1: Number and Operations

1.1: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.

1.1.1: Convert between expressions for positive rational numbers, including fractions, decimals, percents, and ratios.

Percents, Fractions, and Decimals

1.1.2: Use prime factorization to

1.1.2.a: express a whole number as a product of its prime factors and

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

1.1.3: Demonstrate an understanding of fractions as rates, division of whole numbers, parts of a whole, parts of a set, and locations on a real number line.

Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Proportions and Common Multipliers
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

1.1.4: Compare and order integers; and positive fractions, decimals, and percents.

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Comparing and Ordering Decimals
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Modeling Decimals (Area and Grid Models)
Modeling Decimals (Base-10 Blocks)
Modeling Fractions (Area Models)
Rational Numbers, Opposites, and Absolute Values
Subtracting Decimals (Base-10 Blocks)
Toy Factory (Set Models of Fractions)
Treasure Hunter (Decimals on the Number Line)

1.1.5: Express that a number's distance from zero on the number line is its absolute value.

Rational Numbers, Opposites, and Absolute Values

1.1.6: Express the inverse relationships between exponents and roots for perfect squares and cubes.

Square Roots

1.2: Understand and apply numerical operations and their relationship to one another.

1.2.1: Apply and interpret the concepts of addition and subtraction with integers using models.

Adding and Subtracting Integers
Addition of Polynomials

1.2.2: Multiply multi-digit decimals through thousandths.

Multiplying Decimals (Area Model)
Multiplying with Decimals
Square Roots

1.2.4: Multiply and divide fractions.

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers

1.2.5: Provide a mathematical argument to explain operations with two or more fractions or decimals.

Fractions with Unlike Denominators

1.2.6: Apply the commutative, associative, distributive, and identity properties to evaluate numerical expressions involving whole numbers.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations

1.2.7: Simplify numerical expressions (involving fractions, decimals, and exponents) using the order of operations with or without grouping symbols.

Order of Operations

1.3: Use estimation strategies reasonably and fluently while integrating content from each of the other strands.

1.3.2: Make estimates appropriate to a given situation and verify the reasonableness of the results.

Estimating Sums and Differences
Multiplying Decimals (Area Model)

2: Data Analysis, Probability, and Discrete Mathematics

2.1: Understand and apply data collection, organization, and representation to analyze and sort data.

2.1.1: Solve problems by selecting, constructing, and interpreting displays of data, including histograms and stem-and-leaf plots.

Box-and-Whisker Plots
Graphing Skills
Histograms
Polling: City
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

2.1.2: Formulate and answer questions by interpreting, analyzing, and drawing inferences from displays of data, including histograms and stem-and-leaf plots.

Box-and-Whisker Plots
Describing Data Using Statistics
Graphing Skills
Histograms
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

2.1.3: Use extreme values, mean, median, mode, and range to analyze and describe the distribution of a given data set.

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

2.2: Understand and apply the basic concepts of

2.2.1: Use data collected from multiple trials of a single event to form a conjecture about the theoretical probability.

Geometric Probability

2.2.2: Use theoretical probability to

2.2.2.a: predict experimental outcomes,

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

2.2.2.b: compare the outcome of the experiment to the prediction, and

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

2.2.2.c: replicate the experiment and compare results.

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

3: Patterns, Algebra, and Functions

3.2: Describe and model functions and their relationships.

3.2.1: Recognize and describe a relationship between two quantities, given by a chart, table, or graph, using words and expressions.

Mascot Election (Pictographs and Bar Graphs)

3.3: Represent and analyze mathematical situations and structures using algebraic representations.

3.3.2: Create and solve two-step equations that can be solved using inverse properties with fractions and decimals.

Solving Algebraic Equations II

3.3.3: Translate both ways between a verbal description and an algebraic expression or equation.

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

4: Geometry and Measurement

4.1: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

4.1.2: Solve problems using properties of supplementary, complementary, and vertical angles.

Investigating Angle Theorems
Triangle Angle Sum

4.2: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.

4.2.2: Draw a reflection of a polygon in the coordinate plane using a horizontal or vertical line of reflection.

Rock Art (Transformations)
Rotations, Reflections, and Translations

4.3: Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.

4.3.1: Graph ordered pairs in any quadrant of the coordinate plane.

City Tour (Coordinates)
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

4.4: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

4.4.2: Solve problems involving conversion within the U.S.Customary and within the metric system.

Unit Conversions

4.4.4: Solve problems involving the area of simple polygons using formulas for rectangles and triangles.

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

4.4.5: Solve problems involving area and perimeter of regular and irregular polygons.

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

4.4.6: Describe the relationship between the volume of a figure and the area of its base.

Pyramids and Cones