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Grade 7 Math

24 curriculum outcomes with explicit teaching progressions

Select a record to inspect its progression

Ratios Proportional Relationships · 7.RP.A.1

Compute unit rates with fractions

Independently compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. across representations and contexts.

Component progression

  1. 1I can compute a unit rate given a ratio in which one or both quantities are fractions.
  2. 2I can compute a unit rate for a ratio involving two different measurement units, converting as needed.
  3. 3I can interpret a computed unit rate involving fractions in terms of its real-world context.
Ratios Proportional Relationships · 7.RP.A.2

Recognize and represent proportional relationships

Independently recognize and represent proportional relationships between quantities: decide whether two quantities are proportional by testing for equivalent ratios in a table or by graphing on a coordinate plane and observing whether the graph is a straight line through the origin, identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions, represent proportional relationships by equations, and explain what a point (x, y) on the graph means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. across representations and contexts.

Component progression

  1. 1I can test whether a relationship shown in a table or graph is proportional by checking for a constant ratio between quantities.
  2. 2I can identify the constant of proportionality from a table, graph, or equation.
  3. 3I can write an equation for a proportional relationship and explain what a specific point (x, y) on its graph means in context, with special attention to the points (0, 0) and (1, r), where r is the unit rate.
Ratios Proportional Relationships · 7.RP.A.3

Solve multistep percent and ratio problems

Independently use proportional relationships to solve multistep ratio and percent problems, such as those involving simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error. across representations and contexts.

Component progression

  1. 1I can solve a real-world problem involving percent increase or percent decrease, such as markup, markdown, or tax.
  2. 2I can solve a real-world problem involving simple interest, gratuities, commissions, or fees using proportional reasoning.
  3. 3I can solve a multistep problem that requires applying more than one percent or ratio calculation in sequence.
Number System · 7.NS.A.1

Add and subtract rational numbers

Independently apply and extend understanding of addition and subtraction to add and subtract rational numbers, representing addition and subtraction on a horizontal or vertical number line diagram: describe situations in which opposite quantities combine to make zero, understand p + q as the number located a distance |q| from p in the positive or negative direction depending on the sign of q, show that a number and its opposite (additive inverse) have a sum of zero, understand subtraction 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, apply properties of operations as strategies to add and subtract, and interpret sums and differences in real-world contexts. across representations and contexts.

Component progression

  1. 1I can describe real-world situations in which opposite quantities combine to make zero, such as oppositely charged particles or offsetting gains and losses.
  2. 2I can add two rational numbers, including negatives, by representing p + q as the number located a distance |q| from p on a number line, in the direction indicated by the sign of q.
  3. 3I can subtract a rational number by adding its additive inverse (p − q = p + (−q)), show that the distance between two rational numbers on a number line is the absolute value of their difference, and interpret the result in a real-world context such as temperature change or financial transactions.
Number System · 7.NS.A.2

Multiply and divide rational numbers

Independently apply and extend understanding of multiplication and division to multiply and divide rational numbers: understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations (particularly the distributive property), leading to rules such as (−1)(−1) = 1 and the rules for multiplying signed numbers; understand that every quotient of integers with a non-zero divisor is a rational number, and that −(p/q) = (−p)/q = p/(−q); apply properties of operations as strategies to multiply and divide rational numbers; interpret products and quotients of rational numbers in real-world contexts; and convert a rational number to a decimal using long division, knowing that the decimal form of a rational number terminates in 0s or eventually repeats. across representations and contexts.

Component progression

  1. 1I can derive and apply sign rules for multiplying rational numbers by extending the properties of operations (particularly the distributive property) to negative numbers, including showing why (−1)(−1) = 1, and interpret products in real-world contexts.
  2. 2I can show that every quotient of integers with a non-zero divisor is a rational number and that −(p/q) = (−p)/q = p/(−q), apply properties of operations as strategies to divide rational numbers, and interpret quotients in real-world contexts.
  3. 3I can convert a rational number to decimal form using long division, recognizing that the result always terminates in 0s or eventually repeats.
Number System · 7.NS.A.3

Solve real-world problems with rational numbers

Independently solve real-world and mathematical problems involving the four operations with rational numbers, including complex fractions. across representations and contexts.

