### 7.RP: Ratios and Proportional Relationships

#### 1.1: Analyze proportional relationships and use them to solve real world and mathematical problems.

7.RP.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

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

7.RP.2.a: Decide whether two quantities are in a proportional relationship 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.2.b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

7.RP.2.c: Represent proportional relationships by equations.

7.RP.2.d: 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.3: Use proportional relationships to solve multi-step ratio and percent problems.

### 7.NS: The Number System

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

7.NS.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.1.a: Describe situations in which opposite quantities combine to make 0.

7.NS.1.b.i: Understand p + q as the number located a distance |q| from p on a number line, in the direction indicated by the sign of q.

7.NS.1.b.ii: Show that a number and its opposite have a sum of 0 (are additive inverses).

7.NS.1.b.iii: Interpret sums of rational numbers by describing real world contexts.

7.NS.1.c.i: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q).

7.NS.1.c.ii: 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.1.d: Apply properties of operations as strategies to fluently add and subtract rational numbers.

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

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

7.NS.2.b.ii: Interpret quotients of rational numbers by describing real world contexts.

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

7.NS.2.d.i: Convert a rational number to a decimal using long division.

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

### 7.EE: Expressions and Equations

#### 3.1: Use properties of operations to generate equivalent expressions.

7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients with an emphasis on writing equivalent expressions.

7.EE.2: Understand that rewriting an expression in different forms in a problem context can clarify the problem and how the quantities in it are related.

#### 3.2: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

7.EE.3.i: Solve multi-step real-life and mathematical problems posed with rational numbers in any form (positive and negative, fractions, decimals, and integers), using tools strategically.

7.EE.3.ii: Apply properties of operations to calculate with numbers in any form.

7.EE.3.iii: Convert between forms as appropriate.

7.EE.3.iv: Assess the reasonableness of answers using mental computation and estimation strategies.

7.EE.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.4.a.i: 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.4.a.ii: Solve equations of these forms fluently.

7.EE.4.a.iii: Compare the algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

7.EE.4.b.ii: Graph the solution set of the inequality and interpret it in the context of the problem.

### 7.G: Geometry

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

7.G.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.2: Draw geometric shapes from 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. Use a variety of methods such as freehand, with ruler and protractor, and with technology.

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

7.G.4.i: Know the formulas for the area and circumference of a circle and use them to solve problems.

7.G.4.ii: Informally derive the relationship between the circumference and area of a circle.

7.G.5: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure.

7.G.6.i: Solve real world and mathematical problems involving area of two-dimensional figures composed of polygons and/or circles, including composite figures.

7.G.6.ii: Use nets to solve real world and mathematical problems involving surface area of prisms and cylinders, including composite solids.

7.G.6.iii: Solve real world and mathematical problems involving volumes of right prisms, including composite solids.

### 7.SP: Statistics and Probability

#### 5.1: Use random sampling to draw inferences about a population.

7.SP.1.i: Understand that statistics can be used to gain information about a population by examining a sample of the population.

7.SP.1.ii: Understand that generalizations about a population from a sample are valid only if the sample is representative of that population.

7.SP.1.iii: Understand that random sampling tends to produce representative samples and support valid inferences.

7.SP.2.i: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

7.SP.2.ii: Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

#### 5.2: Draw informal comparative inferences about two populations.

7.SP.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.

7.SP.4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

#### 5.3: Investigate chance processes and develop, use, and evaluate probability models.

7.SP.5: Understand that the probability of a chance event is a number from 0 through 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.

7.SP.6.ii: Predict the approximate relative frequency given the probability.

7.SP.7.i: Develop a probability model and use it to find probabilities of events .

7.SP.7.ii: Compare probabilities from a model to observed frequencies. If there is a discrepancy, explain possible sources.

7.SP.7.ii.a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

7.SP.7.ii.b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

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

7.SP.8.a: 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.8.b.i: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams.

7.SP.8.b.ii: For an event described in everyday language (such as “rolling double sixes”), identify the outcomes in the sample space which compose the event.

7.SP.8.c: Design and use a simulation to generate frequencies for compound events.

Correlation last revised: 9/24/2019

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.