word problem with division of a decimal and a whole number Word problem with multiple decimal operations: Problem type 2 Word problem with division of two decimals 3: ALGEBRA AND FUNCTIONS = ALEKS course topic that addresses the standard ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 3/17

4 7.AF.1: Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear expressions, including situations that involve factoring (e.g., given 2x - 10, create an equivalent expression 2(x - 5)). Justify each step in the process. Distributive property: Whole number coefficients Distributive property: Integer coefficients Distributive property: Fractional coefficients Factoring a linear binomial Combining like terms: Whole number coefficients Combining like terms: Integer coefficients Combining like terms: Decimal coefficients Combining like terms: Fractional coefficients Identifying equivalent algebraic expressions Using distribution and combining like terms to simplify: Univariate Identifying properties used to simplify an algebraic expression 7.AF.2: Solve equations of the form px + q= r and p(x + q) = r fluently, where p, q, and r are specific rational numbers. Represent real-world problems using equations of these forms and solve such problems. Using two steps to solve an equation with whole numbers Additive property of equality with a negative coefficient Solving a two-step equation with integers Introduction to solving an equation with parentheses Solving a 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 side lengths of rectangles given one dimension and an area or a perimeter 7.AF.3: Solve inequalities of the form px + q (> or ) r or px + q (< or ) r, where p, q, and r are specific rational numbers. Represent real-world problems using inequalities of these forms and solve such problems. Graph the solution set of the inequality and interpret it in the context of the problem. 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 7.AF.4: Define slope as vertical change for each unit of horizontal change and recognize that a constant rate of change or constant slope describes a linear function. ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 4/17

5 Identify and describe situations with constant or varying rates of change. Finding slope given the graph of a line in quadrant 1 that models a real-world situation Using right triangles to find the slope of a line Identifying linear functions given ordered pairs 7.AF.5: Graph a line given its slope and a point on the line. Find the slope of a line given its graph. Finding slope given the graph of a line on a grid Graphing a line given its slope and y-intercept Graphing a line through a given point with a given slope 7.AF.6: 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 7.AF.7: Identify the unit rate or constant of proportionality in tables, graphs, equations, 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 7.AF.8: Explain what the coordinates of a point on the graph of a proportional relationship mean 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 7.AF.9: Identify real-world and other mathematical situations that involve proportional relationships. Write equations and draw graphs to represent proportional relationships and recognize that these situations are described by a linear function in the form y = mx, where the unit rate, m, is the slope of the line. Making a table and plotting points given a unit rate Writing an equation to represent a proportional relationship ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/17

6 4: GEOMETRY AND MEASUREMENT = ALEKS course topic that addresses the standard 7.GM.1: Draw triangles (freehand, with ruler and protractor, and using technology) with given conditions from three measures of angles or sides, and notice when the conditions determine a unique triangle, more than one triangle, or no triangle. 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 7.GM.2: Identify and describe similarity relationships of polygons including the angle-angle criterion for similar triangles, and solve problems involving similarity. Identifying similar or congruent shapes on a grid Finding angle measures of a triangle given two angles of a similar triangle Finding angle measures and side ratios to determine if two triangles are similar 7.GM.3: Solve real-world and other mathematical problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing. Create a scale drawing by using proportional reasoning. 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 7.GM.4: Solve real-world and other mathematical problems that involve vertical, adjacent, complementary, and supplementary angles. Finding an angle measure in a figure with a right or straight angle Finding supplementary and complementary angles Solving an equation involving complementary or supplementary angles Finding angle measures given two intersecting lines Solving equations involving vertical angles 7.GM.5: Understand the formulas for area and circumference of a circle and use them to solve real-world and other mathematical problems; give an informal derivation of the relationship between circumference and area of a circle. Circumference of a circle Finding the radius or the diameter of a circle given its circumference Circumference ratios Area of a circle Circumference and area of a circle Distinguishing between the area and circumference of a circle ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 6/17

7 7.GM.6: Solve real-world and other mathematical problems involving volume of cylinders and three-dimensional objects composed of right rectangular prisms. Volume of a piecewise rectangular prism Word problem involving the volume of a piecewise rectangular prism Volume of a cylinder Word problem involving the volume of a cylinder 7.GM.7: Construct nets for right rectangular prisms and cylinders and use the nets to compute the surface area; apply this technique to solve real-world and other mathematical problems. Nets of solids 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 cylinder Surface area of a cylinder: Exact answers in terms of pi Word problem involving the surface area of a cylinder 5: DATA ANALYSIS, STATISTICS, AND PROBABILITY = ALEKS course topic that addresses the standard 7.DSP.1: Understand that statistics can be used to gain information about a population by examining a sample of the population and 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 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 7.DSP.2: Use data from a random sample to draw inferences about a population. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. Introduction to expectation Comparing sample means 7.DSP.3: Find, use, and interpret measures of center (mean and median) and measures of spread (range, interquartile range, and mean absolute deviation) for numerical data from random samples to draw comparative inferences about two populations. Mean of a data set Mean and median of a data set Comparing measures of center and variation Using back-to-back stem-and-leaf plots to compare data sets Five-number summary and interquartile range Using box-and-whisker plots to compare data sets ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 7/17

