RP: Ratios and Proportional Relationships

RP.A: Understand and use ratios to solve problems.

RP.A.1: Understand a ratio as a comparison of two quantities and represent these comparisons.

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

RP.A.2: Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate.

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

RP.A.3: Solve problems involving ratios and rates.

RP.A.3.a: Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

RP.A.3.b: Solve unit rate problems.

Household Energy Usage
Road Trip (Problem Solving)

RP.A.3.c: Solve percent problems.

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Polling: Neighborhood
Real-Time Histogram
Time Estimation

RP.A.3.d: Convert measurement units within and between two systems of measurement.

Unit Conversions

NS: Number Sense and Operations

NS.A: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

NS.A.1: Compute and interpret quotients of positive fractions.

NS.A.1.a: Solve problems involving division of fractions by fractions.

Dividing Fractions
Dividing Mixed Numbers

NS.B: Compute with non-negative multi-digit numbers, and find common factors and multiples.

NS.B.1: Demonstrate fluency with division of multi-digit whole numbers.

No Alien Left Behind (Division with Remainders)

NS.B.2: Demonstrate fluency with addition, subtraction, multiplication and division of decimals.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Multiplying with Decimals
Square Roots
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

NS.B.3: Find common factors and multiples.

NS.B.3.a: Find the greatest common factor (GCF) and the least common multiple (LCM).

Pattern Flip (Patterns)

NS.B.3.b: Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers.

Pattern Flip (Patterns)

NS.C: Apply and extend previous understandings of numbers to the system of rational numbers.

NS.C.1: Use positive and negative numbers to represent quantities.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
Integers, Opposites, and Absolute Values

NS.C.2: Locate a rational number as a point on the number line.

NS.C.2.a: Locate rational numbers on a horizontal or vertical number line.

Adding and Subtracting Integers
Adding on the Number Line
City Tour (Coordinates)
Elevator Operator (Line Graphs)
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Points in the Coordinate Plane
Points, Lines, and Equations
Rational Numbers, Opposites, and Absolute Values

NS.C.2.b: Write, interpret and explain problems of ordering of rational numbers.

Comparing and Ordering Decimals
Estimating Population Size
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Rational Numbers, Opposites, and Absolute Values

NS.C.2.c: Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line.

Adding and Subtracting Integers
Adding on the Number Line
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Solving Algebraic Equations I

NS.C.3: Understand that the absolute value of a rational number is its distance from 0 on the number line.

Absolute Value with Linear Functions
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

NS.C.4: Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3).

Modeling Decimals (Area and Grid Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

EEI: Expressions, Equations and Inequalities

EEI.A: Apply and extend previous understandings of arithmetic to algebraic expressions.

EEI.A.1: Describe the difference between an expression and an equation.

Compound Interest
Solving Equations on the Number Line
Using Algebraic Equations

EEI.A.2: Create and evaluate expressions involving variables and whole number exponents.

EEI.A.2.a: Identify parts of an expression using mathematical terminology.

Compound Interest
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Equations
Using Algebraic Expressions

EEI.A.2.b: Evaluate expressions at specific values of the variables.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations
Solving Equations on the Number Line

EEI.A.2.c: Evaluate non-negative rational number expressions.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations
Solving Equations on the Number Line

EEI.A.2.d: Write and evaluate algebraic expressions.

Linear Inequalities in Two Variables
Order of Operations
Solving Equations by Graphing Each Side
Solving Equations on the Number Line

EEI.A.3: Identify and generate equivalent algebraic expressions using mathematical properties.

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

EEI.B: Reason about and solve one-variable equations and inequalities.

EEI.B.1: Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true.

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable

EEI.B.2: Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true.

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable

EEI.B.3: Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation.

Equivalent Algebraic Expressions I
Solving Algebraic Equations II
Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

EEI.B.4: Solve one-step linear equations in one variable involving non-negative rational numbers.

Absolute Value Equations and Inequalities
Modeling One-Step Equations
Solving Algebraic Equations I
Solving Algebraic Equations II
Solving Equations on the Number Line

EEI.B.5: Recognize that inequalities may have infinitely many solutions.

EEI.B.5.a: Write an inequality of the form x > c, x < c, x ≥ c, or x ≤ c to represent a constraint or condition.

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

EEI.B.5.b: Graph the solution set of an inequality.

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

EEI.C: Represent and analyze quantitative relationships between dependent and independent variables.

EEI.C.1: Identify and describe relationships between two variables that change in relationship to one another.

EEI.C.1.b: Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other.

Points, Lines, and Equations

GM: Geometry and Measurement

GM.A: Solve problems involving area, surface area and volume.

GM.A.1: Find the area of polygons by composing or decomposing the shapes into rectangles or triangles.

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

GM.A.2: Find the volume of right rectangular prisms.

GM.A.2.a: Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base.

Balancing Blocks (Volume)
Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

GM.A.2.b: Apply V = l * w * h and V = Bh to find the volume of right rectangular prisms.

Balancing Blocks (Volume)
Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

GM.A.3: Solve problems by graphing points in all four quadrants of the Cartesian coordinate plane.

GM.A.3.a: Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane.

Points in the Coordinate Plane

GM.A.3.b: Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

Points in the Coordinate Plane

GM.A.3.c: Find distances between points with the same first coordinate or the same second coordinate.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

GM.A.3.d: Construct polygons in the Cartesian coordinate plane.

Points in the Coordinate Plane

GM.A.4: Solve problems using nets.

GM.A.4.a: Represent three-dimensional figures using nets made up of rectangles and triangles.

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

GM.A.4.b: Use nets to find the surface area of three-dimensional figures whose sides are made up of rectangles and triangles.

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

DSP: Data Analysis, Statistics and Probability

DSP.A: Develop understanding of statistical variability.

DSP.A.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Polling: City
Polling: Neighborhood
Reaction Time 2 (Graphs and Statistics)

DSP.A.2: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape.

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

DSP.A.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number.

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
Stem-and-Leaf Plots

DSP.B: Summarize and describe distributions.

DSP.B.1: Display and interpret data.

DSP.B.1.a: Use dot plots, histograms and box plots to display and interpret numerical data.

Box-and-Whisker Plots
Histograms
Mascot Election (Pictographs and Bar Graphs)
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

DSP.B.1.b: Create and interpret circle graphs.

Graphing Skills

DSP.B.2: Summarize numerical data sets in relation to the context.

DSP.B.2.b: Describe the nature of the attribute under investigation, including how it was measured and its units of measurement.

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

DSP.B.2.c: Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data.

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
Sight vs. Sound Reactions
Stem-and-Leaf Plots

DSP.B.2.d: Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the 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)