NC.7.PR: Ratio and Proportional Relationships

(Framing Text): Analyze proportional relationships and use them to solve real-world and mathematical problems.

NC.7.RP.1: Compute unit rates associated with ratios of fractions to solve real-world and mathematical problems.

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

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

NC.7.RP.2.a: Understand that a proportion is a relationship of equality between ratios.

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

NC.7.RP.2.a.1: Represent proportional relationships using tables and graphs.

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

NC.7.RP.2.a.2: Recognize whether ratios are in a proportional relationship using tables and graphs.

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

NC.7.RP.2.a.3: Compare two different proportional relationships using tables, graphs, equations, and verbal descriptions.

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

NC.7.RP.2.b: Identify the unit rate (constant of proportionality) within two quantities in a proportional relationship using tables, graphs, equations, and verbal descriptions.

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

NC.7.RP.2.c: Create equations and graphs to represent 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

NC.7.RP.2.d: Use a graphical representation of a proportional relationship in context to:

Direct and Inverse Variation

NC.7.RP.2.d.1: Explain the meaning of any point (x, y).

Direct and Inverse Variation

NC.7.RP.2.d.2: Explain the meaning of (0, 0) and why it is included.

Direct and Inverse Variation

NC.7.RP.2.d.3: Understand that the y-coordinate of the ordered pair (1, r) corresponds to the unit rate and explain its meaning.

Direct and Inverse Variation

NC.7.RP.3: Use scale factors and unit rates in proportional relationships to solve 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

NC.7.NS: The Number System

(Framing Text): Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

NC.7.NS.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, using the properties of operations, and describing real-world contexts using sums and differences.

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

NC.7.NS.2: Apply and extend previous understandings of multiplication and division.

NC.7.NS.2.a: Understand that a rational number is any number that can be written as a quotient of integers with a non-zero divisor.

Rational Numbers, Opposites, and Absolute Values

NC.7.NS.2.b: Apply properties of operations as strategies, including the standard algorithms, to multiply and divide rational numbers and describe the product and quotient in real-world contexts.

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

NC.7.NS.2.c: Use division and previous understandings of fractions and decimals.

NC.7.NS.2.c.1: Convert a fraction to a decimal using long division.

Percents, Fractions, and Decimals

NC.7.NS.2.c.2: Understand that the decimal form of a rational number terminates in 0s or eventually repeats.

Percents, Fractions, and Decimals

NC.7.NS.3: Solve real-world and mathematical problems involving numerical expressions with rational numbers using the four operations.

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

NC.7.EE: Expressions and Equations

(Framing Text): Use properties of operations to generate equivalent expressions.

NC.7.EE.1: Apply properties of operations as strategies to:

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

NC.7.EE.1.a: Add, subtract, and expand linear 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

NC.7.EE.2: Understand that equivalent expressions can reveal real-world and mathematical relationships. Interpret the meaning of the parts of each expression in context.

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

(Framing Text): Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities.

NC.7.EE.3: Solve multi-step real-world and mathematical problems posed with rational numbers in algebraic expressions.

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)

NC.7.EE.3.a: Apply properties of operations to calculate with positive and negative 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
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)

NC.7.EE.3.b: Convert between different forms of a number and equivalent forms of the expression 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
Exponents and Power Rules
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
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)

NC.7.EE.4: Use variables to represent quantities to solve real-world or mathematical problems.

NC.7.EE.4.a: Construct equations to solve problems by reasoning about the quantities.

NC.7.EE.4.a.1: Fluently solve multistep equations with the variable on one side, including those generated by word 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 by Graphing Each Side
Solving Equations on the Number Line
Solving Two-Step Equations

NC.7.EE.4.a.2: Compare an 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

NC.7.EE.4.a.3: Interpret the solution in context.

Estimating Population Size

NC.7.EE.4.b: Construct inequalities to solve problems by reasoning about the quantities.

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

NC.7.EE.4.b.1: Fluently solve multi-step inequalities with the variable on one side, including those generated by word problems.

