7.RP: Ratios and Proportional Relationships

1.1: Analyze proportional relationships and use them to solve real world and mathematical problems.

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.2.a: Decide whether two quantities are in a proportional relationship 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.2.b: 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.2.c: 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.2.d: 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.

Direct and Inverse Variation

7.RP.3: Use proportional relationships to solve multi-step 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: The Number System

2.1: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

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.1.a: 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.1.b.i: Understand p + q as the number located a distance |q| from p on a number line, in the direction indicated by the sign of q.

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.1.b.ii: Show that a number and its opposite have a sum of 0 (are additive inverses).

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.1.b.iii: 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.1.c.i: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q).

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.1.c.ii: 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.1.d: Apply properties of operations as strategies to fluently 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, division, and fractions to multiply and divide rational numbers.

7.NS.2.a: 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 rational numbers. Interpret products of rational numbers by describing real world contexts.

Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

7.NS.2.b.i: Understand that integers can be divided provided the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If ?? and ?? are integers, then ?(??/??) = ???/?? = ??/(???).

Dividing Mixed Numbers

7.NS.2.b.ii: Interpret quotients of rational numbers by describing real world contexts.

Dividing Mixed Numbers

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

Adding and Subtracting Integers
Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

7.NS.2.d.i: Convert a rational number to a decimal using long division.

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: Expressions and Equations

3.1: Use properties of operations to generate equivalent expressions.

7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients with an emphasis on writing equivalent expressions.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations
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 clarify the problem and how the quantities in it are related.

Exponents and Power Rules
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c

3.2: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

7.EE.3.i: Solve multi-step real-life and mathematical problems posed with rational numbers in any form (positive and negative, fractions, decimals, and integers), using tools strategically.

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
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
Proportions and Common Multipliers
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)

7.EE.3.ii: Apply properties of operations to calculate with numbers in any form.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
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.3.iii: Convert between forms as appropriate.

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.3.iv: 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.4.a.i: 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.

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.4.a.ii: Solve equations of these forms fluently.

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.4.a.iii: Compare the 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.4.b.i: Solve word problems leading to inequalities of the form ???? + ?? > ?? or ???? + ?? < ??, where ??, ??, and ?? are specific rational numbers.

Absolute Value Equations and Inequalities
Rational Numbers, Opposites, and Absolute Values
Solving Linear Inequalities in One Variable

7.EE.4.b.ii: 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: Geometry

4.1: Draw, construct, and describe geometrical figures and describe the relationships between them.

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 geometric shapes from 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. Use a variety of methods such as freehand, with ruler and protractor, and with technology.

3D and Orthographic Views
Concurrent Lines, Medians, and Altitudes
Triangle Inequalities

4.2: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

7.G.4.i: Know the formulas for the area and circumference of a circle and use them to solve problems.

Circumference and Area of Circles

7.G.4.ii: Informally derive 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 equations for an unknown angle in a figure.

Investigating Angle Theorems
Triangle Angle Sum

7.G.6.i: Solve real world and mathematical problems involving area of two-dimensional figures composed of polygons and/or circles, including composite figures.

Area of Parallelograms
Area of Triangles
Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Circumference and Area of Circles
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.G.6.ii: Use nets to solve real world and mathematical problems involving surface area of prisms and cylinders, including composite solids.

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.G.6.iii: Solve real world and mathematical problems involving volumes of right prisms, including composite solids.

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: Statistics and Probability

5.1: Use random sampling to draw inferences about a population.

7.SP.1.i: Understand that statistics can be used to gain information about a population by examining a sample of the population.

Polling: City
Polling: Neighborhood
Populations and Samples

7.SP.1.ii: Understand that generalizations about a population from a sample are valid only if the sample is representative of that population.

Polling: City
Polling: Neighborhood
Populations and Samples

7.SP.1.iii: Understand that random sampling tends to produce representative samples and support valid inferences.

Polling: City
Polling: Neighborhood
Populations and Samples

7.SP.2.i: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

Polling: City
Polling: Neighborhood
Populations and Samples

7.SP.2.ii: 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

5.2: Draw informal comparative inferences about two populations.

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)

5.3: Investigate chance processes and develop, use, and evaluate probability models.

7.SP.5: Understand that the probability of a chance event is a number from 0 through 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 ½ 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.i: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency.

Probability Simulations
Theoretical and Experimental Probability

7.SP.6.ii: Predict the approximate relative frequency given the probability.

Probability Simulations
Theoretical and Experimental Probability

7.SP.7.i: Develop a probability model and use it to find probabilities of events .

Independent and Dependent Events
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

7.SP.7.ii: Compare probabilities from a model to observed frequencies. If there is a discrepancy, explain possible sources.

7.SP.7.ii.a: 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.7.ii.b: 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.8.a: 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.8.b.i: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams.

Independent and Dependent Events
Permutations and Combinations

7.SP.8.b.ii: For an event described in everyday language (such as “rolling double sixes”), identify the outcomes in the sample space which compose the event.

Independent and Dependent Events
Permutations and Combinations

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

Independent and Dependent Events

Correlation last revised: 9/15/2020

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