7th grade Mathematics Improvement. Correlation of the ALEKS course RtI 7 to the related CCSS standards for grades 3 through 7 (2010)

Transcription

1 7th grade Mathematics Improvement Correlation of the ALEKS course RtI 7 to the related CCSS standards for grades 3 through 7 (2010) Number & Operations - Whole Numbers Place value and rounding 4.NBT.A.1: 4.NBT.A.2: 4.NBT.A.3: 4.NBT.B.4: 3.OA.A.2: = ALEKS course topic that addresses the standard Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that = 10 by applying concepts of place value and division. Whole number place value: Problem type 1 Whole number place value: Problem type 2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Expanded form Expanded form with zeros Numeral translation: Problem type 1 Numeral translation: Problem type 2 Introduction to inequalities Use place value understanding to round multi-digit whole numbers to any place. Addition and subtraction Rounding to tens or hundreds Rounding to hundreds or thousands Rounding to thousands, ten thousands, or hundred thousands Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiplication and division Addition of 3 or 4 one-digit numbers Adding a 2-digit number and a 1-digit number with carry Addition without carry Addition with carry Addition with carry to the hundreds place Addition of large numbers Subtracting a 1-digit number from a 2-digit number Subtraction without borrowing Subtraction with borrowing Adding or subtracting 10, 100, or 1000 Subtraction with multiple regrouping steps Subtraction and regrouping with zeros Interpret whole-number quotients of whole numbers, e.g., interpret 56 8 as the number of ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/18

2 3.OA.A.4: 3.OA.B.5: 5.NBT.B.5: 6.NS.B.2: objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as Word problem on quotient and remainder Word problem with multiplication or division of whole numbers Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8? = 48, 5 = _ 3, 6 6 =?. One-digit multiplication Division facts Introduction to solving an equation with multiplication or division Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = = 56. (Distributive property.) Introduction to properties of multiplication Fact families for multiplication and division Fluently multiply multi-digit whole numbers using the standard algorithm. Multiplication without carry Multiplication with carry Introduction to multiplication of large numbers Multiplication of large numbers Fluently divide multi-digit numbers using the standard algorithm. Division without carry Division with carry Division with trailing zeros: Problem type 1 Division with trailing zeros: Problem type 2 Division involving quotients with intermediate zeros Quotient and remainder: Problem type 1 Quotient and remainder: Problem type 2 Quotient and remainder: Problem type 3 Factors and multiples 4.OA.B.4: 6.NS.B.4: Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite. Multiples: Problem type 1 Multiples: Problem type 2 Factors Prime numbers Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4 (9 + 2). ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/18

3 Applying operations 4.OA.A.3: 4.OA.C.5: 5.OA.A.1: Greatest common factor of 2 numbers Least common multiple of 2 numbers Understanding the distributive property Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Word problem with division of whole numbers and rounding Word problem with multiplication and addition or subtraction of whole numbers Estimating a product Estimating a quotient Writing a one-step expression for a real-world situation Translating a sentence into a one-step equation Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Finding the next terms of a sequence with whole numbers Finding patterns in shapes Function tables with one-step rules Describing an increasing or decreasing pattern from a table of values Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Introduction to parentheses Order of operations with whole numbers and grouping symbols Number & Operations - Fractions 3.NF.A.1: 3.NF.A.2.B: 3.NF.A.3.D: = ALEKS course topic that addresses the standard Understanding, ordering, and equivalent fraction Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Introduction to fractions Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. Fractional position on a number line Plotting fractions on a number line Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 3/18

4 4.NF.A.1: 4.NF.A.2: conclusions, e.g., by using a visual fraction model. Ordering fractions with the same denominator Ordering fractions with the same numerator Explain why a fraction a/b is equivalent to a fraction (n a)/(n b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Understanding equivalent fractions Equivalent fractions Introduction to simplifying a fraction Simplifying a fraction Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Using a common denominator to order fractions Addition and subtraction 4.NF.B.3.A: 4.NF.B.3.C: 5.NF.A.1: 5.NF.B.4.A: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Addition or subtraction of fractions with the same denominator Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Addition or subtraction of mixed numbers with the same denominator Addition of mixed numbers with the same denominator and carry Subtraction of mixed numbers with the same denominator and borrowing Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/ /12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Multiplication and division Addition or subtraction of unit fractions Introduction to addition or subtraction of fractions with different denominators Addition or subtraction of fractions with different denominators Addition or subtraction of mixed numbers with different denominators Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. For example, use a visual fraction model to show (2/3) 4 = 8/3, and create a story context for this equation. Do the same with (2/3) (4/5) = 8/15. (In general, (a/b) (c/d) = ac/bd.) Product of a unit fraction and a whole number Product of a fraction and a whole number: Problem type 1 Introduction to fraction multiplication Fraction multiplication Mixed number multiplication: Problem type 1 ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 4/18

