MA-08-1: Middle grades students understand fractions, decimals, percents and integers, compare them and locate their relative positions on a number line. They develop and use proportional reasoning to solve problems. They work with large numbers and small numbers. They use factors, multiples and prime factorizations. They perform arithmetic operations with fractions, decimals and integers, use properties in computation, develop fluency and develop strategies to estimate the result of operations on rational numbers.

MA-08-1.1: Number Sense

MA-08-1.1.1: Students will provide examples of and identify rational numbers and irrational numbers (square roots and pi only).

Rational Numbers, Opposites, and Absolute Values

MA-08-1.1.2: Students will describe and provide examples of representations of numbers (rational, square roots, and pi) and operations in a variety of equivalent forms using models, diagrams and symbols (e.g., number lines, 10 by 10 grids, rectangular arrays, number sentences) based on real-world and mathematical problems.

Fractions with Unlike Denominators
Rational Numbers, Opposites, and Absolute Values
Square Roots

MA-08-1.1.3: Students will convert, compare and order multiple numerical representations (e.g., fractions, decimals, percentages) of rational numbers and irrational numbers (square roots and pi only).

Rational Numbers, Opposites, and Absolute Values

MA-08-1.2: Estimation

MA-08-1.2.1: Students will estimate to solve real-world and mathematical problems with rational numbers, checking for reasonable and appropriate computational results.

Estimating Sums and Differences

MA-08-1.3: Number Operations

MA-08-1.3.1: Students will add, subtract, multiply and divide rational numbers to solve real-world problems and apply order of operations (including positive whole number exponents) to simplify numerical expressions.

Adding on the Number Line
Dividing Mixed Numbers
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Order of Operations
Sums and Differences with Decimals

MA-08-1.3.2: Students will explain how operations (additions and subtraction; multiplication and division; squaring and taking the square root of a number) are inversely related.

Dividing Polynomials Using Synthetic Division
Function Machines 3 (Functions and Problem Solving)
Modeling One-Step Equations
Simplifying Algebraic Expressions I
Solving Two-Step Equations
Square Roots

MA-08-1.4: Ratios and Proportional Reasoning

MA-08-1.4.1: Students will apply ratios and proportional reasoning to solve real-world problems (e.g., percents, constant rate of change, unit pricing, percent of increase or decrease).

Beam to Moon (Ratios and Proportions)
Compound Interest
Dilations
Direct and Inverse Variation
Household Energy Usage
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Real-Time Histogram
Road Trip (Problem Solving)

MA-08-1.5: Properties of Numbers and Operations

MA-08-1.5.2: Students will identify the use of properties (commutative properties of addition and multiplication, the associative properties of addition and multiplication, the identity properties for addition and multiplication, inverse properties and the distributive property of multiplication over addition and subtraction) to justify a given step in solving problems.

Chocomatic (Multiplication, Arrays, and Area)

MA-08-2: Students continue to measure and estimate measurements including fractions and decimals. They use formulas to find perimeter, area, circumference and volume. They use rulers and protractors. They use US Customary and metric units of measurement.

MA-08-2.1: Measuring Physical Attributes

MA-08-2.1.3: Students will evaluate the measures of angles by estimation, measurement with a protractor or angle ruler and determine angle measures in mathematical and/or real-world situations (e.g., supplementary, external, vertical).

Investigating Angle Theorems
Triangle Angle Sum

MA-08-2.1.4: Students will apply formulas to determine the volume of right rectangular prisms in real-world problems.

Prisms and Cylinders

MA-08-2.1.5: Students will use formulas to find surface area of right rectangular prisms in real-world and mathematical problems.

Surface and Lateral Areas of Prisms and Cylinders

MA-08-2.1.6: Students will apply the Pythagorean theorem to determine the length of a hypotenuse.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

MA-08-2.2: Systems of Measurement

MA-08-2.2.1: Students will convert units within the same measurement system and use these units to solve real-world problems.

Unit Conversions

MA-08-3: Middle grades students expand analysis of two-dimensional shapes and three-dimensional shapes. They translate shapes in a coordinate plane. They extend work with congruent and similar figures, including proportionality. They use the Pythagorean theorem.

MA-08-3.1: Shapes and Relationships

MA-08-3.1.1: Students will describe and provide examples of basic geometric elements that include points, segments, rays, lines, angles, and planes and will use these elements in real-world and mathematical problems.

Parallel, Intersecting, and Skew Lines
Points in the Coordinate Plane
Slope

MA-08-3.1.2: Students will identify and compare properties of two-dimensional figures (circles, triangles acute, right, obtuse, scalene, isosceles, equilateral], quadrilaterals [square, rectangle, rhombus, parallelogram, trapezoid], regular/irregular polygons), and will apply these properties and figures to solve real-world and mathematical problems.

