7.NS: The Number System

7.NS.1: Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line.

7.NS.1.a: Understand that the additive inverse of a number is its opposite and their sum is equal to zero.

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

7.NS.1.b: Understand that the sum of two rational numbers (p + q) represents a distance from p on the number line equal to |q| where the direction is indicated by the sign of q.

 Adding and Subtracting Integers
 Adding on the Number Line
 Fractions Greater than One (Fraction Tiles)

7.NS.1.c: Translate between the subtraction of rational numbers and addition using the additive inverse, p − q = p + (−q).

 Adding and Subtracting Integers
 Adding on the Number Line
 Simplifying Algebraic Expressions I

7.NS.1.e: Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to add and subtract rational numbers.

 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

7.NS.2: Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers.

7.NS.2.b: Understand sign rules for multiplying rational numbers.

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

7.NS.2.c: Understand sign rules for dividing rational numbers and that a quotient of integers (with a non-zero divisor) is a rational number.

 Dividing Fractions
 Dividing Mixed Numbers

7.NS.2.d: Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to multiply and divide rational numbers.

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

7.NS.2.e: Understand that some rational numbers can be written as integers and all rational numbers can be written as fractions or decimal numbers that terminate or repeat.

 Part-to-part and Part-to-whole Ratios
 Percents, Fractions, and Decimals

7.NS.3: Apply the concepts of all four operations with rational numbers to solve real-world and mathematical problems.

 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

7.NS.4: Understand and apply the concepts of comparing and ordering to rational numbers.

7.NS.4.a: Interpret statements using less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), and equal to (=) as relative locations on the number line.

 Comparing and Ordering Decimals
 Integers, Opposites, and Absolute Values
 Rational Numbers, Opposites, and Absolute Values

7.NS.4.b: Use concepts of equality and inequality to write and explain real-world and mathematical situations.

 Absolute Value Equations and Inequalities
 Comparing and Ordering Decimals
 Linear Functions
 Linear Inequalities in Two Variables
 Solving Equations on the Number Line
 Using Algebraic Equations

7.NS.5: Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Exclude the conversion of repeating decimal numbers to fractions.

 Part-to-part and Part-to-whole Ratios
 Percents, Fractions, and Decimals

7.RP: Ratios and Proportional Relationships

7.RP.1: Compute unit rates, including those involving complex fractions, with like or different units.

 Household Energy Usage

7.RP.2: Identify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations.

7.RP.2.a: Determine when two quantities are in a proportional relationship.

 Beam to Moon (Ratios and Proportions)
 Direct and Inverse Variation
 Geometric Probability
 Part-to-part and Part-to-whole Ratios
 Percents and Proportions
 Proportions and Common Multipliers

7.RP.2.b: Recognize or compute the constant of proportionality.

 Beam to Moon (Ratios and Proportions)
 Dilations
 Direct and Inverse Variation

7.RP.2.c: Understand that the constant of proportionality is the unit rate.

 Beam to Moon (Ratios and Proportions)
 Dilations
 Direct and Inverse Variation

7.RP.2.d: Use equations to model proportional relationships.

 Beam to Moon (Ratios and Proportions)
 Direct and Inverse Variation
 Geometric Probability
 Part-to-part and Part-to-whole Ratios
 Proportions and Common Multipliers

7.RP.2.e: Investigate the graph of a proportional relationship and explain the meaning of specific points (e.g., origin, unit rate) in the context of the situation.

 Direct and Inverse Variation

7.RP.3: Solve real-world and mathematical problems involving ratios and percentages using proportional reasoning (e.g., multi-step dimensional analysis, percent increase/decrease, tax).

 Beam to Moon (Ratios and Proportions)
 Direct and Inverse Variation
 Estimating Population Size
 Geometric Probability
 Part-to-part and Part-to-whole Ratios
 Percent of Change
 Percents and Proportions
 Percents, Fractions, and Decimals
 Proportions and Common Multipliers
 Real-Time Histogram
 Road Trip (Problem Solving)
 Time Estimation

7.EEI: Expressions, Equations, and Inequalities

7.EEI.1: Apply mathematical properties (e.g., commutative, associative, distributive) to simplify and to factor linear algebraic expressions with rational coefficients.

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

7.EEI.2: Recognize that algebraic expressions may have a variety of equivalent forms and determine an appropriate form for a given real-world situation.

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

7.EEI.3: Extend previous understanding of Order of Operations to solve multi-step real-world and mathematical problems involving rational numbers. Include fraction bars as a grouping symbol.

 Order of Operations

7.EEI.4: Apply the concepts of linear equations and inequalities in one variable to real-world and mathematical situations.

7.EEI.4.b: Write and solve multi-step linear equations that include the use of the distributive property and combining like terms. Exclude equations that contain variables on both sides.

 Solving Equations by Graphing Each Side

7.EEI.4.c: Write and solve two-step linear inequalities. Graph the solution set on a number line and interpret its meaning.

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

7.EEI.4.d: Identify and justify the steps for solving multi-step linear equations and two-step linear inequalities.

 Modeling and Solving Two-Step Equations
 Solving Algebraic Equations II
 Solving Two-Step Equations

7.EEI.5: Understand and apply the laws of exponents (i.e., product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property) to simplify numerical expressions that include whole-number exponents.

 Exponents and Power Rules
 Simplifying Algebraic Expressions II

7.GM: Geometry and Measurement

7.GM.1: Determine the scale factor and translate between scale models and actual measurements (e.g., lengths, area) of real-world objects and geometric figures using proportional reasoning.