5 6.NS.A.1: Mixed number multiplication: Problem type 2 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Division involving a whole number and a fraction Fraction division Mixed number division Number & Operations - Decimals Decimals 4.NF.C.6: 5.NBT.A.1: 5.NBT.A.2: 5.NBT.A.3.B: 5.NBT.A.4: 6.NS.B.3: = ALEKS course topic that addresses the standard Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Writing a decimal and a fraction for a shaded region Converting a decimal to a fraction: Basic Converting a decimal to a proper fraction in simplest form: Advanced Converting a fraction with a denominator of 10, 100, or 1000 to a decimal Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Whole number place value: Problem type 1 Whole number place value: Problem type 2 Decimal place value: Tenths and hundredths Decimal place value: Hundreds to ten thousandths Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Multiplication by 10, 100, and 1000 Multiplication with trailing zeros: Problem type 1 Multiplication of a decimal by a power of ten Division of a decimal by a power of ten Power of 10: Positive exponent Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Introduction to ordering decimals Ordering decimals Use place value understanding to round decimals to any place. Rounding decimals Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/18

6 each operation. Addition of aligned decimals Decimal addition with 3 numbers Subtraction of aligned decimals Multiplication of a decimal by a whole number Decimal multiplication: Problem type 1 Decimal multiplication: Problem type 2 Division of a decimal by a whole number Division of a decimal by a 2-digit decimal Ratios & Proportional Relationships 6.RP.A.1: 6.RP.A.3: 6.RP.A.3.B: 6.RP.A.3.C: 6.RP.A.3.D: = ALEKS course topic that addresses the standard Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." Writing ratios for real-world situations Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Word problem on unit rates associated with ratios of whole numbers: Decimal answers Solving a word problem on proportions using a unit rate Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Finding a percentage of a whole number without a calculator: Basic Applying the percent equation Finding the sale price without a calculator given the original price and percent discount Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Conversions involving measurements in feet and inches Adding measurements in feet and inches U.S. Customary unit conversion with whole number values U.S. Customary unit conversion with whole number values: Two-step conversion U.S. Customary unit conversion with mixed number values: One-step conversion U.S. Customary unit conversion with mixed number values: Two-step conversion Metric distance conversion with whole number values Metric mass or capacity conversion with whole number values Metric distance conversion with decimal values Metric conversion with decimal values: Two-step problem Converting between metric and U.S. Customary unit systems Time unit conversion with whole number values ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 6/18

7 Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.RP.A.3: 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 without a calculator: Basic Writing a ratio as a percentage without a calculator Finding the sale price without a calculator given the original price and percent discount Finding the percentage increase or decrease: Advanced Finding simple interest without a calculator Computing a percentage from a table of values Rational Numbers 6.NS.C.5: 6.NS.C.6: 6.NS.C.6.C: 6.NS.C.7: 6.NS.C.7.A: 6.NS.C.7.C: = ALEKS course topic that addresses the standard Apply and extend previous understandings of numbers to the system of rational numbers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Writing a signed number for a real-world situation Reading the temperature from a thermometer Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Fractional position on a number line Plotting fractions on a number line Plotting integers on a number line Reading a point in quadrant 1 Reading a point in the coordinate plane Plotting a point in quadrant 1 Plotting a point in the coordinate plane Understand ordering and absolute value of rational numbers. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret 3 > 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right. Ordering integers Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 7/18

8 7.NS.A.1: 7.NS.A.1.D: 7.NS.A.2: 7.NS.A.2.A: 7.NS.A.2.B: 7.NS.A.2.D: 7.NS.A.3: situation. For example, for an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars. Absolute value of a number 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. Apply properties of operations as strategies to add and subtract rational numbers. 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 Signed fraction addition or subtraction: Basic 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 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. Integer multiplication and division Identifying numbers as integers or non-integers 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 Converting a fraction to a repeating decimal Converting a mixed number to a decimal Solve real-world and mathematical problems involving the four operations with rational numbers. Fractional part of a circle Multi-step word problem involving fractions and multiplication Mixed arithmetic operations with fractions Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Word problem with multiple decimal operations: Problem type 1 Word problem with multiple decimal operations: Problem type 2 Word problem with addition or subtraction of integers Order of operations with integers ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 8/18

