RP: Ratio and Proportional Relationships

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

RP.A.P.1: Proficient students compute unit rates associated with ratios of like or unlike rational numbers;

Beam to Moon (Ratios and Proportions)

RP.A.A.1: Advanced students compute unit rates associated with ratios of rational numbers including complex fractions;

Beam to Moon (Ratios and Proportions)

RP.A.P.4: Proficient student create equations that represent proportional relationships;

Direct and Inverse Variation

RP.A.B.4: Basic students identify the x- and y-coordinates on a graph in a real-world context;

Points in the Coordinate Plane

RP.A.B.5: Basic students solve for an unknown value in proportional problems given the equation a/b = c/d.

Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers

RP.A.P.6: Proficient student use proportional relationships to solve ratio and percent problems that require multi-steps.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents, Fractions, and Decimals
Proportions and Common Multipliers

RP.A.A.5: Advanced students use proportional relationships to solve ratio and percent problems that require multi-steps in a real-world context.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers

NS: The Number System

NS.B: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

NS.B.B.1: Basic students add and subtract two integers;

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials

NS.B.P.1: Proficient student add and subtract up to three 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

NS.B.A.1: Advanced students add and subtract four or more rational numbers and justify the sum or difference of rational numbers using properties of addition and subtraction, numbers, and number lines;

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

NS.B.B.2: Basic students multiply and divide two integers;

Adding and Subtracting Integers

NS.B.P.2: Proficient student multiply and divide up to three rational numbers;

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

NS.B.A.2: Advanced students multiply and divide four or more rational numbers and justify the product or quotient of rational numbers using properties of multiplication and division, numbers, and number lines;

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

NS.B.B.4: Basic students solve mathematical problems involving at least two of the operations with integers.

Adding on the Number Line
Addition of Polynomials

NS.B.P.4: Proficient student solve mathematical and real-world problems involving at least two of the operations with rational numbers.

Adding Fractions (Fraction Tiles)
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

NS.B.A.4: Advanced students solve mathematical and real-world problems involving three or more of the operations, including complex fractions.

Adding Fractions (Fraction Tiles)
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

EE: Expressions and Equations

EE.C: Use properties of operations to generate equivalent expressions.

EE.C.P.1: Proficient students generate equivalent expressions by adding, subtracting, multiplying, and factoring with at least one rational coefficient;

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

EE.C.A.1: Advanced students generate equivalent expressions by adding, subtracting, multiplying, and factoring with multiple rational coefficients;

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

EE.C.A.2: Advanced students interpret the relationships between expressions.

Compound Interest
Simplifying Algebraic Expressions I

EE.D: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

EE.D.P.1: Proficient students solve multi-step real-world and mathematical problems consisting of positive and negative rational numbers given in any form;

Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values

EE.D.P.2: Proficient students approximate answers to real-world and mathematical problems by estimation;

Estimating Sums and Differences

EE.D.A.1: Advanced students assess the reasonableness of answers to real-world and mathematical problems by estimation;

Estimating Sums and Differences

EE.D.B.2: Basic students solve one-step mathematical problems leading to equations involving integers and two-step mathematical problems leading to equations involving whole numbers;

Absolute Value Equations and Inequalities
Solving Equations on the Number Line

EE.D.P.3: Proficient students solve two-step real-world and mathematical problems leading to equations involving rational numbers;

Absolute Value Equations and Inequalities
Solving Equations on the Number Line

EE.D.P.4: Proficient students solve two-step real-world and mathematical problems leading to inequalities involving rational numbers;

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

G: Geometry

G.E: Draw, construct, and describe geometrical figures and describe the relationships between them.

G.E.P.1: Proficient students compute actual lengths from scale drawings and verbal descriptions;

Similar Figures

G.E.B.2: Basic students identify the type of triangle with respect to angle measures and side measures;

Classifying Triangles

G.E.P.2: Proficient students determine if the three measures of angles or sides meets the condition of a unique triangle, more than one triangle, or no triangle;

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Triangle Inequalities

G.F: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

G.F.P.1: Proficient students calculate the area and circumference of a circle;

Circumference and Area of Circles

G.F.A.1: Advanced students solve for a component part (radius or diameter) given the circumference of a circle;

Circumference and Area of Circles

G.F.B.2: Basic students understand the relationship between a pair of supplementary, complementary, or vertical angles;

Triangle Angle Sum

G.F.B.3: Basic students solve real-world and mathematical problems involving the area of a polygon composed of two figures consisting of triangles and rectangles;

Area of Triangles

G.F.P.3: Proficient students solve real-world and mathematical problems involving the area of a polygon composed of no more than three figures consisting of triangles and quadrilaterals;

Area of Triangles

G.F.A.3: Advanced students solve real-world and mathematical problems involving the area of a figure composed of polygons;

Area of Parallelograms
Area of Triangles
Fido's Flower Bed (Perimeter and Area)

G.F.B.4: Basic students solve real-world and mathematical problems involving the volume of a right prism given the area of the base and the height

Prisms and Cylinders

G.F.B.5: Basic students determine the surface area of a right rectangular prism.

Surface and Lateral Areas of Prisms and Cylinders

G.F.P.5: Proficient students solve real-world and mathematical problems involving the surface area of a right prism.

Surface and Lateral Areas of Prisms and Cylinders

G.F.A.5: Advanced students solve real-world and mathematical problems involving the surface area of a solid composed of right prisms.

Surface and Lateral Areas of Prisms and Cylinders

SP: Statistics and Probability

SP.G: Use random sampling to draw inferences about a population.

SP.G.B.1: Basic students identify a statistical question that can be used to sample a population.

Polling: Neighborhood

SP.G.P.1: Proficient students identify the characteristics of valid random samples and how they produce representative samples and valid inferences about a population;

Polling: City

SP.G.A.1: Advanced students examine the validity of inferences about a population;

Polling: City

SP.G.P.2: Proficient students use data from a random sample to draw generalizations and inferences about a population.

Polling: City
Polling: Neighborhood
Populations and Samples

SP.G.A.2: Advanced students compare multiple random samples of the same size from a population to analyze the variations in the population.

Polling: City
Polling: Neighborhood
Populations and Samples

SP.H: Draw informal comparative inferences about two populations.

SP.H.B.1: Basic students compare the measures of center of two data sets.

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)

SP.H.P.1: Proficient students compare two populations with respect to the measures of center and measures of variability.

Polling: City
Populations and Samples
Real-Time Histogram

SP.H.A.1: Advanced students draw inferences about two populations with respect to the measures of center and measures of variability.

Polling: City

SP.I: Investigate chance processes and develop, use, and evaluate probability models.

SP.I.B.1: Basic students describe the probability of a chance event as a number between 0 and 1;

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

SP.I.P.1: Proficient students identify a chance event as an unlikely event, an event that is neither unlikely nor likely, or a likely event given the probability of the chance event as a number between 0 and 1;

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

SP.I.B.2: Basic students determine probabilities of simple probability models;

Independent and Dependent Events
Theoretical and Experimental Probability

SP.I.A.2: Advanced students determine the probability of multiple-event probability models;

Independent and Dependent Events

SP.I.B.3: Basic students determine the sample space from two compound events using lists, tables, and tree diagrams.

Permutations and Combinations

SP.I.P.3: Proficient students determine the probability of compound events consisting of two simple events.

Independent and Dependent Events
Theoretical and Experimental Probability