N: Number Sense, Properties, and Operations

N.1: In the real number system, positive rational numbers are represented in multiple equivalent forms

N.1.a: Read, write, compare, convert and order positive rational numbers in a variety of forms including proper and improper fractions, mixed numbers, decimals, and percents

Comparing and Ordering Decimals
Modeling Decimals (Area and Grid Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values

N.1.b: Express whole numbers as products of prime factors with exponents and use prime factorization to find the greatest common factor and least common multiple of two numbers

Finding Factors with Area Models

N.1.d: Locate positive fractions and decimals on a number line

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Rational Numbers, Opposites, and Absolute Values
Treasure Hunter (Decimals on the Number Line)

N.2: Formulate, represent, and use algorithms with positive rational numbers flexibly, accurately, and efficiently

N.2.a: Model and compute the addition, subtraction, multiplication and division of positive fractions, decimals, and combinations of fractions and decimals

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Adding and Subtracting Integers
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Square Roots
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)
Treasure Hunter (Decimals on the Number Line)

N.2.b: Solve multi-step word problems involving fractions, decimals and whole numbers

Multiplying with Decimals
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Sums and Differences with Decimals

N.2.c: Estimate sums, differences, products and quotients of rational numbers using common fractions, common decimals, and whole numbers

Adding Whole Numbers and Decimals (Base-10 Blocks)
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Improper Fractions and Mixed Numbers
Multiplying Decimals (Area Model)
Multiplying Mixed Numbers
Multiplying with Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

N.2.d: Compare and round positive numbers from thousandths through millions

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

N.3: Quantities can be expressed and compared using ratios and rates

N.3.b: 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

N.3.c: Compute unit rates in real-world situations involving mixtures, concentrations, and distance-time relationships

Household Energy Usage

P: Patterns, Functions, and Algebraic Structures

P.1: Patterns can be described using words, tables, and graphs

P.1.a: Extend the pattern and describe the rule for arithmetic and geometric sequences

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

P.1.b: Model linear situations using tables and graphs, and convert between these two representations

Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Slope-Intercept Form of a Line

P.1.c: Given a linear equation, substitute non-negative input values to create a table and graph coordinate points in the first quadrant

Points, Lines, and Equations
Slope-Intercept Form of a Line

P.2: Variables are used to represent unknown quantities

P.2.a: Describe patterns by using words and variables with mathematical symbols

Arithmetic Sequences
Geometric Sequences

D: Data Analysis, Statistics, and Probability

D.1: Questions can be answered by collecting and analyzing data and data displays

D.1.a: Formulate questions for populations larger than the classroom

Polling: Neighborhood
Real-Time Histogram

D.1.b: Recognize that a sample may not represent a population accurately

Polling: City
Polling: Neighborhood

D.1.c: Recognize bias in surveys

Polling: Neighborhood

D.1.d: Utilize appropriate techniques to design a random sample

Polling: City
Polling: Neighborhood

D.2: Mathematical models are used to determine probability

D.2.a: Determine probabilities through experiments or simulations

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

D.2.b: Express the probability of an event using fractions, decimals, and percents

Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

D.2.c: Make a table, tree diagram or an organized list to determine possible outcomes of two or more compound events

Permutations and Combinations

D.2.d: Predict outcomes of events using experimental and theoretical probabilities

Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

S: Shape, Dimension, and Geometric Relationships

S.1: Polygons can be described, classified, and analyzed by their attributes

S.1.a: Develop and apply formulas and procedures for finding area of triangles, parallelograms, and trapezoids

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles

S.1.c: Classify triangles and apply angle and side properties, including the sum of the interior angles

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Pythagorean Theorem with a Geoboard
Triangle Angle Sum
Triangle Inequalities

S.2: Standard units provide common language for communicating measurements

S.2.a: Connect metric prefixes to place value

Unit Conversions