9 Geometry & Measurement 3.MD.A.1: 3.MD.C.6: 4.MD.A.2: 4.MD.A.3: = ALEKS course topic that addresses the standard Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Telling time Introduction to adding time Introduction to elapsed time Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Perimeter and area on a grid Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Addition with money Subtraction with money Conversions involving measurements in feet and inches Adding measurements in feet and inches Introduction to adding time Adding time Introduction to elapsed time Elapsed time Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Perimeter of a square or a rectangle Sides of polygons having the same perimeter Perimeter of a piecewise rectangular figure Area of a square or a rectangle Distinguishing between the area and perimeter of a rectangle Areas of rectangles with the same perimeter Area of a piecewise rectangular figure Geometric measurement: understand concepts of angle and measure angles. ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 9/18

10 4.MD.C.6: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. Measuring an angle with the protractor Drawing an angle with the protractor Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.C.4: 5.MD.C.5: 5.MD.C.5.B: 4.G.A.1: 4.G.A.2: 4.G.A.3: 6.G.A.1: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Volume of a rectangular prism made of unit cubes Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Apply the formulas V = l w h and V = b h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Volume of a rectangular prism Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Acute, obtuse, and right angles Naming segments, rays, and lines Identifying parallel and perpendicular lines Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Acute, obtuse, and right triangles Identifying parallelograms, rectangles, and squares Properties of quadrilaterals Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Drawing lines of symmetry Solve real-world and mathematical problems involving area, surface area, and volume. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Area of a triangle Area of a piecewise rectangular figure Area of a parallelogram Area of a trapezoid Area involving rectangles and triangles ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 10/18

11 Expressions & Equations 6.EE.A.1: 6.EE.A.2: 6.EE.A.2.C: 6.EE.A.3: 6.EE.B.6: 6.EE.B.7: 6.EE.B.8: = ALEKS course topic that addresses the standard Apply and extend previous understandings of arithmetic to algebraic expressions. Write and evaluate numerical expressions involving whole-number exponents. Introduction to exponents Writing expressions using exponents Order of operations with whole numbers and exponents: Basic Power of 10: Positive exponent Write, read, and evaluate expressions in which letters stand for numbers. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s 3 and A = 6s 2 to find the volume and surface area of a cube with sides of length s = 1/2. Evaluating an algebraic expression: Whole number addition or subtraction Evaluating an algebraic expression: Whole number multiplication or division Evaluating an algebraic expression: Whole numbers with two operations Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Distributive property: Whole number coefficients Reason about and solve one-variable equations and inequalities. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Writing a one-step expression for a real-world situation Writing a one-step variable expression for a real-world situation Translating a sentence into a one-step equation Solving a fraction word problem using a linear equation of the form Ax = B Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Additive property of equality with whole numbers Additive property of equality with decimals Additive property of equality with fractions and mixed numbers Introduction to solving an equation with multiplication or division Multiplicative property of equality with whole numbers Solving a fraction word problem using a linear equation of the form Ax = B Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Translating a sentence by using an inequality symbol Graphing a linear inequality on the number line ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 11/18

12 Analyze and solve linear equations and pairs of simultaneous linear equations. 8.EE.C.7: 8.EE.C.7.B: Solve linear equations in one variable. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Additive property of equality with integers Multiplicative property of equality with whole numbers Multiplicative property of equality with integers Solving a two-step equation with integers Statistics & Probability Represent and interpret data. 3.MD.B.3: 6.SP.A.3: 6.SP.B.4: 6.SP.B.5: 6.SP.B.5.C: 7.SP.C.7: 7.SP.C.7.A: = ALEKS course topic that addresses the standard Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. Constructing a bar graph for non-numerical data Interpreting a pictograph table Interpreting a bar graph Interpreting a double bar graph Develop understanding of statistical variability. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Finding the mode and range of a data set Mean of a data set Summarize and describe distributions. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Constructing a histogram for numerical data Constructing a line plot Summarize numerical data sets in relation to their context, such as by: Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Mode of a data set Mean and median of a data set Investigate chance processes and develop, use, and evaluate probability models. 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. 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. 12/18

