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 square numbers and square roots to reason about the relationship between the side of a square and area of the square (e.g., side of a square with an area of 9 is the square root of 9 or 3, side of a square with area of 5 is the square root of 5)

Square Roots

1.1.3: Apply knowledge of factors and multiples, evens and odds, primes and composites, to generalizations

Arithmetic and Geometric Sequences
Chocomatic (Multiplication, Arrays, and Area)

1.1.4: Explore the meaning of irrational numbers such as pi, or the square root of 3

Circumference and Area of Circles
Simplifying Radical Expressions

1.2: Operations

1.2.1: Perform computations with exponents, powers of 10, and scientific notation

Unit Conversions

1.2.3: Demonstrate the reasonableness of an exact calculation by using an estimation or mental math strategy

Estimating Sums and Differences

1.2.4: Explain how the distributive property is used to multiply (e.g., partial products, mixed numbers)

Chocomatic (Multiplication, Arrays, and Area)
Equivalent Algebraic Expressions II
Square Roots

1.2.6: Apply proportional reasoning strategies to solve real-world problems

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers

1.2.7: 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

Estimating Sums and Differences

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.

2.1: Patterns and change

2.1.1: Determine the slope of a line given two points on the line (as coordinates, in a graph, in a table)

Cat and Mouse (Modeling with Linear Systems)
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

2.1.2: Use y-intercept and slope to graph the equation of a line

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

2.1.3: Compare the rates of change in tables and graphs and classify them as linear or nonlinear

Cat and Mouse (Modeling with Linear Systems)

2.1.4: Recognize exponential rates of growth and decay in tables and graphs

Compound Interest

2.2: Representations

2.2.1: Write an equation given the tabular or graphic form of a linear problem

Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Points, Lines, and Equations

2.2.2: Analyze the interrelationships among tables, graphs, and equations of lines, paying particular attention to the meaning of intercept and slope in the context of the problem

Cat and Mouse (Modeling with Linear Systems)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Point-Slope Form of a Line
Points, Lines, and Equations
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

2.2.3: Demonstrate the equivalence of two algebraic expressions using physical models

Modeling the Factorization of x²+bx+c
Using Algebraic Expressions

2.2.4: Use tables, graphs and symbolic reasoning to identify functions as linear or nonlinear

Absolute Value with Linear Functions
Linear Functions

2.3: Symbols

2.3.1: Apply the order of operations

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations

2.3.2: Explore the factor/product relationship between a quadratic expression and its linear factors.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form

2.3.3: Use physical models to develop and write exponential and power models

Compound Interest
Exponential Functions
Introduction to Exponential Functions

2.3.4: Combine two algebraic expressions to form a new expression

Equivalent Algebraic Expressions I
Simplifying Algebraic Expressions II

2.3.6: Solve linear equations using inverse operations and properties of equality.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Two-Step Equations

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: Apply angle relationships to solve problems

Triangle Angle Sum

3.2: Location and transformation

3.2.1: Apply proportional reasoning strategies to find unknown sides of similar triangle

Beam to Moon (Ratios and Proportions)

3.2.3: Use the Pythagorean Theorem to find missing sides of right triangles

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

3.3: Measurement

3.3.1: Demonstrate the relationship between the area of the base and volume of prisms and cylinders

Pyramids and Cones

3.3.2: Demonstrate the effects of scaling on volume and surface area of rectangular prisms (i.e., how does doubling the side lengths affect the volume?)

Surface and Lateral Areas of Prisms and Cylinders

3.3.4: Find the measures of corresponding parts of similar figures

Beam to Moon (Ratios and Proportions)
Perimeters and Areas of Similar Figures
Similar Figures

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: Pose questions that can be answered by collecting and organizing data from experiments, surveys, and relevant print and electronic resources

Correlation
Describing Data Using Statistics
Stem-and-Leaf Plots

4.1.2: Use random sampling methods to collect the necessary information to answer questions

Polling: City
Polling: Neighborhood

4.2: Represent

4.2.1: Construct displays of data to represent individual sets of data (e.g., histograms, box plots) or to explore the relationship between related sets of data (scatter plots, line graphs); describe the correspondence between data sets and their graphical displays

Box-and-Whisker Plots
Correlation
Histograms
Movie Reviewer (Mean and Median)
Real-Time Histogram
Stem-and-Leaf Plots
Trends in Scatter Plots

4.3: Analyze

4.3.1: Defend or dispute conclusions drawn from the interpretation of data by comparing sets of data or exploring possible relationships based upon scatter plots of related data and approximate lines of fit

Box-and-Whisker Plots
Correlation
Movie Reviewer (Mean and Median)
Trends in Scatter Plots

4.3.2: Analyze a representative sample to make inferences about a population

Polling: City
Polling: Neighborhood

4.3.3: Find and use appropriate measures of center (mean, media, mode) and spread (range, interquartile range) to interpret 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)
Real-Time Histogram
Stem-and-Leaf Plots

0: Compare the usefulness of the mean and median as measures of center; describe the effect of changes in the data on the mean and median of the data set(s)

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Stem-and-Leaf Plots

4.4: Probability

4.4.1: Compare and make predictions based on theoretical and experimental probabilities, using sample data generated through actual experiments or computer simulations

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

4.4.2: Construct an appropriate sample space and apply principles of probability for a simple or compound event

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

4.4.3: Investigate and describe the difference between the experimental probability of a simulated event (experiment) and the theoretical probability of the same event

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

4.4.4: Explore the concepts of randomness and random sample

Polling: City
Polling: Neighborhood
Populations and Samples