M06.A-N: The Number System

M06.A-N.1: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

M06.A-N.1.1: Solve real-world and mathematical problems involving division of fractions.

M06.A-N.1.1.1: Interpret and compute quotients of fractions (including mixed numbers), and solve word problems involving division of fractions by fractions.

Dividing Fractions
Dividing Mixed Numbers

M06.A-N.2: Compute with multi-digit numbers and find common factors and multiples.

M06.A-N.2.1: Compute with multi-digit numbers using the four arithmetic operations with or without a calculator.

M06.A-N.2.1.1: Solve problems involving operations (+, –, ×, and ÷) with whole numbers, decimals (through thousandths), straight computation, or word problems.

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

M06.A-N.2.2: Apply number theory concepts (specifically, factors and multiples).

M06.A-N.2.2.1: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.

Pattern Flip (Patterns)

M06.A-N.2.2.2: Apply the distributive property to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor.

Pattern Flip (Patterns)

M06.A-N.3: Apply and extend previous understandings of numbers to the system of rational numbers.

M06.A-N.3.1: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values and locations on the number line and coordinate plane.

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

M06.A-N.3.1.1: Represent quantities in real-world contexts using positive and negative numbers, explaining the meaning of 0 in each situation (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge).

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

M06.A-N.3.1.2: Determine the opposite of a number and recognize that the opposite of the opposite of a number is the number itself (e.g., –(–3) = 3; 0 is its own opposite).

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

M06.A-N.3.1.3: Locate and plot integers and other rational numbers on a horizontal or vertical number line; locate and plot 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

M06.A-N.3.2: Understand ordering and absolute value of rational numbers.

M06.A-N.3.2.1: 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)

M06.A-N.3.2.2: Interpret the absolute value of a rational number as its distance from 0 on the number line and as a 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

M06.A-N.3.2.3: Solve real-world and mathematical problems by plotting points in all four quadrants of the coordinate plane. Include 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

M06.A-R: Ratios and Proportional Relationships

M06.A-R.1: Understand ratio concepts and use ratio reasoning to solve problems.

M06.A-R.1.1: Represent and/or solve real-world and mathematical problems using rates, ratios, and/or percents.

M06.A-R.1.1.1: Use ratio language and notation (such as 3 to 4, 3:4, 3/4) 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)

M06.A-R.1.1.2: Find the unit rate a/b associated with a ratio a:b (with b ? 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)

M06.A-R.1.1.3: Construct tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and/or plot the pairs of values on the coordinate plane. Use tables to compare ratios.

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

M06.A-R.1.1.4: Solve unit rate problems including those involving unit pricing and constant speed.

Household Energy Usage
Road Trip (Problem Solving)

M06.A-R.1.1.5: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percentage.

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

M06.B-E: Expressions and Equations

M06.B-E.1: Apply and extend previous understandings of arithmetic to numerical and algebraic expressions.

M06.B-E.1.1: Identify, write, and evaluate numerical and algebraic expressions.

M06.B-E.1.1.1: Write and evaluate numerical expressions involving whole-number exponents.

Order of Operations

M06.B-E.1.1.2: Write algebraic expressions from verbal descriptions.

Improper Fractions and Mixed Numbers
Multiplying with Decimals
Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

M06.B-E.1.1.3: Identify parts of an expression using mathematical terms (e.g., sum, term, product, factor, quotient, coefficient, quantity).

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

M06.B-E.1.1.4: 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

M06.B-E.1.1.5: 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

M06.B-E.2: Interpret and solve one-variable equations and inequalities.

M06.B-E.2.1: Create, solve, and interpret one-variable equations or inequalities in real-world and mathematical problems.

M06.B-E.2.1.1: 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

M06.B-E.2.1.2: Write algebraic expressions to represent real-world or mathematical problems.

Linear Inequalities in Two Variables
Modeling One-Step Equations
Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

M06.B-E.2.1.3: 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 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

M06.B-E.2.1.4: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem and/or represent solutions of such inequalities on number lines.

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

M06.C-G: Geometry

M06.C-G.1: Solve real-world and mathematical problems involving area, surface area, and volume.

M06.C-G.1.1: Find area, surface area, and volume by applying formulas and using various strategies.

M06.C-G.1.1.1: Determine the area of triangles and special quadrilaterals (i.e., square, rectangle, parallelogram, rhombus, and trapezoid). Formulas will be provided.

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

M06.C-G.1.1.2: Determine the area of irregular or compound polygons.

Area of Triangles
Balancing Blocks (Volume)
Fido's Flower Bed (Perimeter and Area)

M06.C-G.1.1.3: Determine the volume of right rectangular prisms with fractional edge lengths. Formulas will be provided.

Prisms and Cylinders

M06.C-G.1.1.4: Given coordinates for the vertices of a polygon in the plane, use the coordinates to find side lengths and area of the polygon (limited to triangles and special quadrilaterals). Formulas will be provided.

Points in the Coordinate Plane

M06.C-G.1.1.5: Represent three-dimensional figures using nets made of rectangles and triangles.

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

M06.C-G.1.1.6: Determine the surface area of triangular and rectangular prisms (including cubes). Formulas will be provided.

Surface and Lateral Areas of Prisms and Cylinders

M06.D-S: Statistics and Probability

M06.D-S.1: Demonstrate understanding of statistical variability by summarizing and describing distributions.

M06.D-S.1.1: Display, analyze, and summarize numerical data sets in relation to their context.

M06.D-S.1.1.1: Display numerical data in plots on a number line, including line plots, histograms, and box-and-whisker 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

M06.D-S.1.1.2: Determine quantitative measures of center (e.g., median, mean, mode) and variability (e.g., range, interquartile range, mean absolute deviation).

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
Sight vs. Sound Reactions
Stem-and-Leaf Plots

M06.D-S.1.1.3: Describe any overall pattern and any 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

M06.D-S.1.1.4: 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)