13 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. Outcomes and event probability Introduction to the probability of an event Probability of an 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 quotient and remainder Word problem with division of whole numbers and rounding Word problem with multiplication and addition or subtraction of whole numbers Order of operations with whole numbers Order of operations with whole numbers and grouping symbols Greatest common factor of 2 numbers Least common multiple of 2 numbers Understanding equivalent fractions Using a common denominator to order fractions Fractional part of a circle Multi-step word problem involving fractions and multiplication Fraction division Mixed arithmetic operations with fractions Ordering decimals Converting a decimal to a proper fraction in simplest form: Advanced Converting a fraction to a terminating decimal Converting a fraction to a repeating decimal Converting a mixed number to a decimal Addition with money Subtraction with money Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Word problem with multiple decimal operations: Problem type 1 Word problem with multiple decimal operations: Problem type 2 Sides of polygons having the same perimeter Perimeter of a piecewise rectangular figure Areas of rectangles with the same perimeter Area of a piecewise rectangular figure Area involving rectangles and triangles Adding measurements in feet and inches U.S. Customary unit conversion with whole number values: Two-step conversion U.S. Customary unit conversion with mixed number values: Two-step conversion Metric conversion with decimal values: Two-step problem Introduction to adding time Adding time Introduction to elapsed time Elapsed time Constructing a bar graph for non-numerical data ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 13/18

14 Interpreting a pictograph table Interpreting a bar graph Mean and median of a data set 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 Finding the sale price without a calculator given the original price and percent discount Finding the percentage increase or decrease: Advanced Finding simple interest without a calculator Computing a percentage from a table of values Outcomes and event probability Probability of an event Word problem with addition or subtraction of integers Order of operations with integers Solving a fraction word problem using a linear equation of the form Ax = B Function tables with one-step rules 2: Reason abstractly and quantitatively. Finding the next terms of a sequence with whole numbers Understanding equivalent fractions Equivalent fractions Simplifying a fraction Fractional position on a number line Plotting fractions on a number line Fractional part of a circle Product of a unit fraction and a whole number Writing a mixed number and an improper fraction for a shaded region Constructing a histogram for numerical data Constructing a bar graph for non-numerical data Constructing a line plot Interpreting a pictograph table Interpreting a bar graph Solving a word problem on proportions using a unit rate Word problem on proportions: Problem type 1 Writing a ratio as a percentage without a calculator Outcomes and event probability Introduction to the probability of an event Probability of an event Plotting integers on a number line Evaluating an algebraic expression: Whole number addition or subtraction Evaluating an algebraic expression: Whole number multiplication or division Evaluating an algebraic expression: Whole numbers with two operations Writing a one-step expression for a real-world situation Writing a one-step variable expression for a real-world situation Additive property of equality with whole numbers Additive property of equality with decimals Additive property of equality with fractions and mixed numbers Additive property of equality with integers Introduction to solving an equation with multiplication or division Multiplicative property of equality with whole numbers Multiplicative property of equality with integers Solving a two-step equation with integers ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 14/18

15 Translating a sentence into a one-step equation Solving a fraction word problem using a linear equation of the form Ax = B Translating a sentence by using an inequality symbol Graphing a linear inequality on the number line Function tables with one-step rules Reading a point in quadrant 1 Plotting a point in quadrant 1 3: Construct viable arguments and critique the reasoning of others. 4: Model with mathematics. Prime numbers Finding the next terms of a sequence with whole numbers Identifying parallelograms, rectangles, and squares Distinguishing between the area and perimeter of a rectangle Areas of rectangles with the same perimeter Finding patterns in shapes Identifying numbers as integers or non-integers Function tables with one-step rules Describing an increasing or decreasing pattern from a table of values Word problem on quotient and remainder Word problem with multiplication or division of whole numbers Word problem with multiplication and addition or subtraction of whole numbers Introduction to fractions Understanding equivalent fractions Fractional position on a number line Plotting fractions on a number line Fractional part of a circle Multi-step word problem involving fractions and multiplication Writing a mixed number and an improper fraction for a shaded region Addition with money Subtraction with money Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Word problem with multiple decimal operations: Problem type 1 Word problem with multiple decimal operations: Problem type 2 Perimeter and area on a grid Volume of a rectangular prism made of unit cubes U.S. Customary unit conversion with whole number values U.S. Customary unit conversion with mixed number values: One-step conversion Metric distance conversion with whole number values Metric mass or capacity conversion with whole number values Metric distance conversion with decimal values Writing ratios for real-world situations Solving a word problem on proportions using a unit rate Word problem on proportions: Problem type 1 Finding the percentage of a grid that is shaded Finding the sale price without a calculator given the original price and percent discount Finding the percentage increase or decrease: Advanced Finding simple interest without a calculator Computing a percentage from a table of values ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 15/18

