MA-07-1: 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-07-1.1: Number Sense

MA-07-1.1.1: Students will provide examples of and identify integers, fractions, decimals, percents and pi.

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Percent of Change
Percents, Fractions, and Decimals
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)

MA-07-1.1.2: Students will describe and provide examples of representations of numbers (whole numbers, fractions, decimals, percents, integers, 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.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Chocomatic (Multiplication, Arrays, and Area)
Comparing and Ordering Decimals
Dividing Fractions
Dividing Mixed Numbers
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Square Roots
Toy Factory (Set Models of Fractions)

MA-07-1.1.3: Students will convert among whole numbers, fractions, decimals, percents and pi, and will compare and order these numbers.

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

MA-07-1.2: Estimation

MA-07-1.2.1: Students will estimate to solve real-world and mathematical problems with fractions, decimals and percents, checking for reasonable and appropriate computational results.

Dividing Mixed Numbers
Estimating Sums and Differences
Multiplying with Decimals

MA-07-1.3: Number Operations

MA-07-1.3.2: Students will explain how operations (addition and subtraction; multiplication and division) are inversely related.

Simplifying Algebraic Expressions I

MA-07-1.3.3: Students will add and subtract integers.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials

MA-07-1.4: Ratios and Proportional Reasoning

MA-07-1.4.1: Students will apply ratios and proportional reasoning to solve real-world problems (e.g., percents, sales tax, discounts, rate).

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
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-07-1.5: Properties of Numbers and Operations

MA-07-1.5.1: 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)
Finding Factors with Area Models
Operations with Radical Expressions

MA-07-1.5.2: 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 justify a given step in solving problems.

Chocomatic (Multiplication, Arrays, and Area)

MA-07-2: 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-07-2.1: Measuring Physical Attributes

MA-07-2.1.1: Students will measure lengths (to the nearest eighth of an inch or the nearest centimeter) and will determine and use in real-world and mathematical problems:

MA-07-2.1.1.c: area and circumference of circles and

Measuring Trees

MA-07-2.1.3: Students will explain how measurements and measurement formulas are related or different (e.g., perimeter and area of rectangles).

Perimeter and Area of Rectangles

MA-07-2.2: Systems of Measurement

MA-07-2.2.1: Students will convert units within the same measurement system and use these units to solve real-world problems.

Unit Conversions

MA-07-3: 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-07-3.1: Shapes and Relationships

MA-07-3.1.2: Students will describe and provide examples of the elements (e.g., sides, vertices, angles, congruent parts) of two-dimensional figures (circles, triangles [acute, right, obtuse, scalene, isosceles, equilateral], quadrilaterals [square, rectangle, rhombus, parallelogram, trapezoid], regular polygons), and will apply these elements and figures to solve real-world and mathematical problems.

Classifying Quadrilaterals
Classifying Triangles
Perimeter and Area of Rectangles

MA-07-3.1.3: 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-07-3.1.4: Students will describe and provide examples of congruent and similar figures, and will apply congruent and similar figures to solve real-world and mathematical problems.

Similar Figures
Similarity in Right Triangles

MA-07-3.2: Transformations of Shapes

MA-07-3.2.2: Students will translate (slide) and reflect (flip) figures in a coordinate plane.

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

MA-07-3.2.3: Students will identify rotations (clockwise or counterclockwise) of figures about the origin in the plane (90°, 180°, 270°).

Dilations
Rotations, Reflections, and Translations

MA-07-3.3: Coordinate Geometry

MA-07-3.3.1: 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.

Elevator Operator (Line Graphs)
Point-Slope Form of a Line
Points in the Coordinate Plane
Slope

MA-07-4: 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-07-4.1: Representations of Data Sets

MA-07-4.1.1: 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).

Box-and-Whisker Plots
Compound Inequalities
Correlation
Earthquakes 1 - Recording Station
Elevator Operator (Line Graphs)
Forest Ecosystem
Graphing Skills
Mean, Median, and Mode
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

MA-07-4.1.2: Students will explain how different representations of data (e.g., tables, graphs, diagrams, plots) are related.

Graphing Skills

MA-07-4.1.3: Students will read/interpret, analyze and make inferences from box and whisker plots of data and make predictions and draw conclusions from the data.

Box-and-Whisker Plots

MA-07-4.1.4: Students will determine and construct appropriate data displays (bar graphs, line plots, Venn diagrams, tables, line graphs, stem-and-leaf plots), 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-07-4.2: Characteristics of Data Sets

MA-07-4.2.1: Students will determine the mean, median, mode and range of a set of data, and will identify clusters, gaps and outliers within the 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-07-4.4: Probability

MA-07-4.4.2: Students will:

MA-07-4.4.2.a: determine theoretical probabilities of simple events;

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

MA-07-4.4.2.b: determine probabilities based on the results of an experiment and

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

MA-07-4.4.3: 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-07-5: 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-07-5.1: Patterns, Relations and Functions

MA-07-5.1.1: Students will extend, describe rules for patterns and find a missing term in a pattern from real-world and mathematical problems.

Finding Patterns

MA-07-5.1.2: Students will represent, analyze, and generalize first degree relationships using tables, graphs and words, and will apply the relationships to solve real-world and mathematical problems.

Absolute Value with Linear 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
Slope-Intercept Form of a Line

MA-07-5.1.3: Students will explain how tables, graphs, patterns, verbal rules and equations relate to each other.

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

MA-07-5.1.5: Students will explain how the change in one quantity affects the change in another quantity (e.g., in tables or graphs).

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

MA-07-5.2: Variables, Expressions and Operations

MA-07-5.2.2: 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-07-5.3: Equations and Inequalities

MA-07-5.3.1: Students will model and solve real-world and mathematical problems with one- or two-step single variable, first-degree equations or inequalities (e.g., 2x + 1 = 9, 3x + 3 < 9). (Statements and solutions use only non-negative numbers.)

Modeling and Solving Two-Step Equations
Solving Equations on the Number Line