Component progression

  1. 1I can simplify a complex fraction (a fraction containing fractions) by treating the numerator and denominator as division.
  2. 2I can solve a real-world word problem requiring an appropriate combination of the four operations with rational numbers.
  3. 3I can check that a computed answer to a rational-number problem is reasonable given the context.
Expressions Equations · 7.EE.A.1

Add, subtract, factor, and expand linear expressions

Independently apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. across representations and contexts.

Component progression

  1. 1I can add or subtract linear expressions with rational coefficients by combining like terms.
  2. 2I can expand a linear expression using the distributive property, including with negative coefficients.
  3. 3I can factor a linear expression by pulling out a common rational-coefficient factor.
Expressions Equations · 7.EE.A.2

Rewrite expressions to reveal relationships

Independently understand that rewriting an expression in different forms in a problem context can reveal how the quantities in it are related, such as recognizing that 'increase by 5%' means 'multiply by 1.05'. across representations and contexts.

Component progression

  1. 1I can rewrite a verbal statement of percent increase or decrease as an equivalent multiplication expression.
  2. 2I can rewrite an expression in an equivalent form that makes a relationship between quantities clearer.
  3. 3I can explain what the rewritten form of an expression reveals about the relationship between the quantities involved.
Expressions Equations · 7.EE.B.3

Solve multistep real-life problems with rational numbers

Independently solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically, applying properties of operations to calculate with numbers in any form, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies. across representations and contexts.

Component progression

  1. 1I can convert between fractions, decimals, and percents as needed to solve a multistep real-life problem.
  2. 2I can solve a multistep real-life problem involving positive and negative rational numbers, applying properties of operations and using tools strategically.
  3. 3I can use mental computation or estimation to assess whether a multistep problem's answer is reasonable.
Expressions Equations · 7.EE.B.4

Use equations and inequalities to solve problems

Independently 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: solve word problems leading to equations of the form px + q = r and p(x + q) = r, comparing an algebraic solution to an arithmetic solution and identifying the sequence of operations used in each approach; and solve word problems leading to inequalities of the form px + q > r or px + q < r, graphing the solution set of the inequality and interpreting it in the context of the problem. across representations and contexts.

Component progression

  1. 1I can write and solve word problems leading to equations of the form px + q = r or p(x + q) = r, where p, q, and r are specific rational numbers.
  2. 2I can compare an algebraic solution to an equation with an arithmetic solution to the same problem, identifying the sequence of operations used in each approach.
  3. 3I can write and solve an inequality of the form px + q > r or px + q < r, graph its solution set on a number line, and interpret the solution in the context of the problem.
Geometry · 7.G.A.1

Solve scale drawing problems

Independently 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. across representations and contexts.

Component progression

  1. 1I can use a given scale to find an actual length from a measurement on a scale drawing.
  2. 2I can use a given scale to find an actual area from a scale drawing, accounting for area scaling by the square of the scale factor.
  3. 3I can reproduce a scale drawing at a new specified scale.
Geometry · 7.G.A.2

Draw geometric figures and construct triangles

Independently draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions, focusing 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. across representations and contexts.

Component progression

  1. 1I can construct a triangle using a ruler and protractor given three measures of angles or sides.
  2. 2I can determine whether a given set of three angle or side measures determines a unique triangle.
  3. 3I can determine whether a given set of conditions allows for more than one possible triangle or no triangle at all.
Geometry · 7.G.A.3

Describe plane sections of three-dimensional figures

Independently describe the two-dimensional figures that result from slicing three-dimensional figures, such as plane sections of right rectangular prisms and right rectangular pyramids. across representations and contexts.

Component progression

  1. 1I can visualize how a plane can slice through a three-dimensional figure such as a prism or pyramid.
  2. 2I can identify the two-dimensional shape that results from a specific plane section of a three-dimensional figure.
  3. 3I can compare the different two-dimensional shapes that result from slicing the same three-dimensional figure at different angles or orientations.
Geometry · 7.G.B.4

Apply circle area and circumference formulas

Independently 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 circumference and area of a circle. across representations and contexts.

Component progression

  1. 1I can apply the formula c = 2πr (or c = πd) to find the circumference of a circle.
  2. 2I can apply the formula a = πr² to find the area of a circle.
  3. 3I can give an informal explanation of how a circle's circumference and area formulas are related.
Geometry · 7.G.B.5

Use angle relationships to solve problems

Independently use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. across representations and contexts.

