1: Number Sense, Properties, and Operations

1.1: Make both relative (multiplicative) and absolute (arithmetic) comparisons between quantities. Multiplicative thinking underlies proportional reasoning

1.1: Quantities can be expressed and compared using ratios and rates

1.1.a: Students can: Apply the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

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

1.1.b: Students can: Apply the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship.

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

1.1.c: Students can: Use ratio and rate reasoning to solve real-world and mathematical problems.

1.1.c.i: Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the 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

1.1.c.ii: Use tables to compare ratios.

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

1.1.c.iii: Solve unit rate problems including those involving unit pricing and constant speed.

Household Energy Usage
Road Trip (Problem Solving)

1.1.c.iv: Find a percent of a quantity as a rate per 100.

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

1.1.c.v: Solve problems involving finding the whole, given a part and the percent.

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

1.1.c.vi: Use common fractions and percents to calculate parts of whole numbers in problem situations including comparisons of savings rates at different financial institutions.

Compound Interest
Estimating Sums and Differences
Fraction Artist 1 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Modeling Fractions (Area Models)
Percent of Change
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Real-Time Histogram
Time Estimation
Toy Factory (Set Models of Fractions)

1.1.c.vii: Express the comparison of two whole number quantities using differences, part-to-part ratios, and part-to-whole ratios in real contexts, including investing and saving.

Rational Numbers, Opposites, and Absolute Values

1.1.c.viii: Use ratio reasoning to convert measurement units.

Unit Conversions

1.2: Are fluent with basic numerical and symbolic facts and algorithms, and are able to select and use appropriate (mental math, paper and pencil, and technology) methods based on an understanding of their efficiency, precision, and transparency

1.2: Formulate, represent, and use algorithms with positive rational numbers with flexibility, accuracy, and efficiency

1.2.a: Students can: Fluently divide multi-digit numbers using the standard algorithm.

No Alien Left Behind (Division with Remainders)

1.2.b: Students can: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

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

1.2.c: Students can: Find the greatest common factor of two whole numbers less than or equal to 100.

Pattern Flip (Patterns)

1.2.d: Students can: Find the least common multiple of two whole numbers less than or equal to 12.

Pattern Flip (Patterns)

1.2.e: Students can: Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

Pattern Flip (Patterns)

1.2.f: Students can: Interpret and model quotients of fractions through the creation of story contexts.

Dividing Fractions
Dividing Mixed Numbers

1.2.g: Students can: Compute quotients of fractions.

Dividing Fractions
Dividing Mixed Numbers

1.2.h: Students can: Solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Dividing Fractions
Dividing Mixed Numbers

1.3: Understand the structure and properties of our number system. At their most basic level numbers are abstract symbols that represent real-world quantities

1.3: In the real number system, rational numbers have a unique location on the number line and in space

1.3.a: Students can: Explain why positive and negative numbers are used together to describe quantities having opposite directions or values.

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

1.3.a.i: Use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

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

1.3.b: Students can: Use number line diagrams and coordinate axes to represent points on the line and in the plane with negative number coordinates.

1.3.b.i: Describe a rational number as a point on the number line.

Fraction Garden (Comparing Fractions)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Rational Numbers, Opposites, and Absolute Values

1.3.b.ii: Use opposite signs of numbers to indicate locations on opposite sides of 0 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

1.3.b.iii: Identify that the opposite of the opposite of a number is the number itself.

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

1.3.b.iv: Explain 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

1.3.b.v: Find and position integers and other rational numbers on a horizontal or vertical number line diagram.

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

1.3.b.vi: Find and position pairs of integers and other rational numbers on a coordinate plane.

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

1.3.c: Students can: Order and find absolute value of rational numbers.

1.3.c.i: Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Treasure Hunter (Decimals on the Number Line)

1.3.c.ii: Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Estimating Population Size
Integers, Opposites, and Absolute Values
Modeling Decimals (Area and Grid Models)

1.3.c.iii: Define the absolute value of a rational number as its distance from 0 on the number line and interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

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

1.3.c.iv: Distinguish comparisons of absolute value from statements about order.

Integers, Opposites, and Absolute Values
Points in the Coordinate Plane
Rational Numbers, Opposites, and Absolute Values

1.3.d: Students can: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane including the use of coordinates and absolute value to 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

2: Patterns, Functions, and Algebraic Structures

2.1: Make claims about relationships among numbers, shapes, symbols, and data and defend those claims by relying on the properties that are the structure of mathematics

2.1: Algebraic expressions can be used to generalize properties of arithmetic

2.1.a: Students can: Write and evaluate numerical expressions involving whole-number exponents.

Order of Operations

2.1.b: Students can: Write, read, and evaluate expressions in which letters stand for numbers.

2.1.b.i: Write expressions that record operations with numbers and with letters standing for numbers.

Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

2.1.b.ii: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) and describe one or more parts of an expression as a single entity.

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

2.1.b.iii: Evaluate expressions at specific values of their variables including expressions that arise from formulas used in real-world problems.

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

2.1.b.iv: Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

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

2.1.c: Students can: Apply the properties of operations to generate equivalent expressions.

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

2.1.d: Students can: Identify when two expressions are equivalent.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

2.2: Variables are used to represent unknown quantities within equations and inequalities

2.2.a: Students can: Describe solving an equation or inequality as a process of answering a question: which values from a specified set, if any, 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

2.2.b: Students can: Use substitution to determine whether a given number in a specified set makes an 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

2.2.c: Students can: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.

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

2.2.c.i: Recognize that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

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

2.2.d: Students can: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative 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

2.2.e: Students can: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.

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

2.2.f: Students can: Show that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

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

3: Data Analysis, Statistics, and Probability

3.1: Solve problems and make decisions that depend on understanding, explaining, and quantifying the variability in data

3.1: Visual displays and summary statistics of one-variable data condense the information in data sets into usable knowledge

3.1.a: Students can: Identify 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)

3.1.b: Students can: Demonstrate 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

3.1.c: Students can: Explain 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 with 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

3.1.d: Students can: Summarize and describe distributions.

3.1.d.i: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

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

3.1.d.ii: Summarize numerical data sets in relation to their context.

3.1.d.ii.2: 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

3.1.d.ii.3: 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 in which the data were gathered.

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

3.1.d.ii.4: Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

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)

4: Shape, Dimension, and Geometric Relationships

4.1: Make claims about relationships among numbers, shapes, symbols, and data and defend those claims by relying on the properties that are the structure of mathematics

4.1: Objects in space and their parts and attributes can be measured and analyzed

4.1.a: Students can: Develop and apply formulas and procedures for area of plane figures.

4.1.a.i: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles
Pythagorean Theorem with a Geoboard

4.1.a.ii: Apply these techniques in the context of solving real-world and mathematical problems.

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

4.1.b: Students can: Develop and apply formulas and procedures for volume of regular prisms.

4.1.b.i: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths.

Prisms and Cylinders

4.1.b.ii: Show that volume is the same as multiplying the edge lengths of a rectangular prism.

Prisms and Cylinders

4.1.b.iii: Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Prisms and Cylinders

4.1.c: Students can: Draw polygons in the coordinate plan to solve real-world and mathematical problems.

4.1.c.i: Draw polygons in the coordinate plane given coordinates for the vertices.

Points in the Coordinate Plane

4.1.c.ii: Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate.

Points in the Coordinate Plane

4.1.d: Students can: Develop and apply formulas and procedures for the surface area.

4.1.d.i: 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

4.1.d.ii: Use nets to find the surface area of figures.

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

4.1.d.iii: Apply techniques for finding surface area in the context of solving real-world and mathematical problems.

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