M.O.7.1: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of numbers, ways of representing numbers, and relationships among numbers and number systems, demonstrate meanings of operations and how they relate to one another, and compute fluently and make reasonable estimates.

M.O.7.1.1: compare, order, and differentiate among integers, decimals, fractions, and irrational numbers using multiple representations (e.g., symbols, manipulatives, graphing on a number line).

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

M.O.7.1.2: model the relationship between perfect squares and square roots using physical representations; estimate square root and evaluate using technology.

Square Roots

M.O.7.1.3: using simple computation and problem-solving situations, demonstrate fluency and justify solutions in performing operations with rational numbers including negative numbers for

M.O.7.1.3.a: adding

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

M.O.7.1.3.b: subtracting

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
Estimating Sums and Differences
Sums and Differences with Decimals

M.O.7.1.3.c: multiplying

Adding and Subtracting Integers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

M.O.7.1.3.d: dividing

Dividing Fractions
Dividing Mixed Numbers

M.O.7.1.4: justify the use of the commutative, associative, distributive, identity and inverse properties to simplify numeric expressions.

Order of Operations

M.O.7.1.5: analyze and solve grade-appropriate real-world problems with whole numbers, integers, decimals, fractions and percents including problems involving discounts, interest, taxes, tips, percent increase or decrease, and justify solutions including using estimation and reasonableness.

Compound Interest
Multiplying with Decimals
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Real-Time Histogram
Sums and Differences with Decimals

M.O.7.2: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of patterns, relations and functions, represent and analyze mathematical situations and structures using algebraic symbols, use mathematical models to represent and understand quantitative relationships, and analyze change in various contents.

M.O.7.2.2: evaluate algebraic expressions with whole numbers, integers, absolute value and exponents using the order of operations.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations

M.O.7.2.4: analyze proportional relationships in real-world situations, select an appropriate method to determine the solution and justify reasoning for choice of method to solve.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Part-to-part and Part-to-whole Ratios

M.O.7.2.5: solve one-step linear equations and inequalities using a variety of strategies containing rational numbers with integer solutions; graph solutions, and justify the selection of the strategy and the reasonableness of the solution.

Solving Linear Inequalities in One Variable

M.O.7.2.7: determine the slope of a line from its graphical representation.

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

M.O.7.3: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will: analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships, specify locations and describe spatial relationships using coordinate geometry and other representational systems, apply transformations and use symmetry to analyze mathematical situations, and solve problems using visualization, spatial reasoning, and geometric modeling.

M.O.7.3.1: identify and construct

M.O.7.3.1.b: congruent segments and angles

Classifying Quadrilaterals
Classifying Triangles
Special Parallelograms

M.O.7.3.1.c: perpendicular bisectors of segments

Segment and Angle Bisectors

M.O.7.3.1.d: angle-bisectors

Concurrent Lines, Medians, and Altitudes
Segment and Angle Bisectors
Special Parallelograms

M.O.7.3.3: apply rotations, reflections, translations to plane figures and determine the coordinates of its transformation and compare and contrast the new figure with the original.

Dilations
Rock Art (Transformations)
Rotations, Reflections, and Translations

M.O.7.3.4: pose and solve ratio and proportion problems including scale drawings and similar polygons.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)
Similar Figures

M.O.7.4: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will: demonstrate understanding of measurable attributes of objects and the units, systems, and processes of measurements, and apply appropriate techniques, tools and formulas to determine measurements.

M.O.7.4.2: use the Pythagorean Theorem to find the length of any side of a right triangle and apply to problem solving situations.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

M.O.7.4.3: convert units of measurement, linear, area and volume, within customary and metric systems.

Unit Conversions

M.O.7.5: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will: formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them, select and use appropriate statistical methods to analyze data, develop and evaluate inferences and predictions that are based on models, and apply and demonstrate an understanding of basic concepts of probability

M.O.7.5.1: determine theoretical probability of an event, make and test predictions through experimentation.

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

M.O.7.5.2: determine combinations and permutations by constructing sample spaces (e.g., listing, tree diagrams, frequency distribution tables).

Permutations and Combinations

M.O.7.5.3: collect, organize, graphically represent, and interpret data displays including frequency distributions, line-plots, scatter plots, box and whiskers, and multiple-line graphs.

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Distance-Time Graphs
Elevator Operator (Line Graphs)
Graphing Skills
Mean, Median, and Mode
Polling: City
Populations and Samples
Prairie Ecosystem
Reaction Time 2 (Graphs and Statistics)
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

M.O.7.5.4: analyze and solve application problems involving measures of central tendency (mean, median, mode) and dispersion (range) from data, graphs, tables, and experiments using appropriate technology to compare two sets of data.

Describing Data Using Statistics
Movie Reviewer (Mean and Median)
Polling: City
Populations and Samples
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram