The Common Core in Maryland

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Skills available for Maryland seventh-grade math standards

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Maryland College and Career-Ready Frameworks Maryland College and Career-Ready Frameworks
Maryland College and Career-Ready Standards: Grade 7 Maryland College and Career-Ready Standards: Grade 7
Maryland College and Career-Ready Standards: Mathematical Practices Maryland College and Career-Ready Standards: Mathematical Practices

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7.RP Ratios and Proportional Relationships

Analyze proportional relationships and use them to solve real-world and mathematical problems.
- 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.
  - 7.RP.1.a Ability to describe and identify complex fractions
  - 7.RP.1.b Ability to recognize the difference(s) between a unit rate and a ratio
- 7.RP.2 Recognize and represent proportional relationships between quantities.
  - 7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
    - 7.RP.2a.1 Ability to recognize in a given proportional situation that the two "between ratios" and the two "within ratios" are the same
    - 7.RP.2a.2 Ability to distinguish between additive and multiplicative situations
      - Solve proportions: word problems (7-J.12)
      - Scale drawings: word problems (7-Z.2)
    - 7.RP.2a.3 Ability to recognize that two equal ratios represent a proportion
      - Do the ratios form a proportion? (7-J.9)
      - Do the ratios form a proportion: word problems (7-J.10)
    - 7.RP.2a.4 Ability to recognize and represent the connection between equivalent ratios, values in a table, and graphed ordered pairs
  - 7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
    - 7.RP.2b.1 Ability to express unit rates using a variety of representations, given a contextual situation
      - Find the constant of proportionality from a table (7-K.1)
      - Find the constant of proportionality from a graph (7-K.4)
  - 7.RP.2c Represent proportional relationships by equations.
    - 7.RP.2c.1 Ability to recognize that multiplicative relationships are proportional
  - 7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
    - 7.RP.2d.1 Ability to identify that a proportional relationship intersects (0,0) Essential Skills and Knowledge
      - Interpret graphs of proportional relationships (7-K.10)
    - 7.RP.2d.2 Ability to determine other points using (1, r)
- 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems.
  - 7.RP.3.a Ability to build on prior experience with equivalent fractions to solve multi-step problems with ratio and percent
  - 7.RP.3.b Ability to relate "between" ratios and "within" ratios to the cross-product and factor of change algorithms

7.NS The Number System

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
- 7.NS.1 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.
  - 7.NS.1a Describe situations in which opposite quantities combine to make 0.
    - 7.NS.1a.1 Ability to build on prior experience with positive and negative rational numbers
    - 7.NS.1a.2 Ability to identify additive inverses using rational numbers
    - 7.NS.1a.3 Knowledge of positive or negative values for fractions and decimals
      - Absolute value of rational numbers (7-H.7)
  - 7.NS.1b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
    - 7.NS.1b.1 Ability to build on prior experience with absolute value
    - 7.NS.1b.2 Knowledge of absolute value to add and subtract rational numbers using a horizontal or a vertical number line
  - 7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
  - 7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.
    - 7.NS.1d.1 Ability to identify and apply the following properties:
    - 7.NS.1d.1.1 Commutative Property of Addition
    - 7.NS.1d.1.2 Associative Property of Addition
    - 7.NS.1d.1.3 Identity Property of Addition
- 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
  - 7.NS.2a 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.
    - 7.NS.2a.1 Ability to identity and apply the following properties:
    - 7.NS.2a.1.1 Multiplicative Inverse
      - Multiplicative inverses (7-A.3)
      - Complete multiplication and division equations with integers (7-C.23)
    - 7.NS.2a.1.2 Commutative Property of Multiplication
    - 7.NS.2a.1.3 Associative Property of Multiplication
    - 7.NS.2a.1.4 Identity Property of Multiplication
    - 7.NS.2a.1.5 Recognize that rules for multiplying signed numbers remain the same for all rational numbers
  - 7.NS.2b 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.
    - 7.NS.2b.1 Ability to explore and justify the result of division by 0 (zero)
    - 7.NS.2b.2 Ability to apply and extend knowledge of addition and subtraction of integers (i.e., two color counters, arrows on a number line) to extend to multiplication and division
    - 7.NS.2b.3 Ability to use patterns and concrete models to devise a general rule for dividing integers: - (p/q) = -p/q = p/-q
  - 7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.
    - 7.NS.2c.1 Ability to Identify and apply the following properties:
    - 7.NS.2c.1.1 Distributive Property
    - 7.NS.2c.1.2 Associative Properties
      - Apply multiplication and division rules (7-H.19)
      - Properties of addition and multiplication (7-R.10)
    - 7.NS.2c.1.3 Commutative Properties
      - Apply multiplication and division rules (7-H.19)
      - Properties of addition and multiplication (7-R.10)
    - 7.NS.2c.1.4 Identity Properties
      - Apply multiplication and division rules (7-H.19)
      - Properties of addition and multiplication (7-R.10)
  - 7.NS.2d 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.
    - 7.NS.2d.1 Ability to recognize that when rational numbers in fractional form are converted to decimals, they either terminate or repeat
      - Classify numbers (7-A.11)
      - Convert between decimals and fractions or mixed numbers (7-H.3)
- 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
  - 7.NS.3.a Ability to describe and identify complex fractions
  - 7.NS.3.b Ability to apply knowledge of Order of Operations

7.EE Expressions and Equations

Use properties of operations to generate equivalent expressions.
- 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
  - 7.EE.1.a Ability to understand linear expression terminology: sum, difference, term, product, factor, quotient, coefficient
    - Identify terms and coefficients (7-R.8)
  - 7.EE.1.b Ability to factor by using division to express a linear expression by its factors; i.e., 2x – 6 = 2(x – 3)
    - Sort factors of variable expressions (7-R.9)
    - Factors of linear expressions (7-R.19)
  - 7.EE.1.c Ability to expand by using multiplication to rewrite the factors in a linear expression as a product; i.e., 5(x+ 12) = 5x + 60
- 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.
  - 7.EE.2.a Ability to utilize Properties of Operations in order to rewrite expressions in different forms
  - 7.EE.2.b Ability to develop understanding of equivalent forms of numbers, their various uses and relationships, and how they apply to a problem
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
- 7.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.
- 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.
  - 7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
    - 7.EE.4a.1 Ability to differentiate between an algebraic solution and an arithmetic solution
  - 7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.
    - 7.EE.4b.1 Ability to develop correct usage of all four inequality symbols and related terminology (at least, no more than, etc.)
    - 7.EE.4b.2 Ability to solve inequalities to determine the solution set

7.G Geometry

Draw, construct, and describe geometrical figures and describe the relationships between them.
- 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.
  - 7.G.1.a Ability to describe and identify ratios and proportions
  - 7.G.1.b Ability to reproduce scale drawing at a different scale
    - Dilations: graph the image (8-S.2)
- 7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
- 7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
  - 7.G.3.a Ability to build on prior knowledge with 2-dimensional figures and 3-dimensional figures
  - 7.G.3.b Ability to differentiate between the characteristics of right rectangular prisms and right rectangular pyramids
  - 7.G.3.c Ability to compare the attributes of right rectangular prisms and right rectangular pyramids
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
- 7.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.
  - 7.G.4.a Ability to identify and apply the vocabulary for a circle – radius, diameter, chord, circumference, center, pi (π) ≈3.14159 and 22/7
  - 7.G.4.b Ability to use a near-parallelogram to discover the formula for area of a circle
- 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
  - 7.G.5.a Ability to explore the relationship between the angles of intersecting lines and figures
    - Identify complementary, supplementary, vertical, and adjacent angles (7-W.16)
    - Find measures of complementary, supplementary, vertical, and adjacent angles (7-W.17)
- 7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

7.SP Statistics and Probability

Use random sampling to draw inferences about a population.
- 7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
  - 7.SP.1.a Ability to describe and identify population, sample of a population, random sampling, validity, reliability, invalid, inferences
    - Identify representative, random, and biased samples (7-DD.8)
- 7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
  - Estimate population size using proportions (7-J.13)
Draw informal comparative inferences about two populations.
- 7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.
  - 7.SP.3.a Ability to describe and identify deviation, standard deviation, absolute deviation, measures of central tendency, measures of variability
    - Calculate mean absolute deviation (7-DD.5)
  - 7.SP.3.b Ability to build on prior experience with dot plots to compare/contrast data displayed on two dot plots (see 6.SP.4) and to make inferences from the data
    - Create line plots (7-CC.3)
    - Create and interpret line plots with fractions (7-CC.4)
- 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.
  - 7.SP.4.a Ability to determine which measure of central tendency is most appropriate for a given situation
  - 7.SP.4.b Ability to use statistical findings to draw inferences about populations
Investigate chance processes and develop, use, and evaluate probability models.
- 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, 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.5.a Ability to devise models where outcomes are equally likely versus not equally likely
    - Probability of simple events (7-EE.1)
- 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 relative frequency, and predict the approximate relative frequency given the probability.
  - Experimental probability (7-EE.4)
  - Make predictions using theoretical probability (7-EE.7)
- 7.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.
  - 7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
    - Probability of simple events (7-EE.1)
  - 7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
    - 7.SP.7b.1 Ability to describe and identify possibility versus probability
      - Experimental probability (7-EE.4)
- 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
  - 7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
    - 7.SP.8a.1 Ability to compare simple events with compound events
  - 7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.
  - 7.SP.8c Design and use a simulation to generate frequencies for compound events.
    - 7.SP.8c.1 Ability to use models and simulate a variety of events
      - Which simulation represents the situation? (7-EE.11)

The Common Core in Maryland

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7.RP Ratios and Proportional Relationships

Analyze proportional relationships and use them to solve real-world and mathematical problems.

