mathematics ged® test assessment target...

MATHEMATICS GED® Test Assessment Target Correlations

Lesson Number Lesson GED® Test Content

Topics and Practices Common Core State Standards (CCSS) College and Career Readiness Standards

1.1 Order Rational Numbers on a Number Line

Q.1.a, Q.1.d, Q.2.a (print only), MP.1, MP.2, MP.4

4.NF.2 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. (print only);

6.NS.6 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. (print only);

6.NS.7 Understand ordering and absolute value of rational numbers;

7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and sub-traction on a horizontal or vertical number line diagram (print only);

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers (print only);

M.1 Make sense of problems and persevere in solving them;

M.2 Reason abstractly and quantitatively (print only);

M.4 Model with mathematics (print only);

M.5 Use appropriate tools strategically (online only);

M.7 Look for and make use of structure (print only)

CCSS4.NF.2 Compare two fractions with different numerators and different denomi-nators, e.g., by creating common denominators or numerators, or by com-paring 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. (print only);

CCSS6.NS.6 Understand a rational num-ber 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. (print only);

CCSS6.NS.7 Understand ordering and absolute value of rational numbers;

CCSS7.NS.1 Apply and extend previous understandings of addition and subtrac-tion to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram (print only);

CCSS7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers (print only);

CCSSM.1 Make sense of problems and persevere in solving them;

CCSSM.2 Reason abstractly and quantita-tively (print only);

CCSSM.4 Model with mathematics (print only);

Program: CCA MathematicsFinal Pass

Vendor: Six Red Marbles Component: GED Online Correlations Chart

MATHEMATICS GED® Test Assessment Target Correlations 1

GED®, GED TESTING SERVICE®, and GED PLUS® are registered trademarks owned by American Council on Education (“ACE”). This material is not endorsed or approved by ACE or the GED Testing Service. Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.

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CCSSM.5 Use appropriate tools strategi-cally (online only);

CCSSM.7 Look for and make use of struc-ture (print only)

1.2 Apply Number Properties Q.1.b, Q.2.a, Q.2.d, Q.2.e, Q.3.d (print only), MP.1, MP.2, MP.3 (online only), MP.4

6.NS.4 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 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor;

7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and sub-traction on a horizontal or vertical number line diagram;

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers;

7.NS.3 Solve real-world and mathematical prob-lems involving the four operations with rational numbers;

M.1 Make sense of problems and persevere in solving them (print only);

M.4 Model with mathematics;


M.7 Look for and make use of structure (online only)

CCSS6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common mul-tiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor;

CCSS7.NS.1 Apply and extend previous understandings of addition and subtrac-tion to add and subtract rational num-bers; represent addition and subtraction on a horizontal or vertical number line diagram;

CCSS7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers;

CCSS7.NS.3 Solve real-world and math-ematical problems involving the four operations with rational numbers;

CCSSM.1 Make sense of problems and persevere in solving them (print only);

CCSSM.4 Model with mathematics;


CCSSM.7 Look for and make use of struc-ture (online only)









1.3 Compute with Exponents Q.1.c, Q.2.a, Q.2.b, Q.2.c, Q.2.e, MP.1, MP.2, MP.3, MP.4, MP.5 (online only)

8.EE.1 Know and apply the properties of inte-ger exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1 __

33 = 1 __ 27

;

8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √  2 is irrational (print only);

8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to esti-mate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger;

8.EE.4 Perform operations with numbers expressed in scientific notation, including prob-lems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millime-ters per year for seafloor spreading). Interpret scientific notation that has been generated by technology;


M.2 Reason abstractly and quantitatively (online only);



M.7 Look for and make use of structure;

CCSS8.EE.1 Know and apply the prop-erties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1 __

33 = 1 __ 27

;

CCSS8.EE.2 Use square root and cube root symbols to represent solutions to equa-tions of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √  2 is irrational (print only);

CCSS8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger;

CCSS8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific nota-tion that has been generated by technology;


CCSSM.2 Reason abstractly and quantita-tively (online only);











M.8 Look for and express regularity in repeated reasoning (online only)

CCSSM.7 Look for and make use of structure;

CCSSM.8 Look for and express regularity in repeated reasoning (online only)

1.4 Compute with Roots Q.1.c, Q.2.a, Q.2.b, Q.2.c, Q.2.e, MP.1, MP.2, MP.3 (online only), MP.4

8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1 __

33 = 1 __ 27 ;

8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √  2 is irrational;

8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational num-bers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √  2 , show that √  2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations (print only);

N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5;

N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents;


M.2 Reason abstractly and quantitatively;

CCSS8.EE.1 Know and apply the prop-erties of integer exponents to generate equivalent numerical expressions. For example, example, 32 × 3–5 = 3–3 = 1 __

33 = 1 __ 27 ;

CCSS8.EE.2 Use square root and cube root symbols to represent solutions to equa-tions of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational;

CCSS8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √  2 , show that √  2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get bet-ter approximations (print only);

CCSSN-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5;












M.6 Attend to precision (online only);

M.7 Look for and make use of structure (print only);

M.8 Look for and express regularity in repeated reasoning (print only)

CCSSM.2 Reason abstractly and quantitatively;



CCSSM.6 Attend to precision (online only);

CCSSM.7 Look for and make use of struc-ture (print only);

CCSSM.8 Look for and express regularity in repeated reasoning (print only)

2.1 Apply Ratio and Proportions

Q.2.a (online only), Q.3.a, Q.3.b, Q.3.c, MP.1, MP.2, MP.3 (print only), MP.4, MP.5 (print only)

6.RP.1 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.”;

6.RP.2 Understand the concept of a unit rate a __ b  

associated with a ratio a:b with b≠0, and use rate language in the context of a ratio relationship.For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3 __

4 cup of flour

for each cup of sugar.” “We paid $75 for 15 ham-burgers, which is a rate of $5 per hamburger.”;

6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reason-ing about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations;

7.RP.1 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 frac-tion

1 __ 2 _

1 __ 4 miles per hour, equivalently 2 miles per hour;

CCSS6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quanti-ties. 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.”;

CCSS6.RP.2 Understand the concept of a unit rate a __

b   associated with a ratio a:b with

b≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3 __

4 cup of flour

for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”;

CCSS6.RP.3 Use ratio and rate reason-ing to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations;









7.RP.2 Recognize and represent proportional relationships between quantities (print only);

7.G.1 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;

N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formu-las; choose and interpret the scale and the origin in graphs and data displays (print only);

G-MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios) (print only);






CCSS7.RP.1 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 com-plex fraction

1 __ 2 _

1 __ 4 miles per hour, equivalently

2 miles per hour;

CCSS7.RP.2 Recognize and represent pro-portional relationships between quantities (print only);

CCSS7.G.1 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;

CCSSN-Q.1 Use units as a way to under-stand problems and to guide the solution of multi-step problems; choose and inter-pret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays (print only);






2.2 Calculate Real-World Percents

Q.2.a, Q.2.e, Q.3.d, MP.1, MP.2, MP.3, MP.4, MP.5

6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reason-ing about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations;

CCSS6.RP.3 Use ratio and rate reason-ing to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations;









7.RP.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;

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers;

7.EE.3 Solve multi-step real-life and mathemati-cal 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 estima-tion 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 $27.50. 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;



M.5 Use appropriate tools strategically;

M.6 Attend to precision (print only)

CCSS7.RP.3 Use proportional relation-ships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error;

CCSS7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers;

CCSS7.EE.3 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 $27.50. 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;



CCSSM.5 Use appropriate tools strategically;

CCSSM.6 Attend to precision (print only)









2.3 Use Counting Techniques Q.2.a, Q.8.a, MP.1, MP.2, MP.4

7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation;

