MA-06-1: 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-06-1.1: Number Sense

MA-06-1.1.1: Students will provide examples of and identify fractions, decimals and percents.

Comparing and Ordering Decimals
Fraction Artist 1 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Percent of Change
Percents, Fractions, and Decimals
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)
Treasure Hunter (Decimals on the Number Line)

MA-06-1.1.2: Students will describe and provide examples of representations of numbers (whole numbers, fractions in simplest form, mixed numbers, decimals, percents) 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.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Adding and Subtracting Integers
Adding on the Number Line
Chocomatic (Multiplication, Arrays, and Area)
Comparing and Ordering Decimals
Dividing Fractions
Dividing Mixed Numbers
Fraction Artist 1 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Square Roots
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Toy Factory (Set Models of Fractions)
Treasure Hunter (Decimals on the Number Line)

MA-06-1.1.3: Students will convert between any two of the following numbers: fractions, decimals, and percents (less than or equal to 100%); and will compare and order these numbers.

Modeling Decimals (Area and Grid Models)

MA-06-1.2: Estimation

MA-06-1.2.1: Students will estimate to solve real-world and mathematical problems with whole numbers, fractions, decimals and percents, checking for reasonable and appropriate computational results.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Dividing Mixed Numbers
Estimating Sums and Differences
Multiplying Decimals (Area Model)
Multiplying with Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

MA-06-1.3: Number Operations

MA-06-1.3.2: Students will explain how operations (addition and subtraction; multiplication and division) are inversely related.

Factor Trees (Factoring Numbers)
Simplifying Algebraic Expressions I

MA-06-1.4: Ratios and Proportional Reasoning

MA-06-1.4.1: Students will describe and apply ratios to solve real-world problems.

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

MA-06-1.5: Properties of Numbers and Operations

MA-06-1.5.1: Students will identify and apply prime numbers, composite numbers, prime factorization, factors, multiples and divisibility to solve real-world and mathematical problems (e.g., prime factorization to determine a least common multiple [LCM] or greatest common factor [GCF]).

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Operations with Radical Expressions

MA-06-1.5.2: Students will identify the use of properties (commutative properties of addition and multiplication, the associative properties of addition and multiplication and the identity properties for addition and multiplication) to simplify numerical expressions.

Adding on the Number Line
Addition of Polynomials

MA-06-2: 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-06-2.1: Measuring Physical Attributes

MA-06-2.1.3: Students will explain how measurements and measurement formulas are related or different (perimeter and area of rectangles).

Perimeter and Area of Rectangles

MA-06-2.2: Systems of Measurement

MA-06-2.2.1: Students will convert units within the same measurement system and use these units to solve real-world problems.

Unit Conversions

MA-6-3.1.1: Students will describe and provide examples of the basic geometric elements (points, rays, lines, segments, angles [acute, right, obtuse], planes, radius, diameter, circumference).

Circumference and Area of Circles
Parallel, Intersecting, and Skew Lines
Points in the Coordinate Plane

MA-06-3: 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-06-3.1: Shapes and Relationships

MA-06-3.1.2: Students will describe, and provide examples of the elements (e.g., sides, vertices, angles, congruent parts) of two-dimensional figures (circles, triangles, quadrilaterals, regular polygons), and will apply these elements and figures to solve real-world and mathematical problems.

Triangle Angle Sum

MA-06-3.1.3: Students will describe, provide examples of, and identify elements (e.g., vertices, angles, faces, edges, congruent parts) of common three-dimensional figures (spheres, cones, cylinders, prisms, and pyramids).

Pyramids and Cones
Surface and Lateral Areas of Pyramids and Cones

MA-06-3.2: Transformations of Shapes

MA-06-3.2.1: Students will describe, provide examples of, and apply line symmetry to real-world and mathematical problems.

Holiday Snowflake Designer
Quilting Bee (Symmetry)

MA-06-3.3: Coordinate Geometry

MA-06-3.3.1: Students will identify and graph ordered pairs on a positive coordinate system (Quadrant I), correctly identifying the origin, axes and ordered pairs; and will apply graphing in the coordinate system to solve real-world and mathematical problems.

Elevator Operator (Line Graphs)
Points in the Coordinate Plane

MA-06-4: 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-06-4.1: Representations of Data Sets

MA-06-4.1.1: 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).

Box-and-Whisker Plots
Compound Inequalities
Earthquakes 1 - Recording Station
Elevator Operator (Line Graphs)
Forest Ecosystem
Graphing Skills
Mean, Median, and Mode
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Stem-and-Leaf Plots

MA-06-4.1.2: Students will explain how different representations of data (e.g., tables, graphs, diagrams, plots) are related.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)

MA-06-4.1.4: Students will determine and construct appropriate data displays (bar graphs, line plots, Venn diagrams, tables, line graphs), and will explain why the type of display is appropriate for the data.

Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

MA-06-4.2: Characteristics of Data Sets

MA-06-4.2.1: Students will determine and apply 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)
Reaction Time 2 (Graphs and Statistics)
Sight vs. Sound Reactions
Stem-and-Leaf Plots

MA-06-4.4: Probability

MA-06-4.4.1: Students will describe or determine (e.g., tables, tree diagrams) the sample space of an event for a real-world or mathematical situation.

Permutations and Combinations

MA-06-4.4.3: Students will explore the theoretical probability of simple events.

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

MA-06-5: 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-06-5.1: Patterns, Relations and Functions

MA-06-5.1.1: Students will extend, describe rules for patterns and find a missing term in a pattern from real-world and mathematical problems.

Finding Patterns

MA-06-5.1.3: Students will describe, define, provide examples of, and apply to real-world and mathematical problems functions using tables, graphs and verbal rules.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Points, Lines, and Equations

MA-06-5.1.4: Students will explain how tables, graphs and patterns relate to each other.

Function Machines 2 (Functions, Tables, and Graphs)

MA-06-5.1.5: Students will explain how the change in one quantity affects change in another quantity (e.g., in tables or graphs, input/output tables).

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

MA-06-5.2: Variables, Expressions and Operations

MA-06-5.2.2: 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
Using Algebraic Equations
Using Algebraic Expressions

MA-06-5.3: Equations and Inequalities

MA-06-5.3.1: Students will model and solve real-world and mathematical problems with simple equations and inequalities (e.g., 8x = 4, x + 2 > 5).

Comparing and Ordering Decimals
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations on the Number Line