MGSE7.RP: Ratios and Proportional Relationships

MGSE7.RP.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
Proportions and Common Multipliers

MGSE7.RP.2b: 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

MGSE7.RP.2c: Represent proportional relationships by equations.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Geometric Probability
Polling: Neighborhood
Theoretical and Experimental Probability

MGSE7.RP.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

MGSE7.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

MGSE7.NS: The Number System

MGSE7.NS.1a: Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0.

Adding and Subtracting Integers
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

MGSE7.NS.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. Interpret sums of rational numbers by describing real world contexts.

Adding and Subtracting Integers
Adding on the Number Line
Improper Fractions and Mixed Numbers
Sums and Differences with Decimals

MGSE7.NS.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 on the Number Line
Simplifying Algebraic Expressions I
Sums and Differences with Decimals

MGSE7.NS.1d: Apply properties of operations as strategies to add and subtract rational numbers.

Adding and Subtracting Integers with Chips

MGSE7.NS.2a: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (– 1)(– 1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

MGSE7.NS.2b: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers then – (p/q) = (– p)/q = p/(– q). Interpret quotients of rational numbers by describing real-world contexts.

Dividing Mixed Numbers

MGSE7.EE: Expressions and Equations

MGSE7.EE.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
Solving Algebraic Equations I
Solving Algebraic Equations II

MGSE7.EE.2: Understand that rewriting an expression in different forms in a problem context can clarify the problem and how the quantities in it are related.

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

MGSE7.EE.3: Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) by applying properties of operations as strategies to calculate with numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.

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)
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
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values
Sums and Differences with Decimals

MGSE7.EE.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 One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

MGSE7.EE.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.

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

MGSE7.EE.4c: Solve real-world and mathematical problems by writing and solving equations of the form x+p = q and px = q in which p and q are rational numbers.

Solving Equations on the Number Line

MGSE7.G: Geometry

MGSE7.G.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
Perimeters and Areas of Similar Figures
Similar Figures

MGSE7.G.2: Explore various geometric shapes with given conditions. Focus on creating triangles from three measures of angles and/or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Classifying Quadrilaterals
Concurrent Lines, Medians, and Altitudes
Triangle Inequalities

MGSE7.G.4: Given the formulas for the area and circumference of a circle, 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

MGSE7.G.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

MGSE7.G.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
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

MGSE7.SP: Statistics and Probability

MGSE7.SP.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.

Polling: City
Polling: Neighborhood

MGSE7.SP.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.

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

MGSE7.SP.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the medians by expressing it as a multiple of the interquartile range.

Box-and-Whisker Plots

MGSE7.SP.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)
Real-Time Histogram

MGSE7.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. 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
Theoretical and Experimental Probability

MGSE7.SP.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. Predict the approximate relative frequency given the probability.

Probability Simulations

MGSE7.SP.7a: 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

MGSE7.SP.7b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Lucky Duck (Expected Value)

MGSE7.SP.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

MGSE7.SP.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
Permutations and Combinations

MGSE7.SP.8c: Explain ways to set up a simulation and use the simulation to generate frequencies for compound events.

Independent and Dependent Events

Correlation last revised: 9/24/2019

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