S-CP.9 Use permutations and combinations to compute probabilities of compound events and solve problems;



M.3 Construct viable arguments and critique the reasoning of others;



M.6 Attend to precision;

M.7 Look for and make use of structure

CCSS7.SP.8 Find probabilities of com-pound events using organized lists, tables, tree diagrams, and simulation;



CCSSM.3 Construct viable arguments and critique the reasoning of others;



CCSSM.6 Attend to precision;

CCSSM.7 Look for and make use of structure

2.4 Determine Probability Q.2.a (online only), Q.8.a, Q.8.b, MP.1, MP.2, MP.4, MP.5 (online only)

7.SP.1 Understand that statistics can be used to gain information about a population by examin-ing 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 pro-duce representative samples and support valid inferences (online only);

7.SP.5 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, aprobability around 1 __

2 indicates an event that is

neither unlikely nor likely, and a probability near1 indicates a likely event;

CCSS7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a popu-lation from a sample are valid only if the sample is representative of that popula-tion. Understand that random sampling tends to produce representative samples and support valid inferences (online only);

CCSS7.SP.5 Understand that the probabil-ity 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;









7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run rela-tive frequency, and predict the approximate rela-tive 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 (online only);

7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabili-ties from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy;

7.SP.8 Find probabilities of compound events using organized lists, tables,tree diagrams, and simulation (online only);

S-CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”);

S-CP.2 Understand that two events A and B are independent if the probability of A and B occur-ring together is the product of their probabilities, and use this characterization to determine if they are independent;

S-MD.7 Analyze decisions and strategies using probability concepts (e.g., product testing, medi-cal testing, pulling a hockey goalie at the end of a game) (online only);




M.5 Use appropriate tools strategically

CCSS7.SP.6 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 (online only);

CCSS7.SP.7 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;

CCSS7.SP.8 Find probabilities of com-pound events using organized lists, tables, tree diagrams, and simulation (online only);




CCSSM.5 Use appropriate tools strategically









3.1 Evaluate Linear Expressions

A.1.a, A.1.b, A.1.c, MP.1, MP.2, MP.3 (online only), MP.4

6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers;

6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a vari-able can represent an unknown number, or, depending on the purpose at hand, any number in a specified set (print only);

7.EE.1 Apply properties of operations as strate-gies to add, subtract, factor, and expand linear expressions with rational coefficients;

7.EE.2 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 + 0.05a = 1.05a means that “increase by 5%” is the same as “multi-ply by 1.05.” (print only);

A-SSE.1 Interpret expressions that represent a quantity in terms of its context;

A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a dif-ference of squares that can be factored as (x2 - y2)(x2 + y2) (online only);






CCSS6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers;

CCSS6.EE.6 Use variables to represent numbers and write expressions when solv-ing 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 speci-fied set (print only);

CCSS7.EE.1 Apply properties of opera-tions as strategies to add, subtract, factor, and expand linear expressions with ratio-nal coefficients;

CCSS7.EE.2 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 + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” (print only);

CCSSA-SSE.1 Interpret expressions that represent a quantity in terms of its context;

CCSSA-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2) (online only);














3.2 Solve Linear Equations A.2.a, A.2.b, A.2.c, MP.1, MP.2, MP.3, MP.4, MP.5

7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and con-struct simple equations and inequalities to solve problems by reasoning about the quantities;

8.EE.7 Solve linear equations in one variable;

A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions;

A-REI.1 Explain each step in solving a simple equation as following from the equality of num-bers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method;

A-REI.3 Solve linear equations and inequalities in one variable, including equations with coeffi-cients represented by letters;



M.6 Attend to precision

CCSS7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by rea-soning about the quantities;

CCSS8.EE.7 Solve linear equations in one variable;

CCSSA-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions;

CCSSA-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previ-ous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method;

CCSSA-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters;



CCSSM.6 Attend to precision









3.3 Solve Linear Inequalities A.3.a, A.3.b, A.3.c, A.3.d, MP.1, MP.2, MP.4

6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a speci-fied set makes an equation or inequality true;

