NO: Number and Operations

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

NO.1.3: Compare and order real numbers including irrational numbers and find their approximate location on a number line (Use technology when appropriate)

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A

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

NO.2.1: Apply the addition, subtraction, multiplication and division properties of equality to twostep equations

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Formulas for any Variable
Solving Two-Step Equations

NO.2.3: Use inverse relationships (addition and subtraction, multiplication and division, squaring and square roots) in problem solving situations

Function Machines 3 (Functions and Problem Solving)
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations
Square Roots

NO.2.4: Apply rules (conventions) for order of operations to rational numbers

Order of Operations

NO.2.5: Model and develop addition, subtraction, multiplication and division of rational numbers

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

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

NO.3.1: Compute, with and without appropriate technology, with rational numbers in multi-step problems

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

NO.3.2: Solve, with and without appropriate technology, multistep problems using a variety of methods and tools (i.e. objects, mental computation, paper and pencil)

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

NO.3.3: Use Estimation to solve problems involving rational numbers; including ratio, proportion, percent (increase or decrease) then judge the reasonableness of solutions

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Percent of Change
Polling: Neighborhood
Proportions and Common Multipliers

NO.3.5: Calculate and find approximations of square roots with appropriate technology

Square Roots

NO.3.6: Solve, with and without technology, real world percent problems including percent of increase or decrease

Percent of Change

A: Algebra

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

A.4.1: Find the nth term in a pattern or a function table

Arithmetic and Geometric Sequences
Finding Patterns
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Using Tables, Rules and Graphs

A.4.2: Using real world situations, describe patterns in words, tables, pictures, and symbolic representations

Arithmetic and Geometric Sequences
Finding Patterns

A.4.3: Interpret and represent a two operation function as an algebraic equation

Introduction to Functions
Linear Functions
Using Algebraic Equations
Using Tables, Rules and Graphs

A.4.4: Use tables, graphs, and equations to identify independent/dependent variables (input/output)

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
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
Using Tables, Rules and Graphs

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

A.5.1: Solve and graph two-step equations and inequalities with one-variable and verify the reasonableness of the result with real world application with and without technology

Defining a Line with Two Points
Inequalities Involving Absolute Values
Modeling and Solving Two-Step Equations
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Solving Two-Step Equations
Standard Form of a Line

A.5.2: Solve and graph linear equations (in the form y=mx+b)

Modeling and Solving Two-Step Equations
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Solving Two-Step Equations
Using Tables, Rules and Graphs

A.5.3: Translate sentences into algebraic equations and inequalities and combine like terms within polynomials

Using Algebraic Equations
Using Algebraic Expressions

A.5.4: Write and evaluate algebraic expressions using rational numbers

Dividing Exponential Expressions
Using Algebraic Equations
Using Algebraic Expressions

A.6: Students shall develop and apply mathematical models to represent and understand quantitative relationships.

A.6.1: Describe, with and without appropriate technology, the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change (rise/run) and y-intercept in real-world problems

Defining a Line with Two Points
Function Machines 2 (Functions, Tables, and Graphs)
Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

A.6.2: Represent, with and without appropriate technology, linear relationships concretely, using tables, graphs and equations.

Arithmetic Sequences
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Point-Slope Form of a Line - Activity A
Reaction Time 1 (Graphs and Statistics)
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Using Tables, Rules and Graphs

A.6.4: Represent, with and without appropriate technology, simple exponential and/or quadratic functions using verbal descriptions, tables, graphs and formulas and translate among these representations

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Reaction Time 1 (Graphs and Statistics)
Roots of a Quadratic

A.7: Students shall analyze change in various contexts.

A.7.1: Use, with and without technology, graphs of real life situations to describe the relationships and analyze change including graphs of change (cost per minute) and graphs of accumulation (total cost)

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

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: Form generalizations and validate conclusions about properties of geometric shapes

Classifying Triangles

G.8.2: Make, with and without appropriate technology, and test conjectures about characteristics and properties between two-dimensional figures and three-dimensional objects

Classifying Triangles

G.8.3: Determine appropriate application of geometric ideas and relationships, such as congruence, similarity, and the Pythagorean theorem, with and without appropriate technology

Congruence in Right Triangles
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Perimeters and Areas of Similar Figures
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Similar Figures - Activity A
Similar Polygons

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

G.9.1: Determine a transformation's line of symmetry and compare the properties of the figure and its transformation

Dilations
Holiday Snowflake Designer
Quilting Bee (Symmetry)
Reflections
Rock Art (Transformations)
Rotations, Reflections and Translations

G.9.2: Draw the results of translations and reflections about the xand y-axis and rotations of objects about the origin

Quilting Bee (Symmetry)
Reflections
Rock Art (Transformations)
Rotations, Reflections and Translations
Translations

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

G.10.1: Use coordinate geometry to explore the links between geometric and algebraic representations of problems (lengths of segments/distance between points, slope/perpendicular-parallel lines)

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Slope - Activity B

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

G.11.1: Using isometric dot paper interpret and draw different views of buildings

3D and Orthographic Views - Activity A

M: Measurement

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

M.12.1: Understand, select and use, with and without appropriate technology, the appropriate units and tools to measure angles, perimeter, area, surface area and volume to solve real world problems

Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

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

M.13.1: Draw and apply measurement skills with fluency to appropriate levels of precision

Triple Beam Balance

M.13.2: Solve problems involving volume and surface area of pyramids, cones and composite figures, with and without appropriate technology

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

M.13.3: Apply proportional reasoning to solve problems involving indirect measurements, scale drawings or rates

Distance-Time Graphs

M.13.4: Find the distance between two points on a coordinate plane using with the Pythagorean theorem

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

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.14.2: Explain which types of display are appropriate for various data sets (scatter plot for relationship between two variants and line of best fit)

Box-and-Whisker Plots
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

DAP.14.3: Interpret or solve real-world problems using data from charts, line plots, stem-and leaf plots, double-bar graphs, line graphs, box-and whisker plots, scatter plots, frequency tables or double line graphs

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Graphing Skills
Line Plots
Reaction Time 1 (Graphs and Statistics)
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots

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

DAP.15.2: Analyze, with and without appropriate technology, graphs by comparing measures of central tendencies and measures of spread

Describing Data Using Statistics
Line Plots
Mean, Median and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)

DAP.15.3: Given at least one of the measures of central tendency create a data set

Describing Data Using Statistics
Line Plots
Mean, Median and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)

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

DAP.17.1: Compute, with and without appropriate technology, probabilities of compound events, using organized lists, tree diagrams and logic grid

Compound Independent Events
Compound Independent and Dependent Events
Permutations
Permutations and Combinations

DAP.17.2: Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predict results, and explain differences

Geometric Probability - Activity A
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability