The Common Core in Illinois

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Skills available for Illinois seventh-grade math standards

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

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Illinois Priority Learning Standards Illinois Priority Learning Standards
Illinois Learning Standards Incorporating the Common Core: Grade 7 Illinois Learning Standards Incorporating the Common Core: Grade 7
Illinois Learning Standards Incorporating the Common Core: Mathematical Practices Illinois Learning Standards Incorporating the Common Core: Mathematical Practices

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7.RP Ratios and Proportional Relationships

7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems.
- 7.RP.A.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.
  - Calculate unit rates with fractions (7-L.6)
  - Solve word problems using unit rates (7-L.7)
- 7.RP.A.2 Recognize and represent proportional relationships between quantities.
  - 7.RP.A.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.A.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
    - Find the constant of proportionality from a table (7-N.1)
    - Find the constant of proportionality from a graph (7-N.4)
  - 7.RP.A.2c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
  - 7.RP.A.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.
    - Interpret graphs of proportional relationships (7-N.10)
- 7.RP.A.3-1 Use proportional relationships to solve multistep ratio problems.
  - Unit prices with unit conversions (7-P.4)
  - Unit prices: find the total price (7-P.5)
- 7.RP.A.3-2 Use proportional relationships to solve multistep percent problems. Examples: simple interest, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
- Checkpoint opportunity
  - Checkpoint: Proportional relationships (7-N.)
  - Checkpoint: Unit rates, ratios, and percents (7-P.14)

7.EE Expressions and Equations

7.EE.A Use properties of operations to generate equivalent expressions.
- 7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- 7.EE.A.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."
  - Identify equivalent linear expressions: word problems (7-S.14)
- Checkpoint opportunity
  - Checkpoint: Linear expressions (7-S.)
7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
- 7.EE.B.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&percent; 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.
- 7.EE.B.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.B.4a-1 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.
  - 7.EE.B.4a-2 Fluently solve equations of the form px + q = r and p(x+q) = r, where p, q, and r are specific rational numbers.
  - 7.EE.B.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. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
- Checkpoint opportunity
  - Checkpoint: Solve two-step equations (7-T.16)
  - Checkpoint: Solve two-step inequalities (7-U.9)

7.G Geometry

7.G.A Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.A.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.A.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.
  - Triangle inequality (7-Z.3)
  - Graph triangles and quadrilaterals (7-Z.7)
- 7.G.A.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.
  - Cross sections of three-dimensional figures (7-AA.4)
- Checkpoint opportunity
  - Checkpoint: Scale drawings (7-DD.5)
7.G.B Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
- 7.G.B.4-1 Know the formulas for the area and circumference of a circle and use them to solve problems.
- 7.G.B.4-2 Give an informal derivation of the relationship between the circumference and area of a circle.
- 7.G.B.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.B.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.
- Checkpoint opportunity
  - Checkpoint: Area, circumference, surface area, and volume (7-CC.10)

7.NS The Number System

7.NS.A Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
- 7.NS.A.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.A.1a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
    - Quantities that combine to zero: word problems (7-A.6)
  - 7.NS.A.1b-1 Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative.
  - 7.NS.A.1b-2 Interpret sums of rational numbers by describing real-world contexts.
  - 7.NS.A.1c-1 Understand subtraction of rational numbers as adding the additive inverse, p − q = p + (−q). Apply this principle in real-world contexts.
  - 7.NS.A.1d Apply properties of operations as strategies to add and subtract rational numbers.
- 7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
  - 7.NS.A.2a-1 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.
  - 7.NS.A.2a-2 Interpret products of rational numbers by describing real-world contexts.
  - 7.NS.A.2b-1 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).
  - 7.NS.A.2b-2 Interpret quotients of rational numbers by describing real-world contexts.
    - Identify quotients of rational numbers: word problems (7-I.5)
  - 7.NS.A.2c Apply properties of operations as strategies to multiply and divide rational numbers.
- 7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
- Checkpoint opportunity

7.SP Statistics and Probability

7.SP.A Use random sampling to draw inferences about a population.
- 7.SP.A.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.
  - Populations and samples (7-HH.8)
  - Identify representative, random, and biased samples (7-HH.9)
- 7.SP.A.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. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
- Checkpoint opportunity
7.SP.B Draw informal comparative inferences about two populations.
- 7.SP.B.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. For example, the mean height of players on the basketball team is 10cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
- 7.SP.B.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.
  - Compare populations using measures of center and spread (7-HH.11)
- Checkpoint opportunity
7.SP.C Investigate chance processes and develop, use, and evaluate probability models.
- 7.SP.C.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.
  - Probability of simple events (7-II.2)
- 7.SP.C.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.
- 7.SP.C.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.C.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.
  - 7.SP.C.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
    - Experimental probability (7-II.5)
    - Make predictions using experimental probability (7-II.6)
- 7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
  - 7.SP.C.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.
    - Probability of compound events (7-II.13)
    - Probability of independent and dependent events (7-II.16)
  - 7.SP.C.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.C.8c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40&percent; of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?
    - Which simulation represents the situation? (7-II.14)
- Checkpoint opportunity

7.C Reasoning

7.C.1.1 Base explanations/reasoning on the properties of operations. Content Scope: Knowledge and skills articulated in 7.NS.1 and 7.NS.2
7.C.1.2 Base explanations/reasoning on the properties of operations. Content Scope: Knowledge and skills articulated in 7.EE.1
- Multiply using the distributive property (7-S.5)
- Write equivalent expressions using properties (7-S.6)
7.C.2 Base explanations/reasoning on the relationship between addition and subtraction or the relationship between multiplication and division. Content Scope: Knowledge and skills articulated in 7.NS.1 and 7.NS.2
- Complete addition and subtraction equations with integers (7-B.13)
- Complete multiplication and division equations with integers (7-B.23)
7.C.3 Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response). Content Scope: Knowledge and skills articulated in 7.NS.A
7.C.4 Base explanations/reasoning on a coordinate plane diagram (whether provided in the prompt or constructed by the student in her response). Content Scope: Knowledge and skills articulated in 7.RP.A
7.C.5 Given an equation, present the solution steps as a logical argument that concludes with the set of solutions (if any). Content Scope: Knowledge and skills articulated in 7.EE.4a
- Solve equations: complete the solution (7-T.15)
7.C.7.1 Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures. Content Scope: Knowledge and skills articulated in 7.RP.2
7.C.7.2 Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1 + 4 = 5 + 7 = 12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions. Content Scope: Knowledge and skills articulated in 7.RP.3
7.C.7.3 Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1 + 4 = 5 + 7 = 12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions. Content Scope: Knowledge and skills articulated in 7.NS.2d
- Convert fractions or mixed numbers to decimals (7-H.1)
7.C.7.4 Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1 + 4 = 5 + 7 = 12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions. Content Scope: Knowledge and skills articulated in 7.NS.3
- Price lists (7-P.2)
7.C.8 Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures. Content Scope: Knowledge and skills articulated in 6.NS.C, 6.EE.A, 6.EE.B

7.D Modeling

7.D.1 Solve multi-step contextual word problems with degree of difficulty appropriate to Grade 7, requiring application of knowledge and skills articulated in Type I, Sub-Claim A Evidence Statements.
7.D.2 Solve multi step contextual problems with degree of difficulty appropriate to grade 7, application of knowledge and skills articulated in 6.RP.A, 6.EE.C, and 6.G.
7.D.3 Micro-models: Autonomously apply a technique from pure mathematics to a real -world situation in which the technique yields valuable results even though it is obviously not applicable in a strict mathematical sense (e.g., profitably applying proportional relationships to a phenomenon that is obviously nonlinear or statistical in nature). Content Scope: Knowledge and skills articulated in Type I, Sub-Claim A Evidence Statements
7.D.4 Reasoned estimates: Use reasonable estimates of known quantities in a chain of reasoning that yields an estimate of an unknown quantity. Content Scope: Knowledge and skills articulated in Type I, Sub-Claim A Evidence Statements

The Common Core in Illinois

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7.RP Ratios and Proportional Relationships

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

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

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

7.RP.A.2c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

7.RP.A.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.A.3-1 Use proportional relationships to solve multistep ratio problems.

7.RP.A.3-2 Use proportional relationships to solve multistep percent problems. Examples: simple interest, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Checkpoint opportunity

7.EE Expressions and Equations

7.EE.A Use properties of operations to generate equivalent expressions.

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

7.EE.A.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."

Checkpoint opportunity

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

7.EE.B.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.B.4a-1 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.

7.EE.B.4a-2 Fluently solve equations of the form px + q = r and p(x+q) = r, where p, q, and r are specific rational numbers.

Checkpoint opportunity

7.G Geometry

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

7.G.A.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.A.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.A.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.

Checkpoint opportunity

7.G.B Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

7.G.B.4-1 Know the formulas for the area and circumference of a circle and use them to solve problems.

7.G.B.4-2 Give an informal derivation of the relationship between the circumference and area of a circle.

7.G.B.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.B.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.

Checkpoint opportunity

7.NS The Number System

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

7.NS.A.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.A.1a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

7.NS.A.1b-1 Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative.

7.NS.A.1b-2 Interpret sums of rational numbers by describing real-world contexts.

7.NS.A.1c-1 Understand subtraction of rational numbers as adding the additive inverse, p − q = p + (−q). Apply this principle in real-world contexts.

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

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

7.NS.A.2a-1 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.

7.NS.A.2a-2 Interpret products of rational numbers by describing real-world contexts.

7.NS.A.2b-1 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).

7.NS.A.2b-2 Interpret quotients of rational numbers by describing real-world contexts.

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

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

Checkpoint opportunity

7.SP Statistics and Probability

7.SP.A Use random sampling to draw inferences about a population.

Checkpoint opportunity

7.SP.B Draw informal comparative inferences about two populations.

Checkpoint opportunity

7.SP.C Investigate chance processes and develop, use, and evaluate probability models.

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

7.SP.C.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.C.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.

Checkpoint opportunity

7.C Reasoning

7.C.1.1 Base explanations/reasoning on the properties of operations. Content Scope: Knowledge and skills articulated in 7.NS.1 and 7.NS.2

7.C.1.2 Base explanations/reasoning on the properties of operations. Content Scope: Knowledge and skills articulated in 7.EE.1

7.C.2 Base explanations/reasoning on the relationship between addition and subtraction or the relationship between multiplication and division. Content Scope: Knowledge and skills articulated in 7.NS.1 and 7.NS.2

7.C.3 Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response). Content Scope: Knowledge and skills articulated in 7.NS.A

7.C.4 Base explanations/reasoning on a coordinate plane diagram (whether provided in the prompt or constructed by the student in her response). Content Scope: Knowledge and skills articulated in 7.RP.A

7.C.5 Given an equation, present the solution steps as a logical argument that concludes with the set of solutions (if any). Content Scope: Knowledge and skills articulated in 7.EE.4a

7.C.7.1 Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures. Content Scope: Knowledge and skills articulated in 7.RP.2

7.C.8 Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures. Content Scope: Knowledge and skills articulated in 6.NS.C, 6.EE.A, 6.EE.B

7.D Modeling

7.D.1 Solve multi-step contextual word problems with degree of difficulty appropriate to Grade 7, requiring application of knowledge and skills articulated in Type I, Sub-Claim A Evidence Statements.

7.D.2 Solve multi step contextual problems with degree of difficulty appropriate to grade 7, application of knowledge and skills articulated in 6.RP.A, 6.EE.C, and 6.G.

7.D.4 Reasoned estimates: Use reasonable estimates of known quantities in a chain of reasoning that yields an estimate of an unknown quantity. Content Scope: Knowledge and skills articulated in Type I, Sub-Claim A Evidence Statements