8 Computing mean absolute deviation from a list of numerical values 7.DSP.4: Make observations about the degree of visual overlap of two numerical data distributions represented in line plots or box plots. Describe how data, particularly outliers, added to a data set may affect the mean and/or median. How changing a value affects the mean and median Assessing the degree of overlap of two distributions Finding outliers in a data set 7.DSP.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Understand that 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. Understand that a probability of 1 indicates an event certain to occur and a probability of 0 indicates an event impossible to occur. Classifying likelihood Introduction to the probability of an event Probability involving one die or choosing from n distinct objects Probability involving choosing from objects that are not distinct Understanding likelihood 7.DSP.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its relative frequency from a large sample. Experimental and theoretical probability 7.DSP.7: Develop probability models that include the sample space and probabilities of outcomes to represent simple events with equally likely outcomes. Predict the approximate relative frequency of the event based on the model. Compare probabilities from the model to observed frequencies; evaluate the level of agreement and explain possible sources of discrepancy. Determining a sample space and outcomes for a simple event Experimental and theoretical probability Outcomes and event probability Process Standards for Mathematics = 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: Problem type 2 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 ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 8/17

9 Word problem with addition or subtraction of integers Operations with absolute value: Problem type 1 Operations with absolute value: Problem type 2 Computing the distance between two integers on a number line Computing and understanding distances between integers on a number line Word problem with multiplication or division of integers Order of operations with integers Identifying equivalent signed fractions 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 fractions and multiplication Multi-step word problem involving fractions and multiplication Word problem involving fractions and division Word problem involving multiplication or division with mixed numbers Finding a point on a number line given the length of a segment and another point Computing distances between decimals on a 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 multiple decimal operations: Problem type 1 Word problem with multiplication of two decimals Word problem with division of a decimal and a whole number Word problem with multiple decimal operations: Problem type 2 Word problem with division of two decimals 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 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 Writing a ratio as a percentage without a calculator Finding the rate of a tax or commission 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 Finding a percentage of a total amount: Real-world situations ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 9/17

10 Finding a percentage of a total amount without a calculator: Sales tax, commission, discount Estimating a tip without a calculator Finding a percentage of a total amount in a circle graph Applying the percent equation: Problem type 1 Applying the percent equation: Problem type 2 Finding the total amount given the percentage of a partial amount 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 Factoring a linear binomial Combining like terms: Whole number coefficients Combining like terms: Decimal coefficients Combining like terms: Fractional coefficients 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 equations 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 Finding outputs and rate of increase given the graph of a line that models a real-world situation Finding an angle measure in a figure with a right or straight angle Solving an equation involving complementary or supplementary angles Writing and 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 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 10/17

11 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 Areas of rectangles with the same perimeter Word problem involving the area of a rectangle: Problem type 2 Writing algebraic expressions for the area of a figure Finding side lengths of rectangles given one dimension and an area or a perimeter Finding the perimeter or area of a rectangle given one of these values Finding the perimeter or area of a rectangle in the coordinate plane Finding the area of a trapezoid on a grid by using triangles and rectangles Area of a piecewise rectangular figure Area between two rectangles Word problem involving the area between two rectangles Area involving rectangles and triangles 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 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 Using a net to find the lateral surface area and total 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 Introduction to expectation 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 Probability involving one die or choosing from n distinct objects Probability involving choosing from objects that are not distinct Understanding likelihood ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 11/17

12 Experimental and theoretical probability Determining a sample space and outcomes for a compound event Outcomes and event probability Probabilities involving two dice Identifying outcomes in a random number table used to simulate a compound event Using a random number table to simulate a compound event Generating a random number table with technology to simulate a compound event 2: Reason abstractly and quantitatively. Additive property of equality with whole numbers Translating a sentence into a one-step equation Plotting rational numbers on a number line Fractional part of a circle 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 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 Solving a two-step equation with signed decimals Identifying properties used to solve a linear equation 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 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 Writing an equation to represent a proportional relationship Solving an equation involving complementary or supplementary angles Writing and solving an equation involving complementary or supplementary angles Solving equations involving vertical angles Writing algebraic expressions for the perimeter of a figure Writing algebraic expressions for the area of a figure Finding side lengths of rectangles given one dimension and an area or a perimeter Writing equivalent expressions for the volume of a rectangular prism Constructing a frequency distribution and a histogram ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 12/17

