College and Career-Ready Frameworks

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.

Beam to Moon (Ratios and Proportions)

Household Energy Usage

Road Trip (Problem Solving)

Unit Conversions

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

7.RP.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.

Beam to Moon (Ratios and Proportions)

Direct and Inverse Variation

Estimating Population Size

Part-to-part and Part-to-whole Ratios

Percents and Proportions

Proportions and Common Multipliers

7.RP.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

Direct and Inverse Variation

Perimeters and Areas of Similar Figures

Similar Figures

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

Beam to Moon (Ratios and Proportions)

Direct and Inverse Variation

Geometric Probability

Part-to-part and Part-to-whole Ratios

Polling: Neighborhood

Proportions and Common Multipliers

Theoretical and Experimental Probability

7.RP.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.

7.RP.3: Use proportional relationships to solve multistep ratio and percent problems.

Beam to Moon (Ratios and Proportions)

Estimating Population Size

Part-to-part and Part-to-whole Ratios

Percent of Change

Percents and Proportions

Percents, Fractions, and Decimals

Polling: Neighborhood

Proportions and Common Multipliers

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.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

Rational Numbers, Opposites, and Absolute Values

7.NS.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.

Adding and Subtracting Integers

Adding on the Number Line

Improper Fractions and Mixed Numbers

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations I

Sums and Differences with Decimals

7.NS.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

Adding and Subtracting Integers with Chips

Adding on the Number Line

Equivalent Algebraic Expressions I

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations I

Sums and Differences with Decimals

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

Adding Fractions (Fraction Tiles)

Adding and Subtracting Integers

Adding on the Number Line

Equivalent Algebraic Expressions I

Estimating Sums and Differences

Fractions Greater than One (Fraction Tiles)

Improper Fractions and Mixed Numbers

Sums and Differences with Decimals

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

7.NS.2a: 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.

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

7.NS.2b: 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.

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

Adding and Subtracting Integers

Dividing Fractions

Dividing Mixed Numbers

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

7.NS.2d: 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.

Percents, Fractions, and Decimals

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

Adding Fractions (Fraction Tiles)

Adding and Subtracting Integers

Adding on the Number Line

Dividing Fractions

Dividing Mixed Numbers

Estimating Population Size

Estimating Sums and Differences

Fractions Greater than One (Fraction Tiles)

Improper Fractions and Mixed Numbers

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

Sums and Differences with Decimals

7.EE.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

7.EE.2: Understand 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.

Exponents and Power Rules

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

7.EE.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.

Adding Fractions (Fraction Tiles)

Adding Whole Numbers and Decimals (Base-10 Blocks)

Adding and Subtracting Integers

Adding on the Number Line

Dividing Fractions

Dividing Mixed Numbers

Estimating Sums and Differences

Fraction Garden (Comparing Fractions)

Fractions Greater than One (Fraction Tiles)

Fractions with Unlike Denominators

Improper Fractions and Mixed Numbers

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

Part-to-part and Part-to-whole Ratios

Percent of Change

Percents and Proportions

Percents, Fractions, and Decimals

Subtracting Whole Numbers and Decimals (Base-10 Blocks)

Sums and Differences with Decimals

Toy Factory (Set Models of Fractions)

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.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.

Absolute Value Equations and Inequalities

Circles

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Order of Operations

Solving Algebraic Equations I

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Two-Step Equations

7.EE.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.

Absolute Value Equations and Inequalities

Rational Numbers, Opposites, and Absolute Values

Solving Linear Inequalities in One Variable

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.

Dilations

Perimeters and Areas of Similar Figures

Similar Figures

7.G.2: Draw (freehand, with ruler and protractor, and 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.

3D and Orthographic Views

Concurrent Lines, Medians, and Altitudes

Triangle Inequalities

7.G.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

7.G.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.

Investigating Angle Theorems

Triangle Angle Sum

7.G.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

Area of Triangles

Balancing Blocks (Volume)

Chocomatic (Multiplication, Arrays, and Area)

Fido's Flower Bed (Perimeter and Area)

Perimeter and Area of Rectangles

Prisms and Cylinders

Pyramids and Cones

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

7.SP.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

Populations and Samples

7.SP.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.

Polling: City

Polling: Neighborhood

Populations and Samples

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.

Box-and-Whisker Plots

Describing Data Using Statistics

Mean, Median, and Mode

Movie Reviewer (Mean and Median)

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

Real-Time Histogram

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.

Box-and-Whisker Plots

Polling: City

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

7.SP.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

Independent and Dependent Events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

7.SP.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.

Probability Simulations

Theoretical and Experimental Probability

7.SP.7: 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.

7.SP.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

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

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

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

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

7.SP.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

Theoretical and Experimental Probability

7.SP.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

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

Independent and Dependent Events

Correlation last revised: 9/15/2020