6.EE.8 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;



A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods (print only);





CCSS6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to deter-mine whether a given number in a speci-fied set makes an equation or inequality true;

CCSS6.EE.8 Write an inequality of the form x > c or x < c to represent a con-straint 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 solu-tions of such inequalities on number line diagrams;


CCSSA-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic func-tions, and simple rational and exponential functions;

CCSSA-CED.3 Represent constraints by equations or inequalities, and by sys-tems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combi-nations of different foods (print only);















3.4 Use Equations and Inequalities to Solve Real-World Problems

A.1.b (print only), A.1.c, A.1.g, A.2.a (print only), A.2.b, A.2.c, A.3.a (online only), A.3.c, A.3.d, MP.1, MP.2, MP.3, MP.4, MP.5 (print only)

6.EE.5 Understand solving an equation or inequal-ity as a process of answering a question: which values from a specified set, if any, make the equa-tion or inequality true? Use substitution to deter-mine whether a given number in a specified set makes an equation or inequality true (print only);

6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a vari-able can represent an unknown number, or, depending on the purpose at hand, any number in a specified set (print only);

6.EE.8 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 (print only);

CCSS6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to deter-mine whether a given number in a speci-fied set makes an equation or inequality true (print only);

CCSS6.EE.6 Use variables to represent numbers and write expressions when solv-ing 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 speci-fied set (print only);

CCSS6.EE.8 Write an inequality of the form x > c or x < c to represent a con-straint 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 solu-tions of such inequalities on number line diagrams (print only);















7.EE.4 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 (online only);

8.EE.7 Solve linear equations in one variable (online only);


A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods;


10 of her salary an hour, or

$2.50, for a new salary of $27.50. 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;

CCSS7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by rea-soning about the quantities (online only);

CCSS8.EE.7 Solve linear equations in one variable (online only);















CCSSA-CED.3 Represent constraints by equations or inequalities, and by sys-tems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combi-nations of different foods;






4.1 Evaluate Polynomials A.1.d, A.1.e, A.7.c (print only), MP.1, MP.2, MP.3 (print only), MP.4, MP.5


6.EE.3 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 equiva-lent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y;

A-APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials;


CCSS6.EE.3 Apply the properties of opera-tions to generate equivalent expressions. For example, apply the distributive prop-erty to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expres-sion 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y;









A-SSE.1 Interpret expressions that represent a quantity in terms of its context (print only);

A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2);

A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression;



M.3 Construct viable arguments and critique the reasoning of others (print only);


M.5 Use appropriate tools strategically (print only);


CCSSA-APR.1 Understand that polyno-mials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials;

CCSSA-SSE.1 Interpret expressions that represent a quantity in terms of its context (print only);

CCSSA-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2);

CCSSA-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression;



CCSSM.3 Construct viable arguments and critique the reasoning of others (print only);


CCSSM.5 Use appropriate tools strategi-cally (print only);










4.2 Factor Polynomials Q.1.b, A.1.d (print only), A.1.e, A.1.f, A.1.g, MP.1, MP.2, MP.3, MP.4, MP.5


7.EE.2 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 + 0.05a = 1.05a means that “increase by 5%” is the same as “multi-ply by 1.05.”;


A-APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials;


A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2);







CCSS7.EE.2 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 + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”;


CCSSA-APR.1 Understand that polyno-mials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials;


CCSSA-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2);











M.8 Look for and express regularity in repeated reasoning






CCSSM.8 Look for and express regularity in repeated reasoning

4.3 Solve Quadratic Equations

A.1.f (online only), A.4.a, A.4.b, MP.1, MP.2, MP.3, MP.4, MP.5

A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2) (online only);


A-APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials (online only);

A-APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial (online only);


CCSSA-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2) (online only);


CCSSA-APR.1 Understand that polyno-mials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials (online only);










