Standard Course of Study

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)

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.

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

Direct and Inverse Variation

Proportions and Common Multipliers

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

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

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

Beam to Moon (Ratios and Proportions)

Direct and Inverse Variation

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

Proportions and Common Multipliers

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

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

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

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.

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)

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

NC.7.EE.3.a: Apply properties of operations to calculate with positive and negative numbers in any form.

Adding Fractions (Fraction Tiles)

Adding and Subtracting Integers

Adding on the Number Line

Dividing Fractions

Dividing Mixed Numbers

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.3.b: Convert between different forms of a number and equivalent forms of the expression as appropriate.

Exponents and Power Rules

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

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

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

Percents, Fractions, and Decimals

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.

Modeling and Solving Two-Step Equations

Solving Equations by Graphing Each Side

NC.7.EE.4.a.2: Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Solving Algebraic Equations II

Solving Equations on the Number Line

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

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

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

Compound Inequalities

Linear Inequalities in Two Variables

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

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.

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

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.

Concurrent Lines, Medians, and Altitudes

Isosceles and Equilateral Triangles

Triangle Angle Sum

Triangle Inequalities

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

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:

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

Area of Parallelograms

Area of Triangles

Chocomatic (Multiplication, Arrays, and Area)

Fido's Flower Bed (Perimeter and Area)

Perimeter and Area of Rectangles

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

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

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

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

Polling: City

Polling: Neighborhood

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

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

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.

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.

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

Mean, Median, and Mode

Reaction Time 1 (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

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

Probability Simulations

Spin the Big Wheel! (Probability)

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.

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.

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

Independent and Dependent Events

Correlation last revised: 1/22/2020