CCSS.Math.Content.7.RP: Ratios and Proportional Relationships

CCSS.Math.Content.7.RP.A: Analyze proportional relationships and use them to solve real-world and mathematical problems.

CCSS.Math.Content.7.RP.A.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Road Trip (Problem Solving)
Unit Conversions

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

CCSS.Math.Content.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.

Direct and Inverse Variation

CCSS.Math.Content.7.RP.A.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Direct and Inverse Variation

CCSS.Math.Content.7.RP.A.2c: Represent proportional relationships by equations.

Direct and Inverse Variation

CCSS.Math.Content.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.

Direct and Inverse Variation

CCSS.Math.Content.7.RP.A.3: Use proportional relationships to solve multistep ratio and percent problems.

Fraction, Decimal, Percent (Area and Grid Models)
Percent of Change
Percents, Fractions, and Decimals
Polling: Neighborhood

CCSS.Math.Content.7.NS: The Number System

CCSS.Math.Content.7.NS.A: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

CCSS.Math.Content.7.NS.A.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.

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

Adding and Subtracting Integers with Chips

CCSS.Math.Content.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 contexts.

Adding and Subtracting Integers
Adding on the Number Line

CCSS.Math.Content.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 contexts.

Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Adding on the Number Line

CCSS.Math.Content.7.NS.A.1d: Apply properties of operations as strategies to add and subtract rational numbers.

Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Adding on the Number Line

CCSS.Math.Content.7.NS.A.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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

Fraction, Decimal, Percent (Area and Grid Models)

CCSS.Math.Content.7.NS.A.3: Solve real-world and mathematical problems involving the four operations with rational numbers.

Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Adding on the Number Line

CCSS.Math.Content.7.EE: Expressions and Equations

CCSS.Math.Content.7.EE.A: Use properties of operations to generate equivalent expressions.

CCSS.Math.Content.7.EE.A.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

CCSS.Math.Content.7.EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

CCSS.Math.Content.7.EE.B.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Adding on the Number Line
Fraction, Decimal, Percent (Area and Grid Models)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Percent of Change
Percents, Fractions, and Decimals

CCSS.Math.Content.7.EE.B.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.

CCSS.Math.Content.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 and Solving Two-Step Equations
Perimeter and Area of Rectangles
Solving Algebraic Equations II
Solving Two-Step Equations

CCSS.Math.Content.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 specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Solving Linear Inequalities in One Variable

CCSS.Math.Content.7.G: Geometry

CCSS.Math.Content.7.G.A: Draw, construct, and describe geometrical figures and describe the relationships between them.

CCSS.Math.Content.7.G.A.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
Similar Figures

CCSS.Math.Content.7.G.A.2: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with 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.

Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions
Special Parallelograms
Triangle Inequalities

CCSS.Math.Content.7.G.B: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

CCSS.Math.Content.7.G.B.4: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Circumference and Area of Circles

CCSS.Math.Content.7.G.B.5: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Investigating Angle Theorems
Triangle Angle Sum

CCSS.Math.Content.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, 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

CCSS.Math.Content.7.SP: Statistics and Probability

CCSS.Math.Content.7.SP.A: Use random sampling to draw inferences about a population.

CCSS.Math.Content.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.

Estimating Population Size
Polling: City
Polling: Neighborhood
Populations and Samples

CCSS.Math.Content.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

CCSS.Math.Content.7.SP.B: Draw informal comparative inferences about two populations.

CCSS.Math.Content.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

CCSS.Math.Content.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
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

CCSS.Math.Content.7.SP.C: Investigate chance processes and develop, use, and evaluate probability models.

CCSS.Math.Content.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
Lucky Duck (Expected Value)
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

CCSS.Math.Content.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.

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

CCSS.Math.Content.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.

CCSS.Math.Content.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

CCSS.Math.Content.7.SP.C.7b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

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

CCSS.Math.Content.7.SP.C.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

CCSS.Math.Content.7.SP.C.8a: 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

CCSS.Math.Content.7.SP.C.8b: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

Independent and Dependent Events

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

Independent and Dependent Events