Common Core State Standards

CCSS.Math.Content.7.RP: Ratios and Proportional Relationships

CCSS.Math.Content.7.RP.A: Analyze proportional relationships and use them to solve real-world and mathematical problems.

CCSS.Math.Content.7.RP.A.2a: Decide 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.

Direct and Inverse Variation

Proportions and Common Multipliers

CCSS.Math.Content.7.RP.A.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Beam to Moon (Ratios and Proportions)

Dilations

Perimeters and Areas of Similar Figures

Similar Figures

CCSS.Math.Content.7.RP.A.2c: Represent proportional relationships by equations.

Beam to Moon (Ratios and Proportions)

Estimating Population Size

Geometric Probability

Polling: Neighborhood

Theoretical and Experimental Probability

CCSS.Math.Content.7.RP.A.2d: 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.

CCSS.Math.Content.7.RP.A.3: Use proportional relationships to solve multistep ratio and percent problems.

Estimating Population Size

Percent of Change

Percents and Proportions

Polling: Neighborhood

Real-Time Histogram

Time Estimation

CCSS.Math.Content.7.NS: The Number System

CCSS.Math.Content.7.NS.A: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

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

Adding and Subtracting Integers

Adding and Subtracting Integers with Chips

Integers, Opposites, and Absolute Values

CCSS.Math.Content.7.NS.A.1b: 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.

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations I

Solving Algebraic Equations II

CCSS.Math.Content.7.NS.A.1c: 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.

Adding and Subtracting Integers

Equivalent Algebraic Expressions I

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations I

CCSS.Math.Content.7.NS.A.1d: Apply properties of operations as strategies to add and subtract rational numbers.

Adding and Subtracting Integers with Chips

CCSS.Math.Content.7.EE: Expressions and Equations

CCSS.Math.Content.7.EE.A: Use properties of operations to generate equivalent expressions.

CCSS.Math.Content.7.EE.A.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations I

Solving Algebraic Equations II

CCSS.Math.Content.7.EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

CCSS.Math.Content.7.EE.B.3: 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.

Percent of Change

Percents and Proportions

CCSS.Math.Content.7.EE.B.4a: 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.

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Two-Step Equations

CCSS.Math.Content.7.EE.B.4b: Solve 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.

Solving Linear Inequalities in One Variable

CCSS.Math.Content.7.G: Geometry

CCSS.Math.Content.7.G.A: Draw, construct, and describe geometrical figures and describe the relationships between them.

CCSS.Math.Content.7.G.A.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.

Dilations

Perimeters and Areas of Similar Figures

Similar Figures

CCSS.Math.Content.7.G.B: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

CCSS.Math.Content.7.G.B.4: 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.

Circumference and Area of Circles

CCSS.Math.Content.7.G.B.5: 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.

CCSS.Math.Content.7.G.B.6: 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.

Area of Parallelograms

Balancing Blocks (Volume)

Perimeter and Area of Rectangles

Prisms and Cylinders

Pyramids and Cones

Surface and Lateral Areas of Pyramids and Cones

CCSS.Math.Content.7.SP: Statistics and Probability

CCSS.Math.Content.7.SP.A: Use random sampling to draw inferences about a population.

CCSS.Math.Content.7.SP.A.1: 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.

Polling: City

Polling: Neighborhood

CCSS.Math.Content.7.SP.A.2: 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.

Estimating Population Size

Polling: City

Polling: Neighborhood

Populations and Samples

CCSS.Math.Content.7.SP.B: Draw informal comparative inferences about two populations.

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

Box-and-Whisker Plots

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

CCSS.Math.Content.7.SP.C: Investigate chance processes and develop, use, and evaluate probability models.

CCSS.Math.Content.7.SP.C.5: 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.

Geometric Probability

Lucky Duck (Expected Value)

Probability Simulations

Theoretical and Experimental Probability

CCSS.Math.Content.7.SP.C.6: 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.

Lucky Duck (Expected Value)

Probability Simulations

Theoretical and Experimental Probability

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

Independent and Dependent Events

Probability Simulations

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

CCSS.Math.Content.7.SP.C.8a: 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.

Independent and Dependent Events

CCSS.Math.Content.7.SP.C.8b: 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.

Independent and Dependent Events

Permutations and Combinations

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

Independent and Dependent Events

Correlation last revised: 1/22/2020

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

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