A-REI.1 Explain each step in solving a simple equation as following from the equality of num-bers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method (online only);

A-REI.4 Solve quadratic equations in one variable;







CCSSA-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previ-ous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method (online only);

CCSSA-REI.4 Solve quadratic equations in one variable;







4.4 Evaluate Rational Expressions

A.1.f (print only), A.1.h, A.1.i, A.1.j, MP.1, MP.2, MP.4 (print only), MP.5


6.EE.3 Apply the properties of operations to gen-erate 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 equiva-lent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y;


CCSS6.EE.3 Apply the properties of opera-tions to generate equivalent expressions. For example, apply the distributive prop-erty to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expres-sion 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y;









7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and sub-traction on a horizontal or vertical number line diagram (online only);

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers (online only);

7.NS.3 Solve real-world and mathematical prob-lems involving the four operations with rational numbers (online only);

A-APR.6 Rewrite simple rational expressions in different forms; write a(x)

____ b(x)

in the form q(x) + r(x) ____

b(x) ,

where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system (print only);

A-APR.7 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions;



M.4 Model with mathematics (print only);


M.6 Attend to precision (print only);

M.7 Look for and make use of structure (online only);

M.8 Look for and express regularity in repeated reasoning (online only)

CCSS7.NS.1 Apply and extend previous understandings of addition and subtrac-tion to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram (online only);

CCSS7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers (online only);

CCSS7.NS.3 Solve real-world and mathe-matical problems involving the four opera-tions with rational numbers (online only);

CCSSA-APR.6 Rewrite simple rational expressions in different forms; write a(x)

____ b(x)

in the form q(x) + r(x)

____ b(x)

, where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system (print only);



CCSSM.4 Model with mathematics (print only);


CCSSM.6 Attend to precision (print only);

CCSSM.7 Look for and make use of struc-ture (online only);

CCSSM.8 Look for and express regularity in repeated reasoning (online only)









5.1 Interpret Slope Q.3.a, Q.3.c, A.5.a, A.5.b, A.5.c, A.5.d, A.5.e, A.7.a (print only), MP.1, MP.2, MP.4, MP.5 (print only)

6.NS.6 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;

7.RP.1 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;

7.RP.2 Recognize and represent proportional relationships between quantities;







CCSS6.NS.6 Understand a rational num-ber 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;

CCSS7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities mea-sured in like or different units. For exam-ple, 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;

CCSS7.RP.2 Recognize and represent pro-portional relationships between quantities;


10 of her salary an hour, or

$2.50, for a new salary of $27.50. 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;









8.F.4 Construct a function to model a linear rela-tionship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values;

8.EE.5 Graph proportional relationships, inter-preting the unit rate as the slope of the graph. Compare two different proportional relation-ships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed;


A-REI.10 Understand that the graph of an equa-tion in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line) (print only);








CCSS8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values;

CCSS8.EE.5 Graph proportional relation-ships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example; compare a distance-time graph to a distance-time equation to determine which of two mov-ing objects has greater speed;


CCSSA-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line) (print only);
















5.2 Write the Equation of a Line

Q.6.c (online only), A.5.a (print only), A.5.b, A.5.c (print only), A.5.d (print only), A.6.a, A.6.b, MP.1, MP.2, MP.4

8.F.4 Construct a function to model a linear rela-tionship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values (print only);

8.EE.5 Graph proportional relationships, inter-preting the unit rate as the slope of the graph. Compare two different proportional relation-ships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed (print only);

A-CED.2 Create equations in two or more vari-ables to represent relationships between quanti-ties; graph equations on coordinate axes with labels and scales;




CCSS8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values (print only);

CCSS8.EE.5 Graph proportional relation-ships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example; compare a distance-time graph to a distance-time equation to determine which of two mov-ing objects has greater speed (print only);

CCSSA-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales;












