7.M.1: Number and Operation

7.M.1.1: Understand and use numbers.

7.M.1.1.1: Compare magnitudes and relative magnitudes of rational numbers, including integers, fractions, and decimals.

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

7.M.1.1.2: Solve problems requiring the conversion between simple decimals, fractions, ratios, and percents.

Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

7.M.1.1.3: Locate the position of rational numbers on a number line.

Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Rational Numbers, Opposites, and Absolute Values

7.M.1.1.5: Apply the number theory concepts of primes, composites, and prime factorization and find the Least Common Multiple (LCM) and the Greatest Common Factor (GCF).

Finding Factors with Area Models

7.M.1.1.7: Describe the use of integers in real-world situations.

Integers, Opposites, and Absolute Values

7.M.1.2: Perform computations accurately.

7.M.1.2.1: Recall the common equivalent fractions, decimals, and percents of halves, fourths, and tenths.

Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

7.M.1.2.2: Add, subtract, multiply, and divide whole numbers, fractions and decimals; and add, multiply, and divide integers.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Square Roots
Sums and Differences with Decimals

7.M.1.2.4: Evaluate numerical expressions using the order of operations with whole numbers and decimals.

Order of Operations
Solving Equations on the Number Line

7.M.1.2.6: Use a variety of strategies including common mathematical formulas to compute problems drawn from real life situations.

Estimating Population Size

7.M.1.3: Estimate and judge reasonableness of results.

7.M.1.3.5: Formulate conjectures and discuss why they must be or seem to be true.

Biconditional Statements

7.M.2: Concepts and Principles of Measurement

7.M.2.1: Understand and use U.S. customary and metric measurements.

7.M.2.1.3: Explain the differences between perimeter, area, and volume (capacity) and their measures within both systems.

Circumference and Area of Circles
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles
Pyramids and Cones

7.M.2.1.4: Given the formulas, find the perimeter, circumference, or area of triangles, circles, and quadrilaterals.

Area of Parallelograms
Area of Triangles
Circumference and Area of Circles
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

7.M.2.1.5: Convert units of measurement within each system.

Unit Conversions

7.M.2.1.6: Solve problems involving perimeter and area of 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

7.M.2.2: Apply the concepts of rates, ratios, and proportions.

7.M.2.2.1: Explain rates and their relationship to ratios, and use proportions to solve problems represented with a diagram.

Beam to Moon (Ratios and Proportions)
Proportions and Common Multipliers
Road Trip (Problem Solving)

7.M.2.2.2: Reduce rates to unit rates.

Road Trip (Problem Solving)

7.M.2.3: Apply dimensional analysis.

7.M.2.3.1: Identify properly constructed dimensional analysis conversions.

Unit Conversions

7.M.3: Concepts and Language of Algebra and Functions

7.M.3.1: Use algebraic symbolism as a tool to represent mathematical relationships.

7.M.3.1.1: Use variables in simple expressions and equations.

Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Solving Equations on the Number Line
Using Algebraic Equations

7.M.3.1.2: Translate simple word statements into algebraic expressions and equations.

Linear Functions
Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

7.M.3.1.3: Use symbols "<", ">", "=", "not equal to", "less than or equal to", and "greater than or equal to" to express relationships.

Comparing and Ordering Decimals

7.M.3.2: Evaluate algebraic expressions.

7.M.3.2.1: Evaluate simple numeric and algebraic expressions using commutative, associative, identity, zero, inverse, distributive, and substitution properties.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations
Solving Equations by Graphing Each Side

7.M.3.2.2: Use the order of operations in evaluating simple algebraic expressions.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations

7.M.3.3: Solve algebraic equations and inequalities.

7.M.3.3.1: Solve one-step equations.

Modeling One-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line

7.M.3.4: Understand the concept of functions.

7.M.3.4.1: Extend patterns involving rational numbers and describe the rule that generates the pattern.

Function Machines 1 (Functions and Tables)

7.M.3.4.2: Explain how a change in one quantity impacts a change in another quantity.

Translating and Scaling Functions

7.M.3.4.3: Use appropriate vocabulary and notations.

Function Machines 1 (Functions and Tables)
Points, Lines, and Equations

7.M.3.6: Apply functions to a variety of problems.

7.M.3.6.1: Use patterns and linear functions to represent and solve simple problems.

Compound Interest

7.M.4: Concepts and Principles of Geometry

7.M.4.1: Apply concepts of size, shape, and spatial relationships.

7.M.4.1.4: Explain and model the effects of reflections, translations, and rotations on various shapes.

Holiday Snowflake Designer
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Similar Figures

7.M.4.1.5: Identify congruence, similarities, and line symmetry of shapes.

Holiday Snowflake Designer
Similar Figures
Similarity in Right Triangles

7.M.4.1.6: Describe the concept of surface area and volume (capacity).

Surface and Lateral Areas of Prisms and Cylinders

7.M.4.3: Apply graphing in two dimensions.

7.M.4.3.1: Identify and plot points on a coordinate plane.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

7.M.5: Data Analysis, Probability, and Statistics

7.M.5.1: Understand data analysis.

7.M.5.1.1: Read and interpret tables, charts, and graphs, including frequency tables, scatter plots, broken line graphs, line plots, bar graphs, histograms, circle graphs, and stem-and-leaf plots.

Correlation
Elevator Operator (Line Graphs)
Graphing Skills
Histograms
Mean, Median, and Mode
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

7.M.5.1.3: Use appropriate vocabulary and notations.

Polling: City
Real-Time Histogram

7.M.5.2: Collect, organize, and display data.

7.M.5.2.1: Collect, organize, and display data with appropriate notation in tables, charts and graphs, including scatter plots, broken line graphs, line plots, bar graphs, and stem-and-leaf plots.

Correlation
Describing Data Using Statistics
Distance-Time Graphs
Elevator Operator (Line Graphs)
Graphing Skills
Histograms
Mean, Median, and Mode
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

7.M.5.3: Apply simple statistical measurements.

7.M.5.3.1: Determine the measures of central tendency – mean, median and mode – with sets of 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)
Sight vs. Sound Reactions
Stem-and-Leaf Plots

7.M.5.3.2: Discuss distribution of data, including range, frequency, gaps, and clusters.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

7.M.5.4: Understand basic concepts of probability.

7.M.5.4.1: Predict, perform, and record results of simple probability experiments.

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

7.M.5.4.2: Recognize equally likely outcomes.

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

7.M.5.4.3: Explain that probability ranges from impossible to certain (0% to 100%).

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

7.M.5.4.4: Use the language of probability.

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

7.M.5.5: Make predictions or decisions based on data.

7.M.5.5.1: Make predictions based on simple theoretical probabilities.

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

7.M.5.5.2: Use appropriate vocabulary and notations.

Probability Simulations
Theoretical and Experimental Probability