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Washington Standards

Washington 7th Grade Math Standards

All 27 Washington math standards for 7th grade, each explained in plain English. The official wording is one click away under each one.

27 standards

Data Analysis

12 standards
Formulate statistical investigative questions.
M.7.DA.DS.1
Ask statistical questions about a whole population that can be answered using samples, like what share of students in the school bike to class.
Official wording
Pose statistical investigative questions about a broader population using samples taken from the population.
Collect and consider data.
M.7.DA.DS.2
Explain that a sample only tells about a population if it represents it fairly, and that data can compare different groups at once or one group over time.
Official wording
Understand information from a sample is valid only if the sample is representative of that population. Understand data can be used to make comparisons between different groups at one point in time and the same group over time.
Analyze the data.
M.7.DA.DS.3
Find and interpret mean, median, range and interquartile range to summarize data and answer a question, and compare two groups by reasoning about their distributions.
Official wording
Identify, determine, and interpret measures of center (mean and median) and measures of variability (range, interquartile range) to answer a statistically investigative question, summarizing the distribution of data using the measures of center and variability. Use reasoning about distributions to compare two groups based on the variables.
Interpret results.
M.7.DA.DS.4
Draw conclusions that reach beyond the data while recognizing that results vary from sample to sample, so comparisons carry some uncertainty.
Official wording
Acknowledge that looking beyond the data is feasible and recognize the uncertainty caused by sample-to-sample variability when making comparisons and/or conclusions from data to answer the investigative question.
Use random sampling to draw inferences about a population.
M.7.DA.SP.1
Understand that a random sample can tell you about a whole population, but only if the sample fairly represents it.
Official wording
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.
Common Core 7.SP.1
M.7.DA.SP.2
Use a random sample to estimate something unknown about a population, and run several same-size samples or simulations to see how much estimates vary.
Official wording
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.
Draw informal comparative inferences about two populations.
M.7.DA.SP.3
Judge how much two data sets with similar spread overlap by expressing the gap between their centers as a multiple of the spread, like twice the mean absolute deviation.
Official wording
Informally assess the degree of 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.
M.7.DA.SP.4
Compare two populations informally using the centers and spreads of random samples, like how long seventh and eighth graders sleep.
Official wording
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
Investigate chance processes and develop, use, and evaluate probability models.
M.7.DA.SP.5
Know that a probability is a number from 0 to 1, where near 0 means unlikely, 1/2 means as likely as not, and near 1 means likely.
Official wording
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.
Common Core 7.SP.5
M.7.DA.SP.6
Estimate a probability by repeating a chance process many times and tracking how often an outcome happens, and predict frequencies from a given probability.
Official wording
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.
M.7.DA.SP.7
Build a probability model, either with equally likely outcomes or from observed data, and explain when results do not match it.
Official wording
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.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.bDevelop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
Common Core 7.SP.7
M.7.DA.SP.8
Find the probability of a compound event, like rolling double sixes, by listing outcomes in a table or tree diagram or by running a simulation.
Official wording
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.aUnderstand the probability of a compound event is a fraction of the outcomes of the sample space.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.cDesign and use a simulation to generate frequencies for compound events.
Common Core 7.SP.8

Quantity

3 standards
Apply and extend previous understandings of operations with fractions.
M.7.Q.NS.1
Add and subtract positive and negative numbers on a number line, see that opposites make 0 and that subtracting means adding the opposite, like 4 - 9 = 4 + -9 = -5.
Official wording
Efficiently, flexibly, and accurately 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.aDescribe situations in which opposite quantities combine to make 0.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.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.dApply properties of operations as strategies to add and subtract rational numbers.
M.7.Q.NS.2
Multiply and divide positive and negative numbers using the sign rules, like -3 x -4 = 12, and write fractions as decimals that either end or repeat, like 5/8 = 0.625.
Official wording
Efficiently, flexibly, and accurately apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.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.bUnderstand integers can be divided as long as the divisor isn't zero, resulting in rational numbers.cApply properties of operations as strategies to multiply and divide rational numbers.dConvert rational numbers into decimals using flexible, efficient, and accurate strategies, recognizing that the decimal form either ends in 0s or repeats eventually.
Draw, construct, and describe geometrical figures and describe the relationships between them.
M.7.Q.G.1
Solve scale drawing problems, finding real lengths and areas from a drawing and redrawing it at a new scale, like a map where 1 inch means 5 miles.
Official wording
Efficiently, flexibly, and accurately 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.

Relationships

7 standards
Analyze proportional relationships and use them to solve real-world and mathematical problems.
M.7.R.RP.1
Find unit rates from ratios of fractions, including lengths and areas, like walking 1/2 mile in 1/4 hour is 2 miles per hour.
Official wording
Efficiently, flexibly, and accurately compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
M.7.R.RP.2
Decide whether two quantities are proportional, find the constant of proportionality, and write the relationship as an equation like t = pn.
Official wording
Recognize and represent proportional relationships between quantities.aDecide whether the relationship between two quantities is proportional using equivalent ratios in a table, graphing on the coordinate plane to see of the graph is a straight line through origin.bIdentify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.cWrite equations for proportional relationships.dAnalyze graphs to understand what the data points indicate about the real-world situation, focusing on points like (0, 0) and (1, r) where r is the unit rate.
Common Core 7.RP.2
M.7.R.RP.3
Use proportions to solve multistep percent problems such as sales tax, tips, discounts, markups, interest, commissions and percent change or error.
Official wording
Efficiently, flexibly, and accurately 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.
Use properties of operations to generate equivalent expressions.
M.7.R.EE.1
Add, subtract, factor and expand linear expressions with fraction or decimal coefficients using properties of operations, like 0.5x + 0.25x = 0.75x.
Official wording
Efficiently, flexibly, and accurately use properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
M.7.R.EE.2
Rewrite an expression in another form to see how the quantities in a problem relate, like a + 0.05a = 1.05a showing a 5% increase.
Official wording
Understand that rewriting an expression in different forms in a problem context can bring awareness to parts of the problem and how the quantities in it are related.
Efficiently, flexibly, and accurately solve real-life and mathematical problems using numerical and algebraic expressions and equations.
M.7.R.EE.3
Solve multistep real-world problems with positive and negative whole numbers, fractions and decimals, converting between forms as needed and estimating to check.
Official wording
Efficiently, flexibly, and accurately 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.
M.7.R.EE.4
Write and solve equations like 3x + 5 = 20 and inequalities like 2x - 4 > 10 for word problems, graph inequality solutions and explain them in context.
Official wording
Use variables to represent quantities in a real-world or mathematical problem and write equations and inequalities to efficiently, flexibly, and accurately to solve problems by reasoning about the quantities.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. Compare solving the same problem algebraically vs. with arithmetic, explaining the steps involved in each approach.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 solutions of these inequalities and interpret them in context of the problem.

Spatial Reasoning

5 standards
Draw, construct, and describe geometrical figures and describe the relationships between them.
M.7.SR.G.2
Draw shapes with given conditions, mainly triangles from three angle or side measures, and notice when they make one triangle, several or none.
Official wording
Draw 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.
M.7.SR.G.3
Describe the flat shape you get when you slice through a rectangular box or pyramid.
Official wording
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Common Core 7.G.3
Solve real-world and mathematical problems involving area, surface area, and volume.
M.7.SR.G.4
Use the formulas for a circle's area and circumference to solve problems, like fencing a round garden, and informally explain how the two are connected.
Official wording
Know the formulas for the area and circumference of a circle and use them to solve problems; informally show the relationship between the circumference and area of a circle.
M.7.SR.G.5
Find an unknown angle by writing an equation from angle facts, like two angles on a straight line adding to 180 degrees.
Official wording
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.
Common Core 7.G.5
M.7.SR.G.6
Solve real-world area, volume and surface area problems for cubes, right prisms and shapes built from triangles, quadrilaterals and other polygons, like wrapping a box.
Official wording
Efficiently, flexibly, and accurately 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.

The official Washington documents

Washington State Learning Standards for Mathematics by the Office of Superintendent of Public Instruction are available under a Creative Commons Attribution License (CC BY 4.0).

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

The plain-English lines are EMStudio's own explanations, shown beside the official wording. They are not part of the standards.