Academic Standards

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 integer. Find square roots of perfect square integers.

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.

Circumference and Area of Circles

Comparing and Ordering Decimals

Fraction Garden (Comparing Fractions)

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

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 on the Number Line

Improper Fractions and Mixed Numbers

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

Simplifying Algebraic Expressions I

Solving Algebraic Equations I

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.

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.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 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.

Beam to Moon (Ratios and Proportions)

Household Energy Usage

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.

Compound Interest

Percent of Change

Percents, Fractions, and Decimals

Road Trip (Problem Solving)

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

Estimating Sums and Differences

Fractions Greater than One (Fraction Tiles)

Fractions with Unlike Denominators

Improper Fractions and Mixed Numbers

Multiplying Fractions

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 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

Subtracting Whole Numbers and Decimals (Base-10 Blocks)

Sums and Differences with Decimals

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.

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

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

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

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations 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.

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.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.

Absolute Value Equations and Inequalities

Exploring Linear Inequalities in One Variable

Rational Numbers, Opposites, and Absolute Values

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.

Cat and Mouse (Modeling with Linear Systems)

Compound Interest

Direct and Inverse Variation

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Elevator Operator (Line Graphs)

Point-Slope Form of a Line

Slope

Slope-Intercept Form of a Line

Translating and Scaling Functions

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)

Elevator Operator (Line Graphs)

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

Estimating Population Size

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

Percents and Proportions

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)

Dilations

Direct and Inverse Variation

Perimeters and Areas of Similar Figures

Similar Figures

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.

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.

Beam to Moon (Ratios and Proportions)

Direct and Inverse Variation

Estimating Population Size

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

Percents and Proportions

Perimeters and Areas of Similar Figures

Proportions and Common Multipliers

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.

3D and Orthographic Views

Classifying Triangles

Concurrent Lines, Medians, and Altitudes

Similar Figures

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.

Circles

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

Perimeters and Areas of Similar Figures

Similar Figures

7.GM.4: Solve real-world and other mathematical problems that involve 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.

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.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.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

Populations and Samples

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

Mean, Median, and Mode

Movie Reviewer (Mean and Median)

Polling: City

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)

Sight vs. Sound Reactions

Stem-and-Leaf 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.

Geometric Probability

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

Independent and Dependent Events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

Correlation last revised: 11/9/2021

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