Academic Standards

7.RP.A.1: Compute unit rates associated with ratios involving both simple and complex fractions, including ratios of quantities measured in like or different units.

Beam to Moon (Ratios and Proportions)

Household Energy Usage

Road Trip (Problem Solving)

Unit Conversions

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

7.RP.A.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

Geometric Probability

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

Percents and Proportions

Proportions and Common Multipliers

7.RP.A.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

7.RP.A.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

Proportions and Common Multipliers

7.RP.A.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.A.3: Use proportional relationships to solve multi-step ratio and percent problems (e.g., simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error).

Beam to Moon (Ratios and Proportions)

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

Percent of Change

Percents and Proportions

Percents, Fractions, and Decimals

Proportions and Common Multipliers

7.NS.A.1: Add and subtract integers and other rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

7.NS.A.1a: Describe situations in which opposite quantities combine to make 0.

Adding and Subtracting Integers

Integers, Opposites, and Absolute Values

Rational Numbers, Opposites, and Absolute Values

7.NS.A.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 context.

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.NS.A.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 context.

Adding and Subtracting Integers

Adding on the Number Line

Simplifying Algebraic Expressions I

Sums and Differences with Decimals

7.NS.A.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

Estimating Sums and Differences

Fractions Greater than One (Fraction Tiles)

Improper Fractions and Mixed Numbers

Sums and Differences with Decimals

7.NS.A.2: Multiply and divide integers and other rational numbers.

7.NS.A.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 context.

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying with Decimals

7.NS.A.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 context.

7.NS.A.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.A.2d: Convert a rational number to decimal form using long division; know that the decimal form of a rational number terminates in 0’s or eventually repeats.

Percents, Fractions, and Decimals

7.NS.A.3: Solve mathematical problems and problems in real-world context involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions where a/b divided by c/d when a, b, c, and d are all integers and b, c, and d not equal to 0.

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.A.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Solving Algebraic Equations II

7.EE.A.2: Rewrite an expression in different forms, and understand the relationship between the different forms and their meanings in a problem context.

Exponents and Power Rules

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

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

7.EE.B.3: Solve multi-step mathematical problems and problems in real-world context posed with positive and negative rational numbers in any form. Convert between forms as appropriate and assess the reasonableness of answers.

Adding and Subtracting Integers

Dividing Mixed Numbers

Estimating Sums and Differences

Fraction Garden (Comparing Fractions)

Improper Fractions and Mixed Numbers

Multiplying with Decimals

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

Percents, Fractions, and Decimals

Rational Numbers, Opposites, and Absolute Values

7.EE.B.4: Use variables to represent quantities in mathematical problems and problems in real-world context, and construct simple equations and inequalities to solve problems.

7.EE.B.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.

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Two-Step Equations

7.EE.B.4b: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are 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.A.1: Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

7.G.A.2: Draw geometric shapes with given conditions using a variety of methods. 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.

Concurrent Lines, Medians, and Altitudes

Segment and Angle Bisectors

Triangle Inequalities

7.G.B.4: Understand and use the formulas for the area and circumference of a circle 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.B.5: Use facts about supplementary, complementary, vertical, and adjacent angles in multi-step problems to write and solve simple equations for an unknown angle in a figure.

Investigating Angle Theorems

Triangle Angle Sum

7.G.B.6: Solve mathematical problems and problems in a real-world context involving area of two-dimensional objects composed of triangles, quadrilaterals, and other polygons. Solve mathematical problems and problems in real-world context involving volume and surface area of three-dimensional objects composed of cubes and right prisms.

Area of Parallelograms

Area of Triangles

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

7.SP.A.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.A.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.B.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.B.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

7.SP.C.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

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

7.SP.C.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.

7.SP.C.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.C.7a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

7.SP.C.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

6.1.1: Mathematically proficient students explain to themselves the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. While engaging in productive struggle to solve a problem, they continually ask themselves, “Does this make sense?' to monitor and evaluate their progress and change course if necessary. Once they have a solution, they look back at the problem to determine if the solution is reasonable and accurate. Mathematically proficient students check their solutions to problems using different methods, approaches, or representations. They also compare and understand different representations of problems and different solution pathways, both their own and those of others.

Biconditional Statements

Conditional Statements

Estimating Population Size

6.2.1: Mathematically proficient students make sense of quantities and their relationships in problem situations. Students can contextualize and decontextualize problems involving quantitative relationships. They contextualize quantities, operations, and expressions by describing a corresponding situation. They decontextualize a situation by representing it symbolically. As they manipulate the symbols, they can pause as needed to access the meaning of the numbers, the units, and the operations that the symbols represent. Mathematically proficient students know and flexibly use different properties of operations, numbers, and geometric objects and when appropriate they interpret their solution in terms of the context.

Estimating Population Size

Using Algebraic Expressions

6.3.1: Mathematically proficient students construct mathematical arguments (explain the reasoning underlying a strategy, solution, or conjecture) using concrete, pictorial, or symbolic referents. Arguments may also rely on definitions, assumptions, previously established results, properties, or structures. Mathematically proficient students make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. Mathematically proficient students present their arguments in the form of representations, actions on those representations, and explanations in words (oral or written). Students critique others by affirming or questioning the reasoning of others. They can listen to or read the reasoning of others, decide whether it makes sense, ask questions to clarify or improve the reasoning, and validate or build on it. Mathematically proficient students can communicate their arguments, compare them to others, and reconsider their own arguments in response to the critiques of others.

6.4.1: Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Estimating Population Size

Using Algebraic Expressions

6.6.1: Mathematically proficient students clearly communicate to others using appropriate mathematical terminology, and craft explanations that convey their reasoning. When making mathematical arguments about a solution, strategy, or conjecture, they describe mathematical relationships and connect their words clearly to their representations. Mathematically proficient students understand meanings of symbols used in mathematics, calculate accurately and efficiently, label quantities appropriately, and record their work clearly and concisely.

Biconditional Statements

Using Algebraic Expressions

6.7.1: Mathematically proficient students use structure and patterns to assist in making connections among mathematical ideas or concepts when making sense of mathematics. Students recognize and apply general mathematical rules to complex situations. They are able to compose and decompose mathematical ideas and notations into familiar relationships. Mathematically proficient students manage their own progress, stepping back for an overview and shifting perspective when needed.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

6.8.1: Mathematically proficient students look for and describe regularities as they solve multiple related problems. They formulate conjectures about what they notice and communicate observations with precision. While solving problems, students maintain oversight of the process and continually evaluate the reasonableness of their results. This informs and strengthens their understanding of the structure of mathematics which leads to fluency.

Correlation last revised: 4/4/2018

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