 Similar Figures

7.GM.4: Investigate the concept of circles.

7.GM.4.b: Understand that the constant of proportionality between the circumference and diameter is equivalent to π.

 Circumference and Area of Circles

7.GM.4.c: Explore the relationship between circumference and area using a visual model.

 Circumference and Area of Circles

7.GM.4.d: Use the formulas for circumference and area of circles appropriately to solve real-world and mathematical problems.

 Circumference and Area of Circles

7.GM.5: Write equations to solve problems involving the relationships between angles formed by two intersecting lines, including supplementary, complementary, vertical, and adjacent.

 Triangle Angle Sum

7.GM.6: Apply the concepts of two- and three-dimensional figures to real-world and mathematical situations.

7.GM.6.a: Understand that the concept of area is applied to two-dimensional figures such as triangles, quadrilaterals, and polygons.

 Area of Parallelograms
 Area of Triangles
 Chocomatic (Multiplication, Arrays, and Area)
 Circumference and Area of Circles
 Classifying Quadrilaterals
 Concurrent Lines, Medians, and Altitudes
 Fido's Flower Bed (Perimeter and Area)
 Perimeter and Area of Rectangles
 Polygon Angle Sum
 Special Parallelograms
 Triangle Angle Sum
 Triangle Inequalities

7.GM.6.b: Understand that the concepts of volume and surface area are applied to three-dimensional figures such as cubes, right rectangular prisms, and right triangular prisms.

 Prisms and Cylinders
 Pyramids and Cones
 Surface and Lateral Areas of Prisms and Cylinders
 Surface and Lateral Areas of Pyramids and Cones

7.GM.6.c: Decompose cubes, right rectangular prisms, and right triangular prisms into rectangles and triangles to derive the formulas for volume and surface area.

 Surface and Lateral Areas of Prisms and Cylinders

7.GM.6.d: Use the formulas for area, volume, and surface area appropriately.

 Area of Parallelograms
 Area of Triangles
 Chocomatic (Multiplication, Arrays, and Area)
 Circumference and Area of Circles
 Perimeter and Area of Rectangles
 Prisms and Cylinders
 Surface and Lateral Areas of Prisms and Cylinders
 Surface and Lateral Areas of Pyramids and Cones

7.DSP: Data Analysis, Statistics, and Probability

7.DSP.1: Investigate concepts of random sampling.

7.DSP.1.a: Understand that a sample is a subset of a population and both possess the same characteristics.

 Polling: City
 Polling: Neighborhood
 Populations and Samples

7.DSP.1.b: Differentiate between random and non-random sampling.

 Polling: City
 Polling: Neighborhood
 Populations and Samples

7.DSP.1.c: Understand that generalizations from a sample are valid only if the sample is representative of the population.

 Polling: City

7.DSP.1.d: Understand that random sampling is used to gather a representative sample and supports valid inferences about the population.

 Polling: City
 Polling: Neighborhood

7.DSP.2: Draw inferences about a population by collecting multiple random samples of the same size to investigate variability in estimates of the characteristic of interest.

 Polling: City
 Polling: Neighborhood
 Populations and Samples

7.DSP.3: Visually compare the centers, spreads, and overlap of two displays of data (i.e., dot plots, histograms, box plots) that are graphed on the same scale and draw inferences about this data.

 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

7.DSP.4: Compare the numerical measures of center (mean, median, mode) and variability (range, interquartile range, mean absolute deviation) from two random samples to draw inferences about the populations.

 Box-and-Whisker Plots
 Polling: City
 Populations and Samples

7.DSP.5: Investigate the concept of probability of chance events.

7.DSP.5.a: Determine probabilities of simple events.

 Theoretical and Experimental Probability

7.DSP.5.d: Understand that a probability closer to 1 indicates a likely chance event.

 Spin the Big Wheel! (Probability)

7.DSP.5.e: Understand that a probability close to ½ indicates that a chance event is neither likely nor unlikely.

 Probability Simulations
 Spin the Big Wheel! (Probability)

7.DSP.5.f: Understand that a probability closer to 0 indicates an unlikely chance event.

 Spin the Big Wheel! (Probability)

7.DSP.6: Investigate the relationship between theoretical and experimental probabilities for simple events.

7.DSP.6.a: Determine approximate outcomes using theoretical probability.

 Geometric Probability
 Independent and Dependent Events
 Probability Simulations
 Theoretical and Experimental Probability

7.DSP.6.b: Perform experiments that model theoretical probability.

 Independent and Dependent Events

7.DSP.6.c: Compare theoretical and experimental probabilities.

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

7.DSP.7: Apply the concepts of theoretical and experimental probabilities for simple events.

7.DSP.7.c: Perform experiments to test the validity of probability models.

 Polling: City

7.DSP.8: Extend the concepts of simple events to investigate compound events.

7.DSP.8.a: Understand that the probability of a compound event is between 0 and 1.

 Independent and Dependent Events

7.DSP.8.b: Identify the outcomes in a sample space using organized lists, tables, and tree diagrams.

 Permutations and Combinations

7.DSP.8.c: Determine probabilities of compound events using organized lists, tables, and tree diagrams.

 Permutations and Combinations

7.DSP.8.d: Design and use simulations to collect data and determine probabilities.

 Geometric Probability
 Independent and Dependent Events
 Probability Simulations
 Theoretical and Experimental Probability

7.DSP.8.e: Compare theoretical and experimental probabilities for compound events.

 Independent and Dependent Events
 Theoretical and Experimental Probability

Correlation last revised: 1/19/2017

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