7.N: Number & Operations

7.N.1: Read, write, represent, and compare rational numbers, expressed as integers, fractions, and decimals.

7.N.1.1: Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal.

Rational Numbers, Opposites, and Absolute Values

7.N.1.2: Compare and order rational numbers expressed in various forms using the symbols <, >, and =.

Comparing and Ordering Decimals

7.N.1.3: Recognize and generate equivalent representations of rational numbers, including equivalent fractions.

Fraction Garden (Comparing Fractions)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

7.N.2: Calculate with integers and rational numbers, with and without positive integer exponents, to solve real-world and mathematical problems; explain the relationship between absolute value of a rational number and the distance of that number from zero.

7.N.2.2: Illustrate multiplication and division of integers using a variety of representations.

Adding and Subtracting Integers

7.N.2.3: Solve real-world and mathematical problems involving addition, subtraction, multiplication and division of rational numbers; use efficient and generalizable procedures including but not limited to standard algorithms.

Adding Fractions (Fraction Tiles)
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

7.N.2.4: Raise integers to positive integer exponents.

Order of Operations

7.N.2.5: Solve real-world and mathematical problems involving calculations with rational numbers and positive integer exponents.

Adding Fractions (Fraction Tiles)
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Population Size
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

7.A: Algebraic Reasoning & Algebra

7.A.1: Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.

7.A.1.1: Describe that the relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = kx; distinguish proportional relationships from other relationships, including inversely proportional relationships (xy = k or y = k/x).

Geometric Probability

7.A.1.2: Recognize that the graph of a proportional relationship is a line through the origin and the coordinate (1, r), where both r and the slope are the unit rate (constant of proportionality, k).

Direct and Inverse Variation

7.A.2: Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols, and graphs; solve problems involving proportional relationships and interpret results in the original context.

7.A.2.1: Represent proportional relationships with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. Determine and compare the unit rate (constant of proportionality, slope, or rate of change) given any of these representations.

Direct and Inverse Variation

7.A.2.2: Solve multi-step problems involving proportional relationships involving distance-time, percent increase or decrease, discounts, tips, unit pricing, similar figures, and other real-world and mathematical situations.

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

7.A.2.3: Use proportional reasoning to solve real-world and mathematical problems involving ratios.

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

7.A.3: Represent and solve linear equations and inequalities.

7.A.3.2: Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form x+ p > q and x + p < q, where p, and q are nonnegative rational numbers.

Solving Linear Inequalities in One Variable

7.A.4: Use order of operations and properties of operations to generate equivalent numerical and algebraic expressions containing rational numbers and grouping symbols; evaluate such expressions.

7.A.4.1: Use properties of operations (limited to associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents.

Order of Operations

7.A.4.2: Apply understanding of order of operations and grouping symbols when using calculators and other technologies.

Order of Operations

7.GM: Geometry & Measurement

7.GM.2: Determine the area of trapezoids and area and perimeter of composite figures.

7.GM.2.2: Find the area and perimeter of composite figures to solve real-world and mathematical problems.

Area of Triangles
Fido's Flower Bed (Perimeter and Area)

7.GM.4: Analyze the effect of dilations, translations, and reflections on the attributes of two-dimensional figures on and off the coordinate plane.

7.GM.4.1: Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors resulting from dilations.

Circles
Dilations
Similar Figures
Similarity in Right Triangles

7.GM.4.2: Apply proportions, ratios, and scale factors to solve problems involving scale drawings and determine side lengths and areas of similar triangles and rectangles.

Dilations
Similar Figures

7.GM.4.3: Graph and describe translations and reflections of figures on a coordinate plane and determine the coordinates of the vertices of the figure after the transformation.

Rock Art (Transformations)
Rotations, Reflections, and Translations

7.D: Data & Probability

7.D.1: Display and analyze data in a variety of ways.

7.D.1.1: Design simple experiments, collect data and calculate measures of central tendency (mean, median, and mode) and spread (range). Use these quantities to draw conclusions about the data collected and make predictions.

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
Stem-and-Leaf Plots

7.D.2: Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems.

7.D.2.1: Determine the theoretical probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1.

Geometric Probability