16 Introduction to the probability of an event Word problem with addition or subtraction of integers Solving a fraction word problem using a linear equation of the form Ax = B Graphing a linear inequality on the number line Reading a point in quadrant 1 Power of 10: Positive exponent 5: Use appropriate tools strategically. 6: Attend to precision. Introduction to fractions Understanding equivalent fractions Fractional position on a number line Plotting fractions on a number line Writing a decimal and a fraction for a shaded region Measuring an angle with the protractor Drawing an angle with the protractor Perimeter and area on a grid Volume of a rectangular prism made of unit cubes Drawing lines of symmetry Measuring length to the nearest inch Measuring length to the nearest quarter or half inch Telling time 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 Graphing a linear inequality on the number line Reading a point in quadrant 1 Addition with carry to the hundreds place Adding or subtracting 10, 100, or 1000 Subtraction with multiple regrouping steps Word problem with addition or subtraction of whole numbers Multiplication with trailing zeros: Problem type 1 Multiplication of large numbers Division with trailing zeros: Problem type 1 Division with trailing zeros: Problem type 2 Division involving quotients with intermediate zeros Quotient and remainder: Problem type 1 Word problem on quotient and remainder Quotient and remainder: Problem type 2 Quotient and remainder: Problem type 3 Word problem with division of whole numbers and rounding Word problem with multiplication or division of whole numbers Introduction to inequalities Estimating a sum of whole numbers Estimating a difference of whole numbers Estimating a product Estimating a quotient Using a common denominator to order fractions Addition or subtraction of fractions with different denominators Introduction to fraction multiplication ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 16/18

17 Fraction multiplication Division involving a whole number and a fraction Fraction division Addition of mixed numbers with the same denominator and carry Subtraction of mixed numbers with the same denominator and borrowing Addition or subtraction of mixed numbers with different denominators Mixed number multiplication: Problem type 1 Mixed number multiplication: Problem type 2 Mixed number division Introduction to ordering decimals Converting a decimal to a proper fraction in simplest form: Advanced Converting a fraction to a terminating decimal Converting a fraction to a repeating decimal Converting a mixed number to a decimal Addition of aligned decimals Decimal addition with 3 numbers Subtraction of aligned decimals Estimating a decimal sum or difference Multiplication of a decimal by a power of ten Multiplication of a decimal by a whole number Decimal multiplication: Problem type 1 Decimal multiplication: Problem type 2 Division of a decimal by a power of ten Division of a decimal by a whole number Division of a decimal by a 2-digit decimal Naming segments, rays, and lines Choosing U.S. Customary measurement units Conversions involving measurements in feet and inches Adding measurements in feet and inches Choosing metric measurement units Finding a percentage of a whole number without a calculator: Basic Integer addition: Problem type 1 Integer addition: Problem type 2 Integer subtraction: Problem type 1 Integer subtraction: Problem type 2 Integer subtraction: Problem type 3 Integer multiplication and division Signed fraction addition or subtraction: Basic Signed decimal addition and subtraction Signed decimal addition and subtraction with 3 numbers Power of 10: Positive exponent 7: Look for and make use of structure. Expanded form Expanded form with zeros Understanding multiplication of a one-digit number with a larger number Introduction to parentheses Order of operations with whole numbers Order of operations with whole numbers and grouping symbols Introduction to properties of addition Introduction to properties of multiplication Understanding the distributive property ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 17/18

18 Fact families for addition and subtraction Fact families for multiplication and division Finding patterns in shapes Distributive property: Whole number coefficients 8: Look for and express regularity in repeated reasoning. Multiplication as repeated addition Multiples: Problem type 1 Multiples: Problem type 2 Greatest common factor of 2 numbers Least common multiple of 2 numbers Finding the next terms of a sequence with whole numbers Converting a fraction to a repeating decimal Finding patterns in shapes Describing an increasing or decreasing pattern from a table of values Writing expressions using exponents Power of 10: Positive exponent ALEKS - Copyright 2016 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 18/18