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.

7.RP.1.a Ability to describe and identify complex fractions

7.RP.1.b Ability to recognize the difference(s) between a unit rate and a ratio

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

7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

7.RP.2a.1 Ability to recognize in a given proportional situation that the two "between ratios" and the two "within ratios" are the same

7.RP.2a.2 Ability to distinguish between additive and multiplicative situations

7.RP.2a.3 Ability to recognize that two equal ratios represent a proportion

7.RP.2a.4 Ability to recognize and represent the connection between equivalent ratios, values in a table, and graphed ordered pairs

7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

7.RP.2b.1 Ability to express unit rates using a variety of representations, given a contextual situation

7.RP.2c Represent proportional relationships by equations.

7.RP.2c.1 Ability to recognize that multiplicative relationships are proportional

7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

7.RP.2d.1 Ability to identify that a proportional relationship intersects (0,0) Essential Skills and Knowledge

7.RP.2d.2 Ability to determine other points using (1, r)

7.RP.3 Use proportional relationships to solve multistep ratio and percent problems.

7.RP.3.a Ability to build on prior experience with equivalent fractions to solve multi-step problems with ratio and percent

7.RP.3.b Ability to relate "between" ratios and "within" ratios to the cross-product and factor of change algorithms

7.NS The Number System

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

7.NS.1 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.

7.NS.1a Describe situations in which opposite quantities combine to make 0.

7.NS.1a.1 Ability to build on prior experience with positive and negative rational numbers

7.NS.1a.2 Ability to identify additive inverses using rational numbers

7.NS.1a.3 Knowledge of positive or negative values for fractions and decimals

7.NS.1b.1 Ability to build on prior experience with absolute value

7.NS.1b.2 Knowledge of absolute value to add and subtract rational numbers using a horizontal or a vertical number line

7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.1d.1 Ability to identify and apply the following properties:

7.NS.1d.1.1 Commutative Property of Addition

7.NS.1d.1.2 Associative Property of Addition

7.NS.1d.1.3 Identity Property of Addition

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

7.NS.2a.1 Ability to identity and apply the following properties:

7.NS.2a.1.1 Multiplicative Inverse

7.NS.2a.1.2 Commutative Property of Multiplication

7.NS.2a.1.3 Associative Property of Multiplication

7.NS.2a.1.4 Identity Property of Multiplication

7.NS.2a.1.5 Recognize that rules for multiplying signed numbers remain the same for all rational numbers

7.NS.2b.1 Ability to explore and justify the result of division by 0 (zero)

7.NS.2b.2 Ability to apply and extend knowledge of addition and subtraction of integers (i.e., two color counters, arrows on a number line) to extend to multiplication and division

7.NS.2b.3 Ability to use patterns and concrete models to devise a general rule for dividing integers: - (p/q) = -p/q = p/-q

7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.

7.NS.2c.1 Ability to Identify and apply the following properties:

7.NS.2c.1.1 Distributive Property

7.NS.2c.1.2 Associative Properties

7.NS.2c.1.3 Commutative Properties

7.NS.2c.1.4 Identity Properties

7.NS.2d 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.

7.NS.2d.1 Ability to recognize that when rational numbers in fractional form are converted to decimals, they either terminate or repeat

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

7.NS.3.a Ability to describe and identify complex fractions

7.NS.3.b Ability to apply knowledge of Order of Operations

7.EE Expressions and Equations

Use properties of operations to generate equivalent expressions.

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

7.EE.1.a Ability to understand linear expression terminology: sum, difference, term, product, factor, quotient, coefficient

7.EE.1.b Ability to factor by using division to express a linear expression by its factors; i.e., 2x – 6 = 2(x – 3)

7.EE.1.c Ability to expand by using multiplication to rewrite the factors in a linear expression as a product; i.e., 5(x+ 12) = 5x + 60

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.

7.EE.2.a Ability to utilize Properties of Operations in order to rewrite expressions in different forms

7.EE.2.b Ability to develop understanding of equivalent forms of numbers, their various uses and relationships, and how they apply to a problem

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

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.

7.EE.4a.1 Ability to differentiate between an algebraic solution and an arithmetic solution

7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

7.EE.4b.1 Ability to develop correct usage of all four inequality symbols and related terminology (at least, no more than, etc.)

7.EE.4b.2 Ability to solve inequalities to determine the solution set

7.G Geometry

Draw, construct, and describe geometrical figures and describe the relationships between them.

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.

7.G.1.a Ability to describe and identify ratios and proportions

7.G.1.b Ability to reproduce scale drawing at a different scale