7.NS: The Number System

7.NS.1: Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line.

7.NS.1.a: Understand that the additive inverse of a number is its opposite and their sum is equal to zero.

Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Solving Algebraic Equations I

7.NS.1.b: Understand that the sum of two rational numbers (p + q) represents a distance from p on the number line equal to |q| where the direction is indicated by the sign of q.

Adding and Subtracting Integers
Adding on the Number Line
Fractions Greater than One (Fraction Tiles)
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: Translate between the subtraction of rational numbers and addition using 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.d: Demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference.

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.e: Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to 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: Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers.

7.NS.2.a: Understand that the multiplicative inverse of a number is its reciprocal and their product is equal to one.

Solving Algebraic Equations I

7.NS.2.b: Understand sign rules for multiplying rational numbers.

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

7.NS.2.c: Understand sign rules for dividing rational numbers and that a quotient of integers (with a non-zero divisor) is a rational number.

Dividing Fractions
Dividing Mixed Numbers

7.NS.2.d: Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) 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.2.e: Understand that some rational numbers can be written as integers and all rational numbers can be written as fractions or decimal numbers that terminate or repeat.

Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

7.NS.3: Apply the concepts of all four operations with rational numbers to solve real-world and mathematical problems.

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.NS.4: Understand and apply the concepts of comparing and ordering to rational numbers.

7.NS.4.a: Interpret statements using less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), and equal to (=) as relative locations on the number line.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

7.NS.4.b: Use concepts of equality and inequality to write and explain real-world and mathematical situations.

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Linear Functions
Linear Inequalities in Two Variables
Modeling One-Step Equations
Solving Equations on the Number Line
Using Algebraic Equations

7.NS.5: Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Exclude the conversion of repeating decimal numbers to fractions.

Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

7.RP: Ratios and Proportional Relationships

7.RP.1: Compute unit rates, including those involving complex fractions, with like or different units.

Beam to Moon (Ratios and Proportions)
Household Energy Usage
Road Trip (Problem Solving)
Unit Conversions

7.RP.2: Identify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations.

7.RP.2.a: Determine when two quantities are in a proportional relationship.

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.2.b: Recognize or compute the constant of proportionality.

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

7.RP.2.c: Understand that the constant of proportionality is the unit rate.

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

7.RP.2.d: Use equations to model proportional relationships.

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.e: Investigate the graph of a proportional relationship and explain the meaning of specific points (e.g., origin, unit rate) in the context of the situation.

Direct and Inverse Variation

7.RP.3: Solve real-world and mathematical problems involving ratios and percentages using proportional reasoning (e.g., multi-step dimensional analysis, percent increase/decrease, tax).

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Geometric Probability
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Polling: Neighborhood
Proportions and Common Multipliers
Real-Time Histogram
Road Trip (Problem Solving)
Time Estimation

7.EEI: Expressions, Equations, and Inequalities

7.EEI.1: Apply mathematical properties (e.g., commutative, associative, distributive) to simplify and to factor linear algebraic expressions with rational coefficients.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Solving Algebraic Equations II

7.EEI.2: Recognize that algebraic expressions may have a variety of equivalent forms and determine an appropriate form for a given real-world situation.

Equivalent Algebraic Expressions II
Exponents and Power Rules
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

7.EEI.3: Extend previous understanding of Order of Operations to solve multi-step real-world and mathematical problems involving rational numbers. Include fraction bars as a grouping symbol.

Order of Operations

7.EEI.4: Apply the concepts of linear equations and inequalities in one variable to real-world and mathematical situations.

7.EEI.4.a: Write and fluently solve linear equations of the form ax + b = c and a(x + b) = c where a, b, and c are 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.EEI.4.b: Write and solve multi-step linear equations that include the use of the distributive property and combining like terms. Exclude equations that contain variables on both sides.

Solving Algebraic Equations I
Solving Equations by Graphing Each Side

7.EEI.4.c: Write and solve two-step linear inequalities. Graph the solution set on a number line and interpret its meaning.

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Rational Numbers, Opposites, and Absolute Values
Solving Linear Inequalities in One Variable

7.EEI.4.d: Identify and justify the steps for solving multi-step linear equations and two-step linear inequalities.

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

7.EEI.5: Understand and apply the laws of exponents (i.e., product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property) to simplify numerical expressions that include whole-number exponents.

Exponents and Power Rules
Simplifying Algebraic Expressions II

7.GM: Geometry and Measurement

7.GM.1: Determine the scale factor and translate between scale models and actual measurements (e.g., lengths, area) of real-world objects and geometric figures using proportional reasoning.

Dilations
Perimeters and Areas of Similar Figures
Similar Figures

7.GM.2: Construct triangles and special quadrilaterals using a variety of tools (e.g., freehand, ruler and protractor, technology).

7.GM.2.a: Construct triangles given all measurements of either angles or sides.

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

7.GM.2.b: Decide if the measurements determine a unique triangle, more than one triangle, or no triangle.

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

7.GM.4: Investigate the concept of circles.