Classifying Quadrilaterals
Classifying Triangles
Congruence in Right Triangles
Parallelogram Conditions
Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Special Parallelograms

MA-08-3.1.4: Students will:

MA-08-3.1.4.a: provide examples of congruent and similar figures;

Similar Figures

MA-08-3.1.4.b: apply congruent and similar figures to solve real-world and mathematical problems and

Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

MA-08-3.1.4.c: apply proportional reasoning to solve problems involving scale drawings and proportional figures.

Beam to Moon (Ratios and Proportions)

MA-08-3.2: Transformations of Shapes

MA-08-3.2.1: Students will describe, provide examples of, and apply to real-world and mathematical problems rotational symmetry (90º, 180º, 360º).

Holiday Snowflake Designer
Quilting Bee (Symmetry)

MA-08-3.2.2: Students will transform (translations, reflections, and dilations with the center of dilation at the origin) figures in a coordinate plane and determine the new coordinates of the image after the transformation.

Dilations
Rotations, Reflections, and Translations
Translations

MA-08-3.2.3: Students will identify rotations (clockwise or counterclockwise) of figures about the origin in a coordinate plane.

Dilations
Rotations, Reflections, and Translations

MA-08-3.3: Coordinate Geometry

MA-08-3.3.1: Students will identify and graph ordered pairs on a coordinate system, correctly identifying the origin, axes and ordered pairs; and will apply graphing in the coordinate system to solve real-world and mathematical problems.

Point-Slope Form of a Line
Points in the Coordinate Plane
Slope

MA-08-4: Middle grades students extend the early development of data representations and examine the appropriateness of graphs and representations of data. They examine central tendencies and dispersion. They develop organized approaches to counting and use experimental and theoretical probabilities.

MA-08-4.1: Representations of Data Sets

MA-08-4.1.1: Students will analyze and make inferences from data displays (drawings, tables/charts, pictographs, bar graphs, circle graphs, line plots, Venn diagrams, line graphs, stem-and-leaf plots, scatter plots, histograms, box-and-whiskers plots).

Box-and-Whisker Plots
Compound Inequalities
Correlation
Earthquakes 1 - Recording Station
Forest Ecosystem
Histograms
Least-Squares Best Fit Lines
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

MA-08-4.1.4: Students will:

MA-08-4.1.4.a: construct data displays (Venn diagrams, tables, line graphs, stem-and-leaf plots, circle graphs, scatter plots);

Compound Inequalities
Correlation
Distance-Time Graphs
Least-Squares Best Fit Lines
Prairie Ecosystem
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

MA-08-4.1.4.b: explain why the type of display is appropriate for the data and

Box-and-Whisker Plots
Correlation
Polling: City
Real-Time Histogram
Stem-and-Leaf Plots

MA-08-4.1.5: Students will construct box-and-whiskers plots.

Box-and-Whisker Plots

MA-08-4.2: Characteristics of Data Sets

MA-08-4.2.1: Students will:

MA-08-4.2.1.a: determine the mean, median, mode, and range of a set 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)
Sight vs. Sound Reactions
Stem-and-Leaf Plots

MA-08-4.2.1.b: identify clusters, gaps, and outliers and

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)

MA-08-4.2.1.c: apply these concepts to compare 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)
Real-Time Histogram

MA-08-4.3: Experiments and Samples

MA-08-4.3.1: Students will explain how data gathering, bias issues, and faulty data analysis can affect the results of data collection.

Describing Data Using Statistics
Polling: City
Real-Time Histogram

MA-08-4.4: Probability

MA-08-4.4.2: Students will:

MA-08-4.4.2.a: determine theoretical probabilities of simple events;

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

MA-08-4.4.2.b: determine probabilities based on the results of an experiment and

Geometric Probability
Independent and Dependent Events

MA-08-4.4.3: Students will tabulate experimental results from simulations and explain how theoretical and experimental probabilities are related.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

MA-08-5: Middle grades students extend pattern work to include arithmetic sequences. They use linear functions and linear equations. They plot rational number pairs in the Cartesian plane. They simplify algebraic and numeric expressions. They explore the effects of change on related variables. They use and solve two-step single variable equations and inequalities.

MA-08-5.1: Patterns, Relations and Functions

MA-08-5.1.2: Students will represent, analyze and generalize simple first and second degree relationships using tables, graphs, words and algebraic notations, and will apply the relationships to solve real-world and mathematical problems.

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Arithmetic Sequences
Compound Interest
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Slope-Intercept Form of a Line
Translating and Scaling Functions

MA-08-5.2: Variables, Expressions and Operations

MA-08-5.2.1: Students will evaluate and simplify algebraic expressions applying the order of operations.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Equations on the Number Line

MA-08-5.2.2: Students will describe, define and provide examples of variables and expressions with a missing value based on real-world and mathematical problems.

Solving Equations on the Number Line

MA-08-5.3: Equations and Inequalities

MA-08-5.3.1: Students will model and solve single variable, first-degree real-world and mathematical problems (e.g., 5x + 2 = x + 22, x-4 < -60).

Absolute Value with Linear Functions
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Systems of Linear Inequalities (Slope-intercept form)