RP: Ratios and Proportional Relationships

RP.A: Analyze proportional relationships and use them to solve problems.

RP.A.1: Compute unit rates, including those that involve complex fractions, with like or different units.

Beam to Moon (Ratios and Proportions)
Household Energy Usage
Road Trip (Problem Solving)
Unit Conversions

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

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

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

RP.A.2.b: Identify and/or compute the constant of proportionality (unit rate).

Beam to Moon (Ratios and Proportions)
Dilations
Direct and Inverse Variation
Perimeters and Areas of Similar Figures
Similar Figures

RP.A.2.c: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation.

Direct and Inverse Variation

RP.A.2.d: Recognize that the graph of any proportional relationship will pass through the origin.

Direct and Inverse Variation

RP.A.3: Solve problems involving ratios, rates, percentages and proportional relationships.

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
Polling: Neighborhood
Proportions and Common Multipliers
Real-Time Histogram
Road Trip (Problem Solving)
Time Estimation

NS: Number Sense and Operations

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

NS.A.1: Apply and extend previous understandings of numbers to add and subtract rational numbers.

NS.A.1.a: Add and subtract rational numbers.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Equivalent Algebraic Expressions I
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Sums and Differences with Decimals

NS.A.1.b: Represent addition and subtraction on a horizontal or vertical number line.

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

NS.A.1.c: Describe situations and show that a number and its opposite have a sum of 0 (additive inverses).

Adding and Subtracting Integers
Adding on the Number Line
Improper Fractions and Mixed Numbers
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Sums and Differences with Decimals

NS.A.1.d: Understand subtraction of rational numbers as adding the additive inverse.

Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Adding on the Number Line
Equivalent Algebraic Expressions I
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Sums and Differences with Decimals

NS.A.1.e: Determine the distance between two rational numbers on the number line is the absolute value of their difference.

Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Adding on the Number Line
Equivalent Algebraic Expressions I
Rational Numbers, Opposites, and Absolute Values
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Sums and Differences with Decimals

NS.A.1.f: Interpret sums and differences of 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
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Sums and Differences with Decimals

NS.A.2: Apply and extend previous understandings of numbers to multiply and divide rational numbers.

NS.A.2.a: Multiply and divide rational numbers.

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

NS.A.2.c: Understand that every quotient of integers (with non-zero divisor) is a rational number.

Dividing Mixed Numbers

NS.A.2.d: Convert a rational number to a decimal.

Adding and Subtracting Integers
Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

NS.A.2.e: Understand that all rational numbers can be written as fractions or decimal numbers that terminate or repeat.

Estimating Sums and Differences
Fraction Garden (Comparing Fractions)
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

NS.A.2.f: Interpret products and quotients of rational numbers by describing real-world contexts.

Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

NS.A.3: Solve problems involving the four arithmetic operations with rational numbers.

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

EEI: Expressions, Equations and Inequalities

EEI.A: Use properties of operations to generate equivalent expressions.

EEI.A.1: Apply properties of operations to simplify and to factor linear algebraic 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

EEI.A.2: Understand how to use equivalent expressions to clarify quantities in a problem.

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

EEI.B: Solve problems using numerical and algebraic expressions and equations.

EEI.B.1: Solve multi-step problems posed with rational numbers.

EEI.B.1.a: Convert between equivalent forms of the same number.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Adding and Subtracting Integers
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fraction Garden (Comparing Fractions)
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
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)

EEI.B.1.b: Assess the reasonableness of answers using mental computation and estimation strategies.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Adding and Subtracting Integers
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fraction Garden (Comparing Fractions)
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
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)

EEI.B.2: Write and/or solve linear equations and inequalities in one variable.

EEI.B.2.a: Write and/or solve equations of the form x + p = q and px = q in which p and q are rational numbers.

Solving Algebraic Equations II
Solving Equations on the Number Line

EEI.B.2.b: Write and/or solve two-step equations of the form px + q = r and p(x + q) = r, where p, q and r are rational numbers, and interpret the meaning of the solution in the context of the problem.

