NO: Number and Operations

NO.1: Students shall understand numbers, ways of representing numbers, relationships among numbers and number systems.

NO.1.1: Relate, with and without models and pictures, concepts of ratio, proportion, and percent, including percents less than 1 and greater than 100

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers

NO.1.2: Demonstrate, with and without appropriate technology, an understanding of place value using powers of 10 and write numbers greater than one in scientific notation

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

NO.1.3: Convert between scientific notation and standard notation using numbers greater than one.

Unit Conversions 2 - Scientific Notation and Significant Digits

NO.1.5: Compare and represent integers, fractions, decimals and mixed numbers and find their approximate location on a number line

Adding Fractions (Fraction Tiles)
Adding on the Number Line
Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

NO.2: Students shall understand meanings of operations and how they relate to one another.

NO.2.2: Apply the addition, subtraction, multiplication and division properties of equality to onestep equations with integers, fractions, and decimals

Solving Algebraic Equations II

NO.2.3: Apply rules (conventions) for order of operations to integers and positive rational numbers including parentheses, brackets or exponents

Order of Operations

NO.2.4: Model and develop addition, subtraction, multiplication and division of integers

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

NO.3: Students shall compute fluently and make reasonable estimates.

NO.3.1: Compute, with and without appropriate technology, with integers and positive rational numbers using real-world situations to solve problems

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

NO.3.3: Determine when an Estimate is sufficient and use Estimation to decide whether answers are reasonable in problems including fractions and decimals

Estimating Sums and Differences

NO.3.4: Apply factorization, LCM, and GCF to solve problems using more than two numbers and explain the solution

Finding Factors with Area Models

NO.3.5: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares) with and without appropriate technology

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Rational Numbers, Opposites, and Absolute Values
Square Roots

NO.3.6: Solve, with and without technology, real world percent problems

Percents, Fractions, and Decimals

A: Algebra

A.4: Students shall recognize, describe and develop patterns, relations and functions.

A.4.1: Create and complete a function table (input/output) using a given rule with two operations

Function Machines 1 (Functions and Tables)
Function Machines 3 (Functions and Problem Solving)

A.4.2: Identify and extend patterns in real world situations

Arithmetic Sequences
Finding Patterns
Geometric Sequences

A.5: Students shall represent and analyze mathematical situations and structures using algebraic symbols.

A.5.1: Solve and graph one-step linear equations and inequalities using a variety of methods (i.e., hands-on, inverse operations, symbolic) with real world application with and without technology

Compound Inequalities
Linear Inequalities in Two Variables
Point-Slope Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

A.5.2: Solve simple linear equations using integers and graph on a coordinate plane

Points, Lines, and Equations

A.5.3: Translate phrases and sentences into algebraic expressions and equations including parentheses and positive and rational numbers and simplify algebraic expressions by combining like terms

Addition of Polynomials
Improper Fractions and Mixed Numbers
Multiplying with Decimals
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Equations on the Number Line

G: Geometry

G.8: Students shall analyze characteristics and properties of 2 and 3 dimensional geometric shapes and develop mathematical arguments about geometric relationships.

G.8.1: Identify, draw, classify and compare geometric figures using models and real world examples

Classifying Quadrilaterals

G.8.2: Investigate geometric properties and their relationships in one, two and three dimensions models, including convex and concave polygons

Classifying Quadrilaterals

G.8.3: Recognize the pairs of angles formed and the relationship between the angles including two intersecting lines and parallel lines cut by a transversal (vertical, supplementary, complementary, corresponding, alternate interior, alternate exterior angles and

Triangle Angle Sum

G.8.4: Use paper or physical models to determine the sum of the measures of interior angles of triangles and quadrilaterals

Triangle Angle Sum

G.8.6: Develop the properties of similar figures (ratio of sides and congruent angles)

Similar Figures

G.9: Students shall apply transformations and the use of symmetry to analyze mathematical situations.

G.9.1: Examine the congruence, similarity, and line or rotational symmetry of objects using transformations

Circles
Dilations
Holiday Snowflake Designer
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations

G.9.2: Perform translations and reflections of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper)

Holiday Snowflake Designer
Rock Art (Transformations)

G.10: Students shall specify locations and describe spatial relationships using coordinate geometry and other representational systems.

G.10.1: Plot points in the coordinate plane

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

G.11: Students shall use visualization, spatial reasoning and geometric modeling.

G.11.1: Build three-dimensional solids from two-dimensional patterns (nets)

Surface and Lateral Areas of Prisms and Cylinders

M: Measurement

M.12: Students shall use attributes of measurement to describe and compare mathematical and real-world objects.

M.12.2: Understand relationships among units within the same system

Unit Conversions

M.12.3: Find different areas for a given perimeter and find a different perimeter for a given area

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

M.13: Students shall identify and use units, systems and processes of measurement.

M.13.1: Solve real world problems involving two or more elapsed times, counting forward and backward (calendar and clock)

Elapsed Time

M.13.4: Derive and use formulas for surface area and volume of prisms and cylinders and justify them using geometric models and common materials

Surface and Lateral Areas of Prisms and Cylinders

M.13.5: Apply properties (scale factors, ratio, and proportion) of congruent or similar triangles to solve problems involving missing lengths and angle measures

Similar Figures

M.13.7: Estimate and compute the area of more complex or irregular two-dimensional shapes by dividing them into more basic shapes

Area of Triangles
Fido's Flower Bed (Perimeter and Area)

DAP: Data Analysis and Probability

DAP.14: Students shall formulate questions that can be addressed with data and collect, organize and display relevant data to answer them.

DAP.14.1: Identify different ways of selecting samples and compose appropriate questions

Describing Data Using Statistics
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

DAP.14.2: Explain which types of display are appropriate for various data sets (line graph for change over time, circle graph for part-to-whole comparison, scatter plot for trends)

Correlation
Elevator Operator (Line Graphs)
Graphing Skills

DAP.14.3: Construct and interpret circle graphs, box-and-whisker plots, histograms, scatter plots and double line graphs with and without appropriate technology

Box-and-Whisker Plots
Correlation
Distance-Time Graphs
Elevator Operator (Line Graphs)
Graphing Skills
Histograms
Prairie Ecosystem
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

DAP.15: Students shall select and use appropriate statistical methods to analyze data.

DAP.15.1: Analyze data displays, including ways that they can be misleading

Graphing Skills
Polling: City
Populations and Samples
Reaction Time 2 (Graphs and Statistics)

DAP.15.2: Analyze, with and without appropriate technology, a set of data by using and comparing measures of central tendencies (mean, median, mode) and measures of spread (range, quartile, interquartile range)

Describing Data Using Statistics
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 2 (Graphs and Statistics)

DAP.17: Students shall understand and apply basic concepts of probability.

DAP.17.1: Understand that probability can take any value between 0 and 1 (events that are not going to occur have probability 0, events certain to occur have probability 1)

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