Course of Study

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

7.RP.2.a: 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

Proportions and Common Multipliers

7.RP.2.b: 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

Perimeters and Areas of Similar Figures

Similar Figures

7.RP.2.c: Represent proportional relationships by equations.

Beam to Moon (Ratios and Proportions)

Estimating Population Size

Geometric Probability

Polling: Neighborhood

Theoretical and Experimental Probability

7.RP.2.d: 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.3: Use proportional relationships to solve multistep ratio and percent problems.

Estimating Population Size

Percent of Change

Percents and Proportions

Polling: Neighborhood

Real-Time Histogram

Time Estimation

7.NS.4: 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.

7.NS.4.a: Describe situations in which opposite quantities combine to make 0.

Adding and Subtracting Integers

Adding and Subtracting Integers with Chips

Integers, Opposites, and Absolute Values

7.NS.4.b: 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.

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations I

Solving Algebraic Equations II

7.NS.4.c: 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

Equivalent Algebraic Expressions I

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations I

7.NS.4.d: Apply properties of operations as strategies to add and subtract rational numbers.

Adding and Subtracting Integers with Chips

7.EE.7: 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

Solving Algebraic Equations I

Solving Algebraic Equations II

7.EE.9: 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.

Percent of Change

Percents and Proportions

7.EE.10: 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.

7.EE.10.a: 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

Solving Algebraic Equations II

Solving Two-Step Equations

7.EE.10.b: 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

7.G.11: 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

Perimeters and Areas of Similar Figures

Similar Figures

7.G.14: 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

7.G.15: 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.

7.G.16: 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

Balancing Blocks (Volume)

Perimeter and Area of Rectangles

Prisms and Cylinders

Pyramids and Cones

Surface and Lateral Areas of Pyramids and Cones

7.SP.17: 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

7.SP.18: 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.

Estimating Population Size

Polling: City

Polling: Neighborhood

Populations and Samples

7.SP.20: 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)

Real-Time Histogram

7.SP.21: 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

Theoretical and Experimental Probability

7.SP.22: 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.

Probability Simulations

Theoretical and Experimental Probability

7.SP.23: 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.23.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

7.SP.24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

7.SP.24.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

7.SP.24.b: 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

Permutations and Combinations

7.SP.24.c: Design and use a simulation to generate frequencies for compound events.

Independent and Dependent Events

Correlation last revised: 1/19/2017

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