7.NS: Number Sense

7.NS.1: Find the prime factorization of whole numbers and write the results using exponents.

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

7.NS.2: Understand the inverse relationship between squaring and finding the square root of a perfect square whole number. Find square roots of perfect square whole numbers.

Ordering and Approximating Square Roots
Square Roots

7.NS.3: Know there are rational and irrational numbers. Identify, compare, and order rational and irrational numbers (e.g., square root of 2, square root of 3, square root of 5, pi) and plot them on a number line.

Ordering and Approximating Square Roots
Square Roots

7.C: Computation

7.C.1: 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 on a number line that a number and its opposite have a sum of 0 (are additive inverses). Find and interpret sums of rational numbers in real-world contexts.

Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Adding on the Number Line
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

7.C.2: 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

7.C.3: 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.

Adding and Subtracting Integers
Multiplying Mixed Numbers
Multiplying with Decimals

7.C.5: 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)
Road Trip (Problem Solving)
Unit Conversions

7.C.6: Use proportional relationships to solve ratio and percent problems with multiple operations (e.g., simple interest, tax, markups, markdowns, gratuities, conversions within and across measurement systems, and percent increase and decrease).

Fraction, Decimal, Percent (Area and Grid Models)
Percent of Change
Percents, Fractions, and Decimals

7.C.7: Compute fluently with rational numbers using an algorithmic approach.

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
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Mixed Numbers
Multiplying with Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

7.C.8: Solve real-world problems with rational numbers by using one or two operations.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Multiplying Mixed Numbers
Multiplying with Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

7.AF: Algebra and Functions

7.AF.1: Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear expressions, including situations that involve factoring out a common number (e.g., given 2x – 10, create an equivalent expression 2(x – 5)). Justify each step in the process.

Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

7.AF.2: Solve equations of the form px + q = r and p(x + q) = r fluently, where p, q, and r are specific rational numbers. Represent real-world problems using equations of these forms and solve such problems.

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Two-Step Equations

7.AF.3: Solve inequalities of the form px + q (> or >=) r or px + q (< or <=) r, where p, q, and r are specific rational numbers. Represent real-world problems using inequalities of these forms and solve such problems. Graph the solution set of the inequality and interpret it in the context of the problem.

Exploring Linear Inequalities in One Variable

7.AF.4: Define slope as vertical change for each unit of horizontal change and recognize that a constant rate of change or constant slope describes a linear function. Identify and describe situations with constant or varying rates of change.

Cat and Mouse (Modeling with Linear Systems)
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

7.AF.5: Graph a line given its slope and a point on the line. Find the slope of a line given its graph.

Cat and Mouse (Modeling with Linear Systems)
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

7.AF.6: 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
Proportions and Common Multipliers

7.AF.7: Identify the unit rate or constant of proportionality in tables, graphs, equations, and verbal descriptions of proportional relationships.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation

7.AF.8: Explain what the coordinates of a point on the graph of a proportional relationship mean in terms of the situation, with special attention to the points (0,0) and (1,r), where r is the unit rate.

Direct and Inverse Variation

7.AF.9: Represent real-world and other mathematical situations that involve proportional relationships. Write equations and draw graphs to represent these proportional relationships. Recognize that these situations are described by a linear function in the form y = mx, where the unit rate, m, is the slope of the line.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Perimeters and Areas of Similar Figures
Proportions and Common Multipliers

7.GM: Geometry and Measurement

7.GM.1: Explore triangles with given conditions from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle

Classifying Triangles
Triangle Inequalities

7.GM.2: Identify and describe similarity relationships of polygons including the angle-angle criterion for similar triangles, and solve problems involving similarity.

Similar Figures
Similarity in Right Triangles

7.GM.3: Solve real-world and other mathematical problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing. Create a scale drawing by using proportional reasoning.

Dilations
Similar Figures

7.GM.4: Solve real-world and other mathematical problems using facts about vertical, adjacent, complementary, and supplementary angles.

Investigating Angle Theorems
Triangle Angle Sum

7.GM.5: Understand the formulas for area and circumference of a circle and use them to solve real-world and other mathematical problems; give an informal derivation of the relationship between circumference and area of a circle.

Circumference and Area of Circles

7.GM.6: Solve real-world and other mathematical problems involving volume of cylinders and three-dimensional objects composed of right rectangular prisms.

Prisms and Cylinders

7.GM.7: Construct nets for right rectangular prisms and cylinders and use the nets to compute the surface area; apply this technique to solve real-world and other mathematical problems.

Surface and Lateral Areas of Prisms and Cylinders

7.DSP: Data Analysis, Statistics, and Probability

7.DSP.1: Understand that statistics can be used to gain information about a population by examining a sample of the population. Understand that conclusions and generalizations about a population from a sample are valid only if the sample is representative of that population and that random sampling tends to produce representative samples and support valid inferences.

Estimating Population Size
Polling: City
Polling: Neighborhood

7.DSP.2: Use data from a random sample to draw inferences about a population. 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.DSP.3: Find, use, and interpret measures of center (mean and median) and measures of spread (range, interquartile range, and mean absolute deviation) for numerical data from random samples to draw comparative inferences about two populations.

Box-and-Whisker Plots
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

7.DSP.4: Make observations about the degree of visual overlap of two numerical data distributions represented in line plots or box plots. Describe how data, particularly outliers, added to a data set may affect the mean and/or median.

Box-and-Whisker Plots

7.DSP.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Understand that 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. Understand that a probability of 1 indicates an event certain to occur and a probability of 0 indicates an event impossible to occur. Identify probabilities of events as impossible, unlikely, equally likely, likely, or certain.

Geometric Probability
Lucky Duck (Expected Value)
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

7.DSP.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its relative frequency from a large sample.

Lucky Duck (Expected Value)
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

7.DSP.7: Develop probability models that include the sample space and probabilities of outcomes to represent simple events with equally likely outcomes. Predict the approximate relative frequency of the event based on the model. Compare probabilities from the model to observed frequencies; evaluate the level of agreement and explain possible sources of discrepancy.

Geometric Probability
Probability Simulations
Theoretical and Experimental Probability