PR: Proportional Reasoning

1.1: Develop an understanding of ratio concepts and use reasoning about ratios to solve problems.

PR.1: Students will… Use appropriate notations [a/b, a to b, a:b] to represent a proportional relationship between quantities and use ratio language to describe the relationship between quantities.

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios

PR.2: Students will… Use unit rates to represent and describe ratio relationships.

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

PR.3: Students will… Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

Beam to Moon (Ratios and Proportions)
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Road Trip (Problem Solving)
Unit Conversions

NO: Number Systems and Operations

2.1: Use prior knowledge of multiplication and division to divide fractions.

NO.4: Students will… Interpret and compute quotients of fractions using visual models and equations to represent problems.

NO.4.a: Use quotients of fractions to analyze and solve problems.

Dividing Fractions
Dividing Mixed Numbers

2.2: Compute multi-digit numbers fluently and determine common factors and multiples.

NO.5: Students will… Fluently divide multi-digit whole numbers using a standard algorithm to solve real-world and mathematical problems.

No Alien Left Behind (Division with Remainders)

NO.6: Students will… Add, subtract, multiply, and divide decimals using a standard algorithm.

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

NO.7: Students will… Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.

Equivalent Algebraic Expressions II

NO.8: Students will… Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

NO.8.a: Use factors and multiples to determine prime factorization.

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

2.3: Apply knowledge of the number system to represent and use rational numbers in a variety of forms.

NO.9: Students will… Use signed numbers to describe quantities that have opposite directions or values and to represent quantities in real-world contexts.

Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

NO.10: Students will… Locate integers and other rational numbers on a horizontal or vertical line diagram.

NO.10.a: Define opposites as numbers located on opposite sides of 0 and the same distance from 0 on a number line.

Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

NO.10.b: Use rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.

Integers, Opposites, and Absolute Values

NO.11: Students will… Find the position of pairs of integers and other rational numbers on the coordinate plane.

NO.11.a: Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

Points in the Coordinate Plane

NO.11.b: Identify (a, b) and (a, –b) as reflections across the x-axis.

Rotations, Reflections, and Translations

NO.11.c: Identify (a, b) and (–a, b) as reflections across the y-axis.

Rotations, Reflections, and Translations

NO.11.d: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

City Tour (Coordinates)
Points in the Coordinate Plane

NO.12: Students will… Explain the meaning of absolute value and determine the absolute value of rational numbers in real-world contexts.

Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

NO.13: Students will… Compare and order rational numbers and absolute value of rational numbers with and without a number line in order to solve real-world and mathematical problems.

Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

AF: Algebra and Functions

3.1: Apply knowledge of arithmetic to read, write, and evaluate algebraic expressions.

AF.14: Students will… Write, evaluate, and compare expressions involving whole number exponents.

Order of Operations

AF.15: Students will… Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.

AF.15.a: Interpret a variable as an unknown value for any number in a specified set, depending on the context.

Using Algebraic Expressions

AF.15.b: Write expressions to represent verbal statements and real-world scenarios.

Solving Equations on the Number Line
Using Algebraic Expressions

AF.15.c: Identify parts of an expression using mathematical terms such as sum, term, product, factor, quotient, and coefficient.

Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

AF.15.d: Evaluate expressions (which may include absolute value and whole number exponents) with respect to order of operations.

Circumference and Area of Circles
Equivalent Algebraic Expressions I
Order of Operations
Perimeter and Area of Rectangles

AF.16: Students will… Generate equivalent algebraic expressions using the properties of operations, including inverse, identity, commutative, associative, and distributive.

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

AF.17: Students will… Determine whether two expressions are equivalent and justify the reasoning.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II

3.2: Use equations and inequalities to represent and solve real-world or mathematical problems.

AF.18: Students will… Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true.

Exploring Linear Inequalities in One Variable
Modeling One-Step Equations

AF.19: Students will… Write and solve an equation in the form of x + p = q or px = q for cases in which p, q, and x are all non-negative rational numbers to solve real-world and mathematical problems.

AF.19.a: Interpret the solution of an equation in the context of the problem.

Modeling One-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line

AF.20: Students will… Write and solve inequalities in the form of x > c, x < c, x >= c, or x <= c to represent a constraint or condition in a real-world or mathematical problem.

AF.20.a: Interpret the solution of an inequality in the context of a problem.

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

AF.20.b: Represent the solutions of inequalities on a number line and explain that the solution set may contain infinitely many solutions.

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

3.3: Identify and analyze relationships between independent and dependent variables.

AF.21: Students will… Identify, represent, and analyze two quantities that change in relationship to one another in real-world or mathematical situations.

AF.21.a: Use tables, graphs, and equations to represent the relationship between independent and dependent variables.

Points, Lines, and Equations

DSP: Data Analysis, Statistics, and Probability

4.1: Use real-world and mathematical problems to analyze data and demonstrate an understanding of statistical variability and measures of center.

DSP.22: Students will… Write examples and non-examples of statistical questions, explaining that a statistical question anticipates variability in the data related to the question.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Movie Reviewer (Mean and Median)
Polling: City
Polling: Neighborhood
Reaction Time 2 (Graphs and Statistics)

DSP.23: Students will… Calculate, interpret, and compare measures of center (mean, median, mode) and variability (range and interquartile range) in real-world data sets.

DSP.23.a: Determine which measure of center best represents a real-world data set.

Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)

DSP.23.b: Interpret the measures of center and variability in the context of a problem.

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.24: Students will… Represent numerical data graphically, using dot plots, line plots, histograms, stem and leaf plots, and box plots.

DSP.24.a: Analyze the graphical representation of data by describing the center, spread, shape (including approximately symmetric or skewed), and unusual features (including gaps, peaks, clusters, and extreme values).

Box-and-Whisker Plots
Describing Data Using Statistics
Polling: City
Populations and Samples
Real-Time Histogram

DSP.24.b: Use graphical representations of real-world data to describe the context from which they were collected.

Box-and-Whisker Plots
Histograms
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

GM: Geometry and Measurement

5.1: Graph polygons in the coordinate plane to solve real-world and mathematical problems.

GM.25: Students will… Graph polygons in the coordinate plane given coordinates of the vertices to solve real-world and mathematical problems.

GM.25.a: Determine missing vertices of a rectangle with the same x-coordinate or the same y-coordinate when graphed in the coordinate plane.

Points in the Coordinate Plane

GM.25.b: Use coordinates to find the length of a side between points having the same x-coordinate or the same y-coordinate.

Points in the Coordinate Plane

5.2: Solve real-world and mathematical problems to determine area, surface area, and volume.

GM.26: Students will… Calculate the area of triangles, special quadilaterals, and other polygons by composing and decomposing them into known shapes.

GM.26.a: Apply the techniques of composing and decomposing polygons to find area in the context of solving real-world and mathematical problems.

Area of Parallelograms
Area of Triangles

GM.27: Students will… Determine the surface area of three-dimensional figures by representing them with nets composed of rectangles and triangles to solve real-world and mathematical problems.

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

GM.28: Students will… Apply previous understanding of volume of right rectangular prisms to those with fractional edge lengths to solve real-world and mathematical problems.

GM.28.a: Use models (cubes or drawings) and the volume formulas (V = lwh and V = Bh) to find and compare volumes of right rectangular prisms.

Balancing Blocks (Volume)
Prisms and Cylinders

Correlation last revised: 3/2/2020

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