7.GM.4.a: Demonstrate an understanding of the proportional relationships between diameter, radius, and circumference of a circle.

Circumference and Area of Circles

7.GM.4.b: Understand that the constant of proportionality between the circumference and diameter is equivalent to π.

Circumference and Area of Circles

7.GM.4.c: Explore the relationship between circumference and area using a visual model.

Circumference and Area of Circles

7.GM.4.d: Use the formulas for circumference and area of circles appropriately to solve real-world and mathematical problems.

Circumference and Area of Circles

7.GM.5: Write equations to solve problems involving the relationships between angles formed by two intersecting lines, including supplementary, complementary, vertical, and adjacent.

Investigating Angle Theorems
Triangle Angle Sum

7.GM.6: Apply the concepts of two- and three-dimensional figures to real-world and mathematical situations.

7.GM.6.a: Understand that the concept of area is applied to two-dimensional figures such as triangles, quadrilaterals, and polygons.

Area of Parallelograms
Area of Triangles
Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Circumference and Area of Circles
Classifying Quadrilaterals
Concurrent Lines, Medians, and Altitudes
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles
Polygon Angle Sum
Prisms and Cylinders
Pyramids and Cones
Special Parallelograms
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones
Triangle Angle Sum
Triangle Inequalities

7.GM.6.b: Understand that the concepts of volume and surface area are applied to three-dimensional figures such as cubes, right rectangular prisms, and right triangular 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.6.c: Decompose cubes, right rectangular prisms, and right triangular prisms into rectangles and triangles to derive the formulas for volume and surface area.

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.6.d: Use the formulas for area, volume, and surface area appropriately.

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.DSP: Data Analysis, Statistics, and Probability

7.DSP.1: Investigate concepts of random sampling.

7.DSP.1.a: Understand that a sample is a subset of a population and both possess the same characteristics.

Polling: City
Polling: Neighborhood
Populations and Samples

7.DSP.1.b: Differentiate between random and non-random sampling.

Polling: City
Polling: Neighborhood
Populations and Samples

7.DSP.1.c: Understand that generalizations from a sample are valid only if the sample is representative of the population.

Polling: City
Polling: Neighborhood
Populations and Samples

7.DSP.1.d: Understand that random sampling is used to gather a representative sample and supports valid inferences about the population.

Polling: City
Polling: Neighborhood
Populations and Samples

7.DSP.2: Draw inferences about a population by collecting multiple random samples of the same size to investigate variability in estimates of the characteristic of interest.

Polling: City
Polling: Neighborhood
Populations and Samples

7.DSP.3: Visually compare the centers, spreads, and overlap of two displays of data (i.e., dot plots, histograms, box plots) that are graphed on the same scale and draw inferences about this data.

Box-and-Whisker Plots
Describing Data Using Statistics
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)
Real-Time Histogram

7.DSP.4: Compare the numerical measures of center (mean, median, mode) and variability (range, interquartile range, mean absolute deviation) from two random samples to draw inferences about the populations.

Box-and-Whisker Plots
Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)

7.DSP.5: Investigate the concept of probability of chance events.

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

7.DSP.5.a: Determine probabilities of simple events.

Probability Simulations
Theoretical and Experimental Probability

7.DSP.5.b: Understand that probability measures likelihood of a chance event occurring.

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

7.DSP.5.c: Understand that the probability of a chance event is a number between 0 and 1.

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

7.DSP.5.d: Understand that a probability closer to 1 indicates a likely chance event.

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

7.DSP.5.e: Understand that a probability close to ½ indicates that a chance event is neither likely nor unlikely.

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

7.DSP.5.f: Understand that a probability closer to 0 indicates an unlikely chance event.

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

7.DSP.6: Investigate the relationship between theoretical and experimental probabilities for simple events.

7.DSP.6.a: Determine approximate outcomes using theoretical probability.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

7.DSP.6.b: Perform experiments that model theoretical probability.

Geometric Probability
Independent and Dependent Events

7.DSP.6.c: Compare theoretical and experimental probabilities.

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

7.DSP.7: Apply the concepts of theoretical and experimental probabilities for simple events.

7.DSP.7.b: Develop both uniform and non-uniform probability models.

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

7.DSP.7.c: Perform experiments to test the validity of probability models.

Polling: City

7.DSP.8: Extend the concepts of simple events to investigate compound events.

7.DSP.8.a: Understand that the probability of a compound event is between 0 and 1.

Independent and Dependent Events
Theoretical and Experimental Probability

7.DSP.8.b: Identify the outcomes in a sample space using organized lists, tables, and tree diagrams.

Independent and Dependent Events
Permutations and Combinations

7.DSP.8.c: Determine probabilities of compound events using organized lists, tables, and tree diagrams.

Independent and Dependent Events
Permutations and Combinations

7.DSP.8.d: Design and use simulations to collect data and determine probabilities.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

7.DSP.8.e: Compare theoretical and experimental probabilities for compound events.

Independent and Dependent Events
Theoretical and Experimental Probability