Academic Standards

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.

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.

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

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.

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: 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

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

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

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 *x*^{2}+*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

3.1: 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)

4.1: 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.

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

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.

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

Correlation last revised: 9/22/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.