13 Assessing the degree of overlap of two distributions Interpreting a tree diagram Introduction to the probability of an event Probability involving one die or choosing from n distinct objects Probability involving choosing from objects that are not distinct Experimental and theoretical probability Outcomes and event probability Probabilities involving two dice 3: Construct viable arguments and critique the reasoning of others. 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 4: Model with mathematics. 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 Word problem with addition or subtraction of integers Computing and understanding distances between integers on a number line Word problem with multiplication or division of integers 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 fractions and multiplication Multi-step word problem involving fractions and multiplication Word problem involving fractions and division Word problem involving multiplication or division with mixed numbers Finding a point on a number line given the length of a segment and another point Computing distances between decimals on a 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 multiple decimal operations: Problem type 1 Word problem with multiplication of two decimals Word problem with division of a decimal and a whole number Word problem with multiple decimal operations: Problem type 2 Word problem with division of two decimals Finding a unit price Using tables to compare ratios ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 13/17

14 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 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 Writing a ratio as a percentage without a calculator Finding the rate of a tax or commission 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 Finding a percentage of a total amount in a circle graph Finding the total amount given the percentage of a partial amount 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 Creating triangles from given side lengths: Problem type 1 Creating triangles from given side lengths: Problem type 2 Drawing a circle with a given radius or diameter Drawing and identifying a polygon in the coordinate plane Word problem involving the area of a rectangle: Problem type 2 Finding side lengths of rectangles given one dimension and an area or a perimeter Finding the perimeter or area of a rectangle given one of these values Finding the perimeter or area of a rectangle in the coordinate plane Finding the area of a triangle or parallelogram in the coordinate plane ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 14/17

15 Finding the area of a trapezoid on a grid by using triangles and rectangles Area between two rectangles Word problem involving the area between two rectangles Finding the area of a trapezoid, rhombus, or kite 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 Nets of solids 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 piecewise rectangular prism Word problem involving the volume of a triangular prism Surface area of a rectangular prism made of unit cubes Using a net to find the surface area of a rectangular prism Using a net to find the lateral surface area and total 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 Introduction to expectation 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 Probability of independent events Probability of dependent events 5: Use appropriate tools strategically. 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 ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 15/17

16 Generating a random number table with technology to simulate a compound event 6: Attend to precision. Area of a rectangle with one-digit side lengths Area of a rectangle with two-digit by one-digit side lengths Division involving zero Word problem with division of whole numbers and rounding: Problem type 2 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 Identifying equivalent signed fractions 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 fraction multiplication: Basic Signed fraction multiplication: Advanced Signed fraction division 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 Writing a ratio as a percentage without a calculator 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 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 with fractional side lengths Area of a rectangle involving mixed number and fractional side lengths Distinguishing between the area and perimeter of a rectangle Area of a parallelogram Area of a triangle Area of a trapezoid Circumference of a circle ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 16/17

17 Finding the radius or the diameter of a circle given its circumference Area of a circle Circumference and area of a circle Distinguishing between the area and circumference of a circle Volume of a rectangular prism Volume of a triangular prism Surface area of a cube or a rectangular prism Distinguishing between surface area and volume Surface area of a triangular prism Choosing an appropriate method for gathering data: Problem type 1 7: Look for and make use of structure. Operations with absolute value: Problem type 1 Operations with absolute value: Problem type 2 Introduction to the distributive property Understanding the distributive property Distributive property: Whole number coefficients Distributive property: Integer coefficients Distributive property: Fractional coefficients Factoring a linear binomial Introduction to properties of addition Combining like terms: Whole number coefficients Properties of addition Introduction to properties of multiplication Properties of real numbers Combining like terms: Integer coefficients Combining like terms: Decimal coefficients Combining like terms: Fractional coefficients Identifying parts in an algebraic expression Identifying equivalent algebraic expressions 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 Identifying proportional relationships in tables by calculating unit rates: Whole numbers 8: Look for and express regularity in repeated reasoning. Power of 10: Positive exponent Least common multiple of 2 numbers Converting a fraction to a repeating decimal: Basic Converting a fraction to a repeating decimal: Advanced Writing a function rule given a table of ordered pairs: One-step rules ALEKS - Copyright 2017 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 17/17