5.3 Graph Linear Equations A.2.a (online only), A.2.b (online only), A.5.a, A.5.b, A.5.d, A.5.e (online only), MP.1, MP.2, MP.4, MP.5 (print only)


A-CED.2 Create equations in two or more vari-ables to represent relationships between quanti-ties; graph equations on coordinate axes with labels and scales

A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods (online only)

A-CED.4 Rearrange formulas to highlight a quan-tity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R (print only);

A-REI.3 Solve linear equations and inequalities in one variable, including equations with coeffi-cients represented by letters (online only)

A-REI.10 Understand that the graph of an equa-tion in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line) (print only);

F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more com-plicated cases;

CCSS8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and ini-tial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values (print only);


CCSSA-CED.3 Represent constraints by equations or inequalities, and by sys-tems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combi-nations of different foods (online only);

CCSSA-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R (print only);

CCSSA-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters (online only);

CCSSA-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line) (print only);









M.1 Make sense of problems and persevere in solving them

M.3 Construct viable arguments and critique the reasoning of others

M.4 Model with mathematics (online only)

M.6 Attend to precision (print only)

CCSSF-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases;



CCSSM.4 Model with mathematics (online only);

CCSSM.6 Attend to precision (print only)

5.4 Solving Systems of Linear Equations

A.2.b (print only), A.2.c, A.2.d, MP.1, MP.2, MP.4

6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a vari-able can represent an unknown number, or, depending on the purpose at hand, any number in a specified set;

8.EE.8 Analyze and solve pairs of simultaneous linear equations;

A-CED.2 Create equations in two or more vari-ables to represent relationships between quanti-ties; graph equations on coordinate axes with labels and scales;

A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods;

A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables;

CCSS6.EE.6 Use variables to represent numbers and write expressions when solv-ing 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 speci-fied set;

CCSS8.EE.8 Analyze and solve pairs of simultaneous linear equations;


CCSSA-CED.3 Represent constraints by equations or inequalities, and by sys-tems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combi-nations of different foods;









A-REI.7 Solve a simple system consisting of a lin-ear equation and a quadratic equation in two vari-ables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3 (print only);



M.3 Construct viable arguments and critique the reasoning of others (online only);



CCSSA-REI.6 Solve systems of linear equa-tions exactly and approximately (e.g., with graphs), focusing on pairs of linear equa-tions in two variables;



CCSSM.3 Construct viable arguments and critique the reasoning of others (online only);



6.1 Identify a Function A.5.a, A.7.b, A.7.c, MP.1, MP.2, MP.3, MP.4, MP.5 (print only)

6.NS.6 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;

8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs con-sisting of an input and the corresponding output;

8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line;

CCSS6.NS.6 Understand a rational num-ber 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;

CCSS8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output;

CCSS8.F.3 Interpret the equation y = mx + b as defining a linear func-tion, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line;










F-IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equa-tion y = f(x);

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context;

F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a ver-bal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; rela-tive maximums and minimums; symmetries; end behavior; and periodicity;

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative rela-tionship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function;

F-BF.4 Find inverse functions;


CCSSF-IF.1 Understand that a func-tion from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x);

CCSSF-IF.2 Use function notation, evalu-ate functions for inputs in their domains, and interpret statements that use function notation in terms of a context;

CCSSF-IF.4 For a function that models a relationship between two quantities, inter-pret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal descriptionof the relationship. Key fea-tures include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity;
















CCSSF-IF.5 Relate the domain of a func-tion to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assem-ble n engines in a factory, then the positive integers would be an appropriate domain for the function;








6.2 Identify Linear and Qua-dratic Functions

A.5.a, A.5.b, A.5.d, A.7.b, A.7.c, MP.1, MP.2, MP.3, MP.4, MP.5

6.NS.6 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. (online only);

8.F.3 Interpret the equation y = mx + b as defin-ing a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line (online only);

CCSS6.NS.6 Understand a rational num-ber 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 neg-ative number coordinates. (online only);










F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret state-ments that use function notation in terms of a context;