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

NC.7.EE.4.b.3: Graph the solution set of the inequality and interpret in context.

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

NC.7.G: Geometry

(Framing Text): Draw, construct, and describe geometrical figures and describe the relationships between them.

NC.7.G.1: Solve problems involving scale drawings of geometric figures by:

Dilations
Perimeters and Areas of Similar Figures
Similar Figures

NC.7.G.1.a: Building an understanding that angle measures remain the same and side lengths are proportional.

Dilations
Similar Figures
Similarity in Right Triangles

NC.7.G.1.b: Using a scale factor to compute actual lengths and areas from a scale drawing.

Dilations
Perimeters and Areas of Similar Figures
Similar Figures

NC.7.G.1.c: Creating a scale drawing.

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

NC.7.G.2: Understand the characteristics of angles and side lengths that create a unique triangle, more than one triangle or no triangle. Build triangles from three measures of angles and/or sides.

3D and Orthographic Views
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Triangle Angle Sum
Triangle Inequalities

(Framing Text): Solve real-world and mathematical problems involving angle measure, area, surface area, and volume.

NC.7.G.4: Understand area and circumference of a circle.

Circumference and Area of Circles

NC.7.G.4.a: Understand the relationships between the radius, diameter, circumference, and area.

Circumference and Area of Circles

NC.7.G.4.b: Apply the formulas for area and circumference of a circle to solve problems.

Circumference and Area of Circles

NC.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

NC.7.G.6: Solve real-world and mathematical problems involving:

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

NC.7.G.6.a: Area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.

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

NC.7.G.6.b: Volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right 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

NC.7.SP: Statistics and Probability

(Framing Text): Use random sampling to draw inferences about a population.

NC.7.SP.1: Understand that statistics can be used to gain information about a population by:

Polling: City
Polling: Neighborhood
Populations and Samples

NC.7.SP.1.a: Recognizing 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

NC.7.SP.1.b: Using random sampling to produce representative samples to support valid inferences.

Polling: City
Polling: Neighborhood
Populations and Samples

NC.7.SP.2: Generate multiple random samples (or simulated samples) of the same size to gauge the variation in estimates or predictions, and use this data to draw inferences about a population with an unknown characteristic of interest.

Polling: City
Polling: Neighborhood
Populations and Samples

(Framing Text): Make informal inferences to compare two populations.

NC.7.SP.3: Recognize the role of variability when comparing two populations.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

NC.7.SP.3.a: Calculate the measure of variability of a data set and understand that it describes how the values of the data set vary with a single number.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

NC.7.SP.3.a.2: Understand that the range describes the spread of the entire data set.

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)
Stem-and-Leaf Plots

NC.7.SP.3.a.3: Understand that the interquartile range describes the spread of the middle 50% of the data.

Box-and-Whisker Plots

NC.7.SP.3.b: Informally assess the difference between two data sets by examining the overlap and separation between the graphical representations of two data sets.

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

NC.7.SP.4: Use measures of center and measures of variability for numerical data from random samples to draw comparative inferences about two populations.

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

(Framing Text): Investigate chance processes and develop, use, and evaluate probability models.

NC.7.SP.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.

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

NC.7.SP.6: Collect data to calculate the experimental probability of a chance event, observing its long-run relative frequency. Use this experimental probability to predict the approximate relative frequency.

Probability Simulations
Theoretical and Experimental Probability

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

NC.7.SP.7.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

NC.7.SP.7.b: Develop a probability model (which may not be uniform) by repeatedly performing a chance process and observing frequencies in the data generated.

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

NC.7.SP.7.c: Compare theoretical and experimental probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

Probability Simulations

NC.7.SP.8: Determine probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

NC.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

NC.7.SP.8.b: For an event described in everyday language, identify the outcomes in the sample space which compose the event, when the sample space is represented using organized lists, tables, and tree diagrams.

Independent and Dependent Events
Permutations and Combinations

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

Independent and Dependent Events