7 Math Standards / Action Plan
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Domain
Description of DomainStandardDescription of StandardCombined Standard# of Students Requiring Intervention# of Students Achieving Mastery% of Students Achieving Mastery
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■ 7.RP
Ratios and Proportional Relationships
AAnalyze proportional relationships and use them to solve real-world and mathematical problems.■ 7.RP.A
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■ 7.RP
Ratios and Proportional Relationships
A.1Compute 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.A.1
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■ 7.RP
Ratios and Proportional Relationships
A.2Recognize and represent proportional relationships between quantities.■ 7.RP.A.2
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■ 7.RP
Ratios and Proportional Relationships
A.2.ADecide 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.2.A
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■ 7.RP
Ratios and Proportional Relationships
A.2.BIdentify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.■ 7.RP.A.2.B
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■ 7.RP
Ratios and Proportional Relationships
A.2.CRepresent 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.2.C
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■ 7.RP
Ratios and Proportional Relationships
A.2.DExplain 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.2.D
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■ 7.RP
Ratios and Proportional Relationships
A.3Use 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.RP.A.3
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■ 7.NSThe Number SystemAApply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.■ 7.NS.A
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■ 7.NSThe Number SystemA.1Apply 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.1
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■ 7.NSThe Number SystemA.1.ADescribe situations in which opposite quantities combine to make 0. For example, in the first round of a game, Maria scored 20 points. In the second round of the same game, she lost 20 points. What is her score at the end of the second round?■ 7.NS.A.1.A
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■ 7.NSThe Number SystemA.1.BUnderstand 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.A.1.B
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■ 7.NSThe Number SystemA.1.CUnderstand 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.A.1.C
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■ 7.NSThe Number SystemA.1.DApply properties of operations as strategies to add and subtract rational numbers.■ 7.NS.A.1.D
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■ 7.NSThe Number SystemA.2Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.■ 7.NS.A.2
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■ 7.NSThe Number SystemA.2.AUnderstand 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.A.2.A
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■ 7.NSThe Number SystemA.2.BUnderstand 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.A.2.B
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■ 7.NSThe Number SystemA.2.CApply properties of operations as strategies to multiply and divide rational numbers.■ 7.NS.A.2.C
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■ 7.NSThe Number SystemA.2.DConvert 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.A.2.D
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■ 7.NSThe Number SystemA.3Solve real-world and mathematical problems involving the four operations with rational numbers.■ 7.NS.A.3
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■ 7.EEExpressions and EquationsAUse properties of operations to generate equivalent expressions.■ 7.EE.A
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■ 7.EEExpressions and EquationsA.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.■ 7.EE.A.1
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■ 7.EEExpressions and EquationsA.2Understand 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.”■ 7.EE.A.2
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■ 7.EEExpressions and EquationsBSolve real-life and mathematical problems using numerical and algebraic expressions and equations.■ 7.EE.B
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■ 7.EEExpressions and EquationsB.3Solve 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.■ 7.EE.B.3
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■ 7.EEExpressions and EquationsB.4Use 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.4
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■ 7.EEExpressions and EquationsB.4.ASolve 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. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?■ 7.EE.B.4.A
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■ 7.EEExpressions and EquationsB.4.BSolve 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.■ 7.EE.B.4.B
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○ 7.GGeometryADraw, construct, and describe geometrical figures and describe the relationships between them.○ 7.G.A
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○ 7.GGeometryA.1Solve 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.1
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○ 7.GGeometryA.2Draw (with technology, with ruler and protractor, as well as freehand) 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.2
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○ 7.GGeometryA.3Describe 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.A.3
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○ 7.GGeometryBSolve real-life and mathematical problems involving angle measure, area, surface area, and volume.○ 7.G.B
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○ 7.GGeometryB.4Know 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.B.4
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○ 7.GGeometryB.5Use 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.5
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○ 7.GGeometryB.6Solve 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.G.B.6
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□ 7.SPStatistics and ProbabilityAUse random sampling to draw inferences about a population.□ 7.SP.A
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□ 7.SPStatistics and ProbabilityA.1Understand 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.A.1
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□ 7.SPStatistics and ProbabilityA.2Use 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.□ 7.SP.A.2
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○ 7.SPStatistics and ProbabilityBDraw informal comparative inferences about two populations.○ 7.SP.B
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○ 7.SPStatistics and ProbabilityB.3Informally 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 10 cm 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.3
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○ 7.SPStatistics and ProbabilityB.4Use 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.○ 7.SP.B.4
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□ 7.SPStatistics and ProbabilityCInvestigate chance processes and develop, use, and evaluate probability models.□ 7.SP.C
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□ 7.SPStatistics and ProbabilityC.5Understand 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.C.5
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□ 7.SPStatistics and ProbabilityC.6Approximate 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.6
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□ 7.SPStatistics and ProbabilityC.7Develop 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.7
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□ 7.SPStatistics and ProbabilityC.7.ADevelop 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.7.A
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□ 7.SPStatistics and ProbabilityC.7.BDevelop 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?□ 7.SP.C.7.B
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□ 7.SPStatistics and ProbabilityC.8Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.□ 7.SP.C.8
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□ 7.SPStatistics and ProbabilityC.8.AUnderstand 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.8.A
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□ 7.SPStatistics and ProbabilityC.8.BRepresent 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.8.B
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□ 7.SPStatistics and ProbabilityC.8.CDesign 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% 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?□ 7.SP.C.8.C