7.1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

7.1.1: Generate and solve complex abstract problems that involve modeling physical, social, or mathematical phenomena.

Estimating Population Size

7.1.2: Evaluate conjectures and pose follow-up questions to prove or disprove conjectures.

Biconditional Statements

7.1.4: Understand equivalent symbolic expressions as distinct symbolic forms that represent the same relationship.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Expressions

7.1.6: Use correct and clearly written or spoken words, variables, and notation to communicate about significant mathematical tasks.

Using Algebraic Expressions

7.1.7: Generalize connections among a variety of representational forms and real-world situations.

Estimating Population Size

7.1.8: Use standard and nonstandard representations to convey and support mathematical relationships.

Linear Functions

7.2: The student will demonstrate through the mathematical processes an understanding of the representation of rational numbers, percentages, and square roots of perfect squares; the application of ratios, rates, and proportions to solve problems; accurate, efficient, and generalizable methods for operations with integers; the multiplication and division of fractions and decimals; and the inverse relationship between squaring and finding the square roots of perfect squares.

7.2.1: Understand fractional percentages and percentages greater than one hundred.

Percents, Fractions, and Decimals

7.2.2: Represent the location of rational numbers and square roots of perfect squares on a number line.

Fraction Garden (Comparing Fractions)
Rational Numbers, Opposites, and Absolute Values

7.2.3: Compare rational numbers, percentages, and square roots of perfect squares by using the symbols "less than or equal to", "greater than or equal to", <, >, and =.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

7.2.4: Understand the meaning of absolute value.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

7.2.5: Apply ratios, rates, and proportions to discounts, taxes, tips, interest, unit costs, and similar shapes.

Beam to Moon (Ratios and Proportions)
Compound Interest
Household Energy Usage
Percent of Change
Road Trip (Problem Solving)
Similar Figures

7.2.7: Translate between standard form and scientific notation.

Unit Conversions 2 - Scientific Notation and Significant Digits

7.2.8: Generate strategies to add, subtract, multiply, and divide integers.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials

7.2.9: Apply an algorithm to multiply and divide fractions and decimals.

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

7.2.10: Understand the inverse relationship between squaring and finding the square roots of perfect squares.

Square Roots

7.3: The student will demonstrate through the mathematical processes an understanding of proportional relationships.

7.3.1: Analyze geometric patterns and pattern relationships.

Arithmetic and Geometric Sequences
Finding Patterns

7.3.2: Analyze tables and graphs to describe the rate of change between and among quantities.

Elevator Operator (Line Graphs)

7.3.3: Understand slope as a constant rate of change.

Cat and Mouse (Modeling with Linear Systems)
Distance-Time and Velocity-Time Graphs
Elevator Operator (Line Graphs)
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

7.3.4: Use inverse operations to solve two-step equations and two-step inequalities.

Modeling One-Step Equations
Solving Equations by Graphing Each Side
Solving Two-Step Equations

7.3.5: Represent on a number line the solution of a two-step inequality.

Absolute Value Equations and Inequalities
Compound Inequalities

7.3.6: Represent proportional relationships with graphs, tables, and equations.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers

7.3.7: Classify relationships as either directly proportional, inversely proportional, or nonproportional.

Direct and Inverse Variation

7.4: The student will demonstrate through the mathematical processes an understanding of proportional reasoning, tessellations, the use of geometric properties to make deductive arguments. the results of the intersection of geometric shapes in a plane, and the relationships among angles formed when a transversal intersects two parallel lines.

7.4.4: Translate between two- and three-dimensional representations of compound figures.

3D and Orthographic Views
Surface and Lateral Areas of Prisms and Cylinders

7.4.5: Analyze the congruent and supplementary relationships-specifically, alternate interior, alternate exterior, corresponding, and adjacent-of the angles formed by parallel lines and a transversal.

Triangle Angle Sum

7.4.6: Compare the areas of similar shapes and the areas of congruent shapes.

Circumference and Area of Circles

7.5: The student will demonstrate through the mathematical processes an understanding of how to use ratio and proportion to solve problems involving scale factors and rates and how to use one-step unit analysis to convert between and within the U.S. Customary System and the metric system.

7.5.1: Use ratio and proportion to solve problems involving scale factors and rates.

Beam to Moon (Ratios and Proportions)
Dilations
Percents and Proportions
Proportions and Common Multipliers
Road Trip (Problem Solving)
Similar Figures

7.5.2: Apply strategies and formulas to determine the surface area and volume of the three-dimensional shapes prism, pyramid, and cylinder.

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

7.5.4: Recall equivalencies associated with length, mass and weight, and liquid volume: 1 square yard = 9 square feet, 1 cubic meter = 1 million cubic centimeters, 1 kilometer = 5/8 mile, 1 inch = 2.54 centimeters; 2.2 kilograms = 1 pound; and 1.06 quarts = 1 liter.

Unit Conversions

7.5.5: Use one-step unit analysis to convert between and within the U.S. Customary System and the metric system.

Unit Conversions

7.6: The student will demonstrate through the mathematical processes an understanding of the relationships between two populations or samples.

7.6.1: Predict the characteristics of two populations based on the analysis of sample data.

Polling: City
Polling: Neighborhood

7.6.2: Organize data in box plots or circle graphs as appropriate.

Box-and-Whisker Plots
Graphing Skills
Reaction Time 2 (Graphs and Statistics)

7.6.3: Apply procedures to calculate the interquartile range.

Box-and-Whisker Plots

7.6.4: Interpret the interquartile range for data.

Box-and-Whisker Plots

7.6.5: Apply procedures to calculate the probability of mutually exclusive simple or compound events.

Probability Simulations

7.6.6: Interpret the probability of mutually exclusive simple or compound events.

Probability Simulations

7.6.7: Differentiate between experimental and theoretical probability of the same event.

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