7.NS: Number Sense

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

Finding Factors with Area Models

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

Square Roots

7.NS.3: Know there are rational and irrational numbers. Identify, compare, and order rational and common irrational numbers (√2, √3, √5, π) and plot them on a number line.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions, and Decimals Greater Than 1

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 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 and Subtracting Integers with Chips
Adding on the Number Line
Sums and Differences with Decimals

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.

Rational Numbers, Opposites, and Absolute Values
Sums and Differences with Decimals

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.

Chocomatic (Multiplication, Arrays, and Area)
Multiplying Fractions
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.

Area of Triangles
Part-to-part and Part-to-whole Ratios
Polling: Neighborhood
Road Trip (Problem Solving)
Unit Conversions

7.C.6: Use proportional relationships to solve ratio and percent problems with multiple operations, such as the following: simple interest, tax, markups, markdowns, gratuities, commissions, fees, conversions within and across measurement systems, percent increase and decrease, and percent error.

Part-to-part and Part-to-whole Ratios
Percent of Change
Polling: Neighborhood
Simple and Compound Interest

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

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

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

Dividing Fractions
Dividing Mixed Numbers
Estimating Population Size
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

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 (e.g., given 2x - 10, create an equivalent expression 2(x - 5)). Justify each step in the process.

Chocomatic (Multiplication, Arrays, and Area)
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

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 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.

Compound Inequalities
Solving 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.

Direct and Inverse Variation
Distance-Time and Velocity-Time Graphs
Elevator Operator (Line Graphs)
Slope - Activity B

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

Elevator Operator (Line Graphs)
Point-Slope Form of a Line - Activity A
Slope - Activity B
Standard 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).

Fraction Garden (Comparing Fractions)
Linear Functions
Points, Lines, and Equations
Polling: Neighborhood
Toy Factory (Set Models of Fractions)

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

Elevator Operator (Line Graphs)
Points, Lines, and Equations
Road Trip (Problem Solving)

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.

Elevator Operator (Line Graphs)
Road Trip (Problem Solving)

7.AF.9: Identify real-world and other mathematical situations that involve proportional relationships. Write equations and draw graphs to represent proportional relationships and 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.

Elevator Operator (Line Graphs)
Estimating Population Size
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line - Activity B

7.GM: Geometry and Measurement

7.GM.1: Draw triangles (freehand, with ruler and protractor, and using technology) with given conditions from three measures of angles or sides, and notice when the conditions determine a unique triangle, more than one triangle, or no triangle.

Classifying Triangles
Segment and Angle Bisectors

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 - Activity A

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.

Area of Triangles

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 - Activity A

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
Surface and Lateral Areas of Pyramids and Cones

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 and 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
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

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
Probability Simulations

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
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
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
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

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.

Spin the Big Wheel! (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.

Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability