Grade 7 Math South Dakota Standards

Write and solve equations (𝑦𝑦 = 𝑘𝑘𝑘𝑘 or 𝑦𝑦 = 𝑚𝑚𝑚𝑚 + 𝑏𝑏) to represent relationships between quantities.

Add, subtract, factor, and expand linear expressions with rational coefficients using multiple grouping symbols.

Write and solve two-step equations in real-world and mathematical problems in the form of 𝑝𝑝𝑝𝑝 + 𝑞𝑞 = 𝑟𝑟 and 𝑝𝑝(𝑥𝑥 + 𝑞𝑞) = 𝑟𝑟 where 𝑝𝑝, 𝑞𝑞, and 𝑟𝑟 are specific rational numbers.

Write, solve, and graph two-step inequalities in real-world and mathematical problems in the forms of 𝑝𝑝𝑝𝑝 + 𝑞𝑞 > 𝑟𝑟, 𝑝𝑝𝑝𝑝 + 𝑞𝑞 ≥ 𝑟𝑟, 𝑝𝑝𝑝𝑝 + 𝑞𝑞 < 𝑟𝑟, and 𝑝𝑝𝑝𝑝 + 𝑞𝑞 ≤ 𝑟𝑟, where 𝑝𝑝, 𝑞𝑞, and 𝑟𝑟 are specific rational numbers.

Use tables, graphs, and equations to distinguish between proportional and non-proportional relationships.

Identify, describe, and draw elements of circles, including center, radius, and diameter.

Use the constant ratio pi (𝜋𝜋 = 𝐶𝐶 𝑑𝑑 ) to calculate the circumference and area of a circle.

Use area (𝐴𝐴 = 𝜋𝜋𝑟𝑟2) and circumference (𝐶𝐶 = 2𝜋𝜋𝜋𝜋) formulas of a circle to solve real-world and mathematical problems.

Solve real-world and mathematical problems involving area, volume and surface area of two and three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Describe the two-dimensional figure (cross section) that results from slicing a three-dimensional figure including right rectangular prisms, triangular prisms, pyramids and cylinders.

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.

Solve multi-step problems involving supplementary, complementary, vertical, and adjacent angles to include solving for an unknown angle in a figure.

Calculate the scale factor, compute the actual lengths from the scale in a drawing, and reproduce a scale drawing using another scale.

Model and describe additive inverse in real-world situations to show opposite quantities combine to make zero (positive or negative).

Demonstrate in real-world contexts the distance between two rational numbers on the number line as the absolute value of their differences.

Convert a rational number in fraction form to decimal form and recognize that the decimal form of a rational number terminates in zeros or eventually repeats (using bar notation).

Understand that integers can be divided, provided the divisor is not zero.

Add and subtract rational numbers using horizontal or vertical number lines and real-world contexts.

Solve multi-step problems with rational numbers (whole numbers, fractions, and decimals) and justify the steps taken.

Multiply and divide rational numbers (integers, fractions, decimals etc.) in real-world and mathematical problems.

Calculate unit rates in real-world contexts that include complex fractions.

Determine the unit rate (constant of proportionality 𝑦𝑦 = 𝑘𝑘𝑘𝑘) from tables, graphs, equations, diagrams, or verbal descriptions of proportional relationships.

Solve multi-step ratio and percent problems using proportional reasoning.

Determine whether two quantities are in a proportional relationship, by determining if each have a constant rate of change that starts at (0,0), using tables, graphs, equations, diagrams, and verbal descriptions.

Explain what a point (𝑥𝑥, 𝑦𝑦) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1, 𝑟𝑟) where 𝑟𝑟 is the unit rate.

Understand sampling to be a selection of a smaller group (sample) from a larger group (population).

Calculate the probability for a compound event using organized lists, tables, tree diagrams, and a simulation.

Compare random and convenience sampling to determine if a sample is representative of a population.

Draw conclusions, such as mean, median, mode, and range of data, about a larger population using data from a representative sample.

Understand a sample space to be the set of all possible outcomes for a situation or experiment.

Understand probability as the likelihood or chance of an event occurring.

Recognize that probabilities in a simple experiment can be qualitative descriptors of likelihood: impossible (0), unlikely, neither likely nor unlikely, likely, or certain (1).

Calculate the probability for a single event by dividing the number of favorable outcomes by the number of total outcomes.

Determine experimental probabilities in simple experiments and represent as fractions, decimals, and percents.

Use theoretical probability of an event in a simple experiment to predict the number of times that an event will occur for a large number of experiments.

Algebra

Geometry

Measurement

Relationships between Quantities

Constant of Proportionality

Rational Numbers

Expressions

Equations and Inequalities

Rational Number Operations

Cross Sections

Scale

Sampling and Population

Probability

Area, Volume, and Surface Area

Ratio and Rates

Triangle and Angles

Numbers Concepts and Computations

Proportional Relationships

Statistics and Probability

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients to include multiple grouping symbols (parentheses, brackets, and/or braces).

Understand the reason for rewriting an expression in different forms in contextual problems is to provide multiple ways of interpreting 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".

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. 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.

Assess the reasonableness of answers using mental computation and estimation strategies. For example, if you want to place a towel bar 9 ¾ inches long in the center of a door that is 27 ½ 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.

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, 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.

Solve word problems leading to inequalities of the form px + q > r, px + q ≥ r, px + q < r, and 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.

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.

Draw (freehand, with ruler and protractor/angle ruler, and/or 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.

Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

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.

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.

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.

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.

Describe situations in which opposite quantities combine to make 0. For example, if you get paid $5 for babysitting but you owe your friend $5, you have $0.

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.

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.

Apply properties of operations as strategies to add and subtract rational numbers.

Apply and extend previous understandings of multiplication and division and of fractions 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 products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

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.

Apply properties of operations as strategies to multiply and divide rational numbers.

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.

Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)

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 ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½/¼ miles per hour, equivalently 2 miles per hour.

Recognize and represent proportional relationships between quantities.

Decide whether two quantities are in a proportional relationship. For example, 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.

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

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.

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.

Use proportional relationships to solve multistep ratio and percent problems. For example, simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

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.

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.

Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, using quantitative measures of center (focusing on mean and median) and variability (interquartile range, mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. 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.

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.

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 ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

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.

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.

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.

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 from the spinning penny appear to be equally likely based on the observed frequencies?

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

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.

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.

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% 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?

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

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

Draw informal comparative inferences about two populations.

Ratios and Proportional Relationships

Use properties of operations to generate equivalent expressions.

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

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

The Number System

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

Standards for Mathematical Practice

Expressions and Equations

Statistics and Probability

Investigate chance processes and develop, use and evaluate probability models.

Use random sampling to draw inferences about a population.

Geometry