1: Numeric Reasoning: Students will develop Numeric Reasoning and an understanding of Number and Operations by solving problems in which there is a need to represent and model real numbers verbally, physically, and symbolically; to explain the relationship between numbers; to determine the relative magnitude of real numbers; to use operations with understanding; and to select appropriate methods of calculations from among mental math, paper-and-pencil, calculators, or computers.

1.1: Number sense

1.1.2: Use factors and multiples to demonstrate part whole relationships

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Modeling Fractions (Area Models)
Operations with Radical Expressions

1.1.3: Use factors and multiples to develop equivalent fraction families

Factor Trees (Factoring Numbers)

1.1.5: Use place value structure to describe the size of decimals

Adding Whole Numbers and Decimals (Base-10 Blocks)
Comparing and Ordering Decimals
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Treasure Hunter (Decimals on the Number Line)

1.1.6: Demonstrate equivalence of decimals, fractions, and percents using multiple models

Modeling Decimals (Area and Grid Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

1.2: Operations

1.2.2: Multiply fractions by other fractions using physical models, ratio/rate tables, and arrays

Multiplying Fractions

1.2.4: Add and subtract fractions with unlike denominators and use physical models to justify your answer

Adding Fractions (Fraction Tiles)
Fraction Artist 2 (Area Models of Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)

1.2.5: Calculate the decimal equivalent of fractions

Modeling Decimals (Area and Grid Models)

1.2.7: Explain the role of place value in adding and subtracting decimals

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

1.2.8: Multiply decimals to solve real-world problems (e.g., find the cost of 3 1/2 pounds of grapes at $1.95 per pound)

Multiplying with Decimals

1.2.10: Select and use appropriate methods and tools for computing (e.g., mental computation, estimation, calculators, paper, and pencil) depending on the context and nature of the computation

Multiplying Decimals (Area Model)

2: Algebraic Reasoning: Students will develop Algebraic Reasoning and an understanding of Patterns and Functions by solving problems in which there is a need to recognize and extend a variety of patterns; to progress from the concrete to the abstract using physical models, equations, and graphs; to describe, represent, and analyze relationships among variable quantities; and to analyze, represent, model, and describe real-world functional relationships.

2.2: Representations

2.2.1: Demonstrate that a given situation may be represented by a table, graph or equation

Absolute Value Equations and Inequalities
Mascot Election (Pictographs and Bar Graphs)
Using Algebraic Equations

2.2.2: Explore informal methods to model and solve real-world situations that involve equivalent fractions (e.g., use a table of equivalent ratios to solve proportional reasoning problems)

Fractions with Unlike Denominators
Part-to-part and Part-to-whole Ratios

3: Geometric Reasoning: Students will develop Geometric Reasoning and an understanding of Geometry and Measurement by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships among geometric figures; and to measure to a required degree pf accuracy by selecting appropriate tools and units.

3.1: Classification

3.1.1: Estimate, measure, and classify angles

Triangle Angle Sum

3.1.3: Explore the measure of a single angle and find the sum of the angles of a regular polygon

Polygon Angle Sum

3.2: Location and transformation

3.2.1: Measure angles and sides to demonstrate that transformations such as reflections (flips), translations (slides), and rotations (turns) maintain congruence

Rotations, Reflections, and Translations

3.3: Measurement

3.3.1: Use the conceptual knowledge of the area of rectangles to develop formulas for the areas of triangles and parallelograms

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles

3.3.2: Demonstrate an understanding that the perimeters of rectangles with a fixed area can vary

Perimeter and Area of Rectangles

3.3.3: Demonstrate an understanding that the areas of rectangles with a fixed perimeter can vary

Perimeter and Area of Rectangles

3.3.7: Find the circumference of circles and explore finding the area.

Circumference and Area of Circles

4: Quantitative Reasoning: Students will develop Quantitative Reasoning and an understanding of Data Analysis and Probability by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions and to present convincing arguments; and to model mathematical situations to determine the probability.

4.1: Collect

4.1.1: Collect and organize numerical (whole number or decimal) data in order to answer a question

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

4.2: Represent

4.2.1: Construct displays of data (e.g., circle graphs, scatter plots, frequency counts) for a single data set

Box-and-Whisker Plots
Graphing Skills
Histograms
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots
Trends in Scatter Plots

4.3: Analyze

4.3.1: Defend conclusions drawn from the interpretation of data by comparing one data set to another

Box-and-Whisker Plots
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

4.3.2: Find and use summary measures of center (mean, median, mode) and spread (range) to compare sets of single variable data

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

4.4: Probability

4.4.1: Use real-world data to estimate the probability of future events (e.g., batting averages, weather predictions)

Polling: City

4.4.2: Analyze simple games to determine favorable outcomes and chances of winning or losing

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