F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a ver-bal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; rela-tive maximums and minimums; symmetries; end behavior; and periodicity (online only);

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative rela-tionship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function (online only);

F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph (online only);



CCSS8.F.3 Interpret the equation y = mx + b as defining a linear func-tion, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line (online only);


CCSSF-IF.2 Use function notation, evalu-ate functions for inputs in their domains, and interpret statements that use function notation in terms of a context;

CCSSF-IF.4 For a function that models a relationship between two quantities, inter-pret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key fea-tures include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity (online only);














CCSSF-IF.5 Relate the domain of a func-tion to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assem-ble n engines in a factory, then the positive integers would be an appropriate domain for the function (online only);

CCSSF-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph (online only);








6.3 Identify Key Features of a Graph

A.5.a, A.5.b (online only), A.5.e, MP.1, MP.2, MP.3, MP.4

8.F.3 Interpret the equation y = mx + b as defin-ing a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line;

CCSS8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a func-tion of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line;









8.F.5 Describe qualitatively the functional rela-tionship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally;

F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a ver-bal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; rela-tive maximums and minimums; symmetries; end behavior; and periodicity;


F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more com-plicated cases;




M.4 Model with mathematics (online only);




CCSS8.F.5 Describe qualitatively the func-tional relationship between two quanti-ties by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally;

CCSSF-IF.4 For a function that models a relationship between two quantities, inter-pret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key fea-tures include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity;


CCSSF-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases;












CCSSM.4 Model with mathematics (online only);




6.4 Compare Functions Q.3.a (online only), Q.3.c (online only), A.2.b (online only), A.4.a (online only), A.5.b, A.5.c, A.5.e (online only), A.7.a, A.7.d, MP.1, MP.2, MP.3, MP.4, MP.5 (print only)

8.EE.5 Graph proportional relationships, inter-preting the unit rate as the slope of the graph. Compare two different proportional relation-ships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed;

8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear func-tion represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change;

8.F.3 Interpret the equation y = mx + b as defin-ing a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line (print only);

CCSS8.EE.5 Graph proportional relation-ships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example; compare a distance-time graph to a distance-time equation to determine which of two mov-ing objects has greater speed;

CCSS8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give exam-ples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph con-tains the points (1,1), (2,4) and (3,9), which are not on a straight line (print only);

CCSS8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values (print only);










F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a ver-bal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; rela-tive maximums and minimums; symmetries; end behavior; and periodicity (online only);


F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more com-plicated cases (print only);

F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum;



M.4 Model with mathematics

CCSSF-IF.4 For a function that models a relationship between two quantities, inter-pret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key fea-tures include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity (online only);


CCSSF-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases (print only);

CCSSF-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numeri-cally in tables, or by verbal descriptions). For example, given a graph of one qua-dratic function and an algebraic expres-sion for another, say which has the larger maximum;



CCSSM.4 Model with mathematics









7.1 Compute Perimeter and Area of Polygons

Q.2.a, Q.4.a, Q.4.c, Q.4.e, MP.1, MP.2, MP.3, MP.4, MP.5 (print only)

6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers (print only);

7.G.6 Solve real-world and mathematical prob-lems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms;

8.G.7 Apply the Pythagorean Theorem to deter-mine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions;

G-MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder);









CCSS6.EE.2 Write, read, and evaluate expressions in which letters stand for num-bers (print only);

CCSS7.G.6 Solve real-world and math-ematical problems involving area, volume and surface area of two- and three-dimen-sional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms;

CCSS8.G.7 Apply the Pythagorean Theo-rem to determine unknown side lengths in right triangles in real-world and mathemat-ical problems in two and three dimensions;

















7.2 Compute Circumference and Area of Circles

Q.2.a (online only), Q.2.b (online only), Q.4.b, MP.1, MP.2, MP.3 (online only), MP.4


7.G.4 Know the formulas for the area and cir-cumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle;