Absolute Value Equations and Inequalities
Circles
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Order of Operations
Solving Algebraic Equations I
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

EEI.B.2.c: Write, solve and/or graph inequalities of the form px + q > r or px + q < r, where p, q and r are rational numbers.

Absolute Value Equations and Inequalities
Rational Numbers, Opposites, and Absolute Values
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable

GM: Geometry and Measurement

GM.A: Draw and describe geometrical figures and describe the relationships between them.

GM.A.1: Solve problems involving scale drawings of real objects and geometric figures, including computing actual lengths and areas from a scale drawing and reproducing the drawing at a different scale.

Dilations
Perimeters and Areas of Similar Figures
Similar Figures

GM.A.2: Use a variety of tools to construct geometric shapes.

GM.A.2.a: Determine if provided constraints will create a unique triangle through construction.

3D and Orthographic Views
Concurrent Lines, Medians, and Altitudes
Triangle Inequalities

GM.A.2.b: Construct special quadrilaterals given specific parameters.

3D and Orthographic Views
Concurrent Lines, Medians, and Altitudes
Triangle Inequalities

GM.A.4: Understand concepts of circles.

GM.A.4.a: Analyze the relationships among the circumference, the radius, the diameter, the area and Pi in a circle.

Circumference and Area of Circles

GM.A.4.b: Know and apply the formulas for circumference and area of circles to solve problems.

Circumference and Area of Circles

GM.B: Apply and extend previous understanding of angle measure, area and volume.

GM.B.1: Use angle properties to write and solve equations for an unknown angle.

Investigating Angle Theorems
Triangle Angle Sum

GM.B.2: Understand the relationship between area, surface area and volume.

GM.B.2.a: Find the area of triangles, quadrilaterals and other polygons composed of triangles and rectangles.

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

GM.B.2.b: Find the volume and surface area of prisms, pyramids and cylinders.

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

DSP: Data Analysis, Statistics and Probability

DSP.A: Use random sampling to draw inferences about a population.

DSP.A.1: Understand that statistics can be used to gain information about a population by examining a sample of the population.

DSP.A.1.a: Understand that a sample is a subset of a population.

Polling: City
Polling: Neighborhood
Populations and Samples

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

Polling: City
Polling: Neighborhood
Populations and Samples

DSP.A.1.c: Understand that random sampling is used to produce representative samples and support valid inferences.

Polling: City
Polling: Neighborhood
Populations and Samples

DSP.A.2: Use data from multiple samples to draw inferences about a population and investigate variability in estimates of the characteristic of interest.

Polling: City
Polling: Neighborhood
Populations and Samples

DSP.B: Draw informal comparative inferences about two populations.

DSP.B.1: Analyze different data distributions using statistical measures.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

DSP.B.2: Compare the numerical measures of center, measures of frequency and measures of variability from two random samples to draw inferences about the population.

Box-and-Whisker Plots
Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram

DSP.C: Develop, use and evaluate probability models.

DSP.C.1: Investigate the probability of chance events.

DSP.C.1.a: Determine probabilities of simple events.

Independent and Dependent Events
Theoretical and Experimental Probability

DSP.C.1.b: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.

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

DSP.C.2: Investigate the relationship between theoretical and experimental probabilities for simple events.

DSP.C.2.a: Predict outcomes using theoretical probability.

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

DSP.C.2.b: Perform experiments that model theoretical probability.

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

DSP.C.2.c: Compare theoretical and experimental probabilities.

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

DSP.C.3: Explain possible discrepancies between a developed probability model and observed frequencies.

DSP.C.3.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

DSP.C.3.b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Lucky Duck (Expected Value)

DSP.C.4: Find probabilities of compound events using organized lists, tables, tree diagrams and simulations.

DSP.C.4.a: Represent the sample space of a compound event.

Independent and Dependent Events
Permutations and Combinations

DSP.C.4.b: Design and use a simulation to generate frequencies for compound events.

Independent and Dependent Events