Component progression

  1. 1I can identify supplementary, complementary, vertical, and adjacent angle pairs in a geometric figure.
  2. 2I can write an equation representing an angle relationship to solve for an unknown angle measure.
  3. 3I can solve a multistep problem requiring more than one angle relationship to find an unknown angle.
Geometry · 7.G.B.6

Solve area, volume, and surface-area problems

Independently 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. across representations and contexts.

Component progression

  1. 1I can find the area of a two-dimensional figure composed of triangles, quadrilaterals, and other polygons.
  2. 2I can find the volume of right prisms and solids composed of cubes and right prisms.
  3. 3I can find the surface area of a three-dimensional object composed of familiar shapes, accounting for every face.
Statistics Probability · 7.SP.A.1

Use random samples to make population inferences

Independently understand that statistics can be used to gain information about a population by examining a sample; generalizations about a population from a sample are valid only if the sample is representative of that population, and random sampling tends to produce representative samples and support valid inferences. across representations and contexts.

Component progression

  1. 1I can distinguish between a population and a sample drawn from it, and explain why sampling is used.
  2. 2I can explain why a randomly selected sample tends to be representative of the population it was drawn from.
  3. 3I can evaluate whether a described sampling method would produce a sample that supports valid generalizations about the population.
Statistics Probability · 7.SP.A.2

Use sample data to draw population inferences

Independently use data from a random sample to draw inferences about a population with an unknown characteristic of interest, generating multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. across representations and contexts.

Component progression

  1. 1I can use data from a random sample to make an inference about an unknown characteristic of the population.
  2. 2I can generate several random samples of the same size and compare their resulting estimates.
  3. 3I can interpret the variation observed across multiple sample estimates as a measure of how much a single estimate might differ from the true population value.
Statistics Probability · 7.SP.B.3

Compare data distributions visually and numerically

Independently 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. across representations and contexts.

Component progression

  1. 1I can visually assess the degree of overlap between two data distributions displayed on the same scale.
  2. 2I can find the numerical difference between the centers of two data distributions.
  3. 3I can express the difference between two distributions' centers as a multiple of a measure of variability, such as the mean absolute deviation.
Statistics Probability · 7.SP.B.4

Use center and variability for comparative inference

Independently use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. across representations and contexts.

Component progression

  1. 1I can compute a measure of center and a measure of variability for numerical data from two random samples.
  2. 2I can use the computed measures of center and variability to make an informal comparative inference about the two populations.
  3. 3I can justify a comparative inference about two populations using both the measures of center and variability from the samples.
Statistics Probability · 7.SP.C.5

Understand probability as a number between zero and one

Independently understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring, with larger numbers indicating 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. across representations and contexts.

Component progression

  1. 1I can interpret a given probability value between 0 and 1 in terms of how likely the event is to occur, recognizing values near 0 as unlikely, values around 1/2 as neither unlikely nor likely, and values near 1 as likely.
  2. 2I can compare the likelihood of two events using their probability values.
  3. 3I can identify a probability of 0 as an impossible event and a probability of 1 as a certain event.
Statistics Probability · 7.SP.C.6

Approximate probability using repeated observations

Independently 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. across representations and contexts.

Component progression

  1. 1I can collect data by repeating a chance process and recording the outcomes.
  2. 2I can compute the relative frequency of an event from collected data.
  3. 3I can predict the approximate relative frequency of an event over a given number of trials using its known probability.
Statistics Probability · 7.SP.C.7

Develop and compare probability models

Independently develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events; develop a probability model, which may not be uniform, by observing frequencies in data generated from a chance process, and compare probabilities from the model to observed frequencies, explaining possible sources of discrepancy if the agreement is not good. across representations and contexts.

Component progression

  1. 1I can develop a probability model assigning equal probability to all outcomes of a chance process and use it to find event probabilities.
  2. 2I can develop a probability model from observed frequencies in data, when outcomes are not equally likely.
  3. 3I can compare probabilities predicted by a probability model to frequencies actually observed in data, explaining any discrepancy.
Statistics Probability · 7.SP.C.8

Find probabilities of compound events

Independently find probabilities of compound events using organized lists, tables, tree diagrams, and simulation, understanding that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. across representations and contexts.

Component progression

  1. 1I can organize the full sample space for a compound event using a list, table, or tree diagram.
  2. 2I can find the probability of a compound event as the fraction of outcomes in the sample space where the event occurs.
  3. 3I can design and use a simulation to estimate the probability of a compound event.
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