G-GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments (online only);

G-MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylin-der) (online only);










CCSS7.G.4 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;


CCSM.2 Reason abstractly and quantitatively;















7.3 Compute Surface Area and Volume

Q.2.a (online only), Q.2.b (online only), Q.5.a, Q.5.b, Q.5.c, Q.5.d, Q.5.e, MP.1, MP.2, MP.3, MP.4, MP.5 (print only)



8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems;

G-GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments (online only);

G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems (online only);











CCSSG-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems (online only);

















7.4 Compute Perimeter, Area, Surface Area and Volume of Composite Figures

Q.2.a (online only), Q.2.b (online only), Q.4.d, Q.5.f, MP.1, MP.2, MP.3, MP.4


7.G.4 Know the formulas for the area and cir-cumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle (online only);


8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems;

G-MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylin-der) (online only);

G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems (online only);








CCSS7.G.4 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 (online only);


CCSSG-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems (online only);















8.1 Calculate Measures of Central Tendency

Q.7.a, MP.1, MP.2, MP.3, MP.4

6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of varia-tion describes how its values vary with a single number;

6.SP.5 Summarize numerical data sets in relation to their context;

7.SP.4 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;

A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods (print only);

S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets;






CCSS6.SP.3 Recognize that a measure of center for a numerical data set summa-rizes all of its values with a single number, while a measure of variation describes how its values vary with a single number;

CCSS6.SP.5 Summarize numerical data sets in relation to their context;

CCSS7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two popula-tions. 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;

CCSSA-CED.3 Represent constraints by equations or inequalities, and by sys-tems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combi-nations of different foods (print only);






CCSSM.6 Attend to precision (print only);









M.6 Attend to precision (print only);





8.2 Display Categorical Data Q.2.e (online only), Q.6.a, MP.1, MP.2, MP.4, MP.5 (print only)

3.MD.3 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;


S-ID.5 Summarize categorical data for two cat-egories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional rela-tive frequencies). Recognize possible associations and trends in the data (online only);








CCSS3.MD.3 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;


CCSSS-ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequen-cies). Recognize possible associations and trends in the data (online only);
















8.3 Display One-Variable Data Q.6.b, Q.7.a, MP.1, MP.2, MP.3 (online only), MP.4, MP.5 (print only)

6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of varia-tion describes how its values vary with a single number (online only);

6.SP.4 Display numerical data in plots on a num-ber line, including dot plots, histograms, and box plots (print only);


7.SP.4 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 (online only);

S-ID.1 Represent data with plots on the real num-ber line (dot plots, histograms, and box plots);

S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets (online only);

S-ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outli-ers) (online only);




CCSS6.SP.3 Recognize that a measure of center for a numerical data set summa-rizes all of its values with a single number, while a measure of variation describes how its values vary with a single number (online only);

CCSS6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots (print only);


CCSS7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two popula-tions. 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 sci-ence book (online only);

CCSSS-ID.1 Represent data with plots on the real number line (dot plots, histo-grams, and box plots);

CCSSS-ID.3 Interpret differences in shape; center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers) (online only);


















8.4 Display Two-Variable Data

Q.6.c, A.4.a (online only), MP.1, MP.2, MP.3 (online only), MP.4, MP.5 (online only)

8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear associa-tion, and nonlinear association;

8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line;

S-ID.5 Summarize categorical data for two cat-egories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional rela-tive frequencies). Recognize possible associations and trends in the data;

S-ID.6 Represent data on two quantitative vari-ables on a scatter plot, and describe how the variables are related;

S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data;

S-ID.9 Distinguish between correlation and causa-tion (online only);


CCSS8.SP.1 Construct and interpret scat-ter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association;

CCSS8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear asso-ciation, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line;

CCSSS-ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequen-cies). Recognize possible associations and trends in the data;

CCSSS-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data;

CCSSS-ID.9 Distinguish between correla-tion and causation (online only);







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