A: Number and Operations

A.1: Students will understand numerical concepts and mathematical operations

A.1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

A.1.1.1: Sort numbers by their properties (e.g., prime, composite, square, square root).

Chocomatic (Multiplication, Arrays, and Area)
Square Roots

A.1.2: Understand the meaning of operations and how they relate to one another.

A.1.2.1: Use real number properties (e.g., commutative, associative, distributive) to perform various computational procedures.

Adding and Subtracting Integers
Chocomatic (Multiplication, Arrays, and Area)
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Square Roots

A.1.2.2: Perform arithmetic operations and their inverses (e.g., addition/subtraction, multiplication/division, square roots of perfect squares, cube roots of perfect cubes) on real numbers.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Solving Two-Step Equations
Square Roots
Sums and Differences with Decimals

A.1.2.3: Find roots of real numbers using calculators.

Square Roots

A.1.3: Compute fluently and make reasonable estimates.

A.1.3.3: Differentiate between rational and irrational numbers.

Rational Numbers, Opposites, and Absolute Values

A.1.3.5: Perform and explain computations with rational numbers, pi, and first-degree algebraic expressions in one variable in a variety of situations.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Compound Interest
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

A.1.3.6: Select and use appropriate forms of rational numbers to solve real-world problems including those involving proportional relationships.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers

A.1.3.7: Approximate, mentally and with calculators, the value of irrational numbers as they arise from problem situations.

Circumference and Area of Circles

A.1.3.8: Express numbers in scientific notation (including negative exponents) in appropriate problem situations using a calculator.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

B: Algebra

B.1: Students will understand algebraic concepts and applications.

B.1.1: Understand patterns, relations, and functions.

B.1.1.1: Move between numerical, tabular, and graphical representations of linear relationships.

Compound Interest
Exponential Functions
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

B.1.1.2: Use variables to generalize patterns and information presented in tables, charts, and graphs:

B.1.1.2.a: graph linear functions noting that the vertical change per unit of horizontal change (the slope of the graph) is always the same

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

B.1.1.2.b: plot the values of quantities whose ratios are always the same, fit a line to the plot, and understand that the slope of the line equals the quantities.

Cat and Mouse (Modeling with Linear Systems)
Least-Squares Best Fit Lines
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line
Solving Using Trend Lines

B.1.2: Represent and analyze mathematical situations and structures using algebraic symbols.

B.1.2.1: Demonstrate the difference between an equation and an expression.

Absolute Value Equations and Inequalities
Compound Interest
Linear Functions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

B.1.2.2: Solve two-step linear equations and inequalities in one variable with rational solutions.

Absolute Value with Linear Functions
Compound Inequalities
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Point-Slope Form of a Line
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Two-Step Equations
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form)

B.1.2.4: Demonstrate understanding of the relationships between ratios, proportions, and percents and solve for a missing term in a proportion.

Beam to Moon (Ratios and Proportions)
Geometric Probability
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values

B.1.2.5: Graph solution sets of linear equations in two variables on the coordinate plane.

Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

B.1.2.6: Formulate and solve problems involving simple linear relationships, find percents of a given number, variable situations, and unknown quantities.

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Percent of Change
Polling: Neighborhood
Slope-Intercept Form of a Line

B.1.2.7: Use symbols, variables, expressions, inequalities, equations, and simple systems of equations to represent problem situations that involve variables or unknown quantities.

Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Linear Systems (Standard Form)
Using Algebraic Equations
Using Algebraic Expressions

B.1.3: Use mathematical models to represent and understand quantitative relationships.

B.1.3.1: Generate different representations to model a specific numerical relationship given one representation of data (e.g., a table, a graph, an equation, a verbal description).

Absolute Value Equations and Inequalities
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Functions
Linear Functions
Multiplying with Decimals
Points, Lines, and Equations

B.1.4: Analyze changes in various contexts.

B.1.4.1: Use graphs, tables, and algebraic representations to make predictions and solve problems that involve change.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Functions
Points, Lines, and Equations
Translating and Scaling Functions
Using Algebraic Expressions

B.1.4.2: Estimate, find, and justify solutions to problems that involve change using tables, graphs, and algebraic expressions.

Compound Interest
Points, Lines, and Equations

B.1.4.3: Use appropriate problem-solving strategies (e.g., drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table or graph, working a simpler problem, writing an algebraic expression or working backward) to solve problems that involve change.

Arithmetic Sequences
Geometric Sequences
Translating and Scaling Functions

B.1.4.5: Analyze problems that involve change by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing, and observing patterns.

Estimating Population Size

B.1.4.6: Generalize a pattern of change using algebra and show the relationship among the equation, graph, and table of values.

Function Machines 1 (Functions and Tables)
Geometric Sequences

B.1.4.7: Recognize the same general pattern of change presented in different representations.

Function Machines 1 (Functions and Tables)

C: Geometry

C.1: Students will understand geometric concepts and applications.

C.1.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

C.1.1.1: Recognize, classify, and discuss properties of all geometric figures including point, line, and plane.

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

C.1.1.2: Identify arc, chord, and semicircle and explain their attributes.

Chords and Arcs
Inscribed Angles

C.1.1.3: Use the Pythagorean Theorem and its converse to find the missing side of a right triangle and the lengths of the other line segments.

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

C.1.3: Apply transformations and use symmetry to analyze mathematical situations.

C.1.3.2: Describe and perform single and multiple transformations that include rotation, reflection, translation, and dilation (i.e., shrink or magnify) to two-dimensional figures.

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

C.1.4: Use visualization, spatial reasoning, and geometric modeling to solve problems.

C.1.4.2: Recognize and apply properties of corresponding parts of similar and congruent triangles and quadrilaterals.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles

C.1.4.3: Represent and solve problems relating to size, shape, area, and volume using geometric models.

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Circumference and Area of Circles
Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures
Prisms and Cylinders
Pyramids and Cones

C.1.4.4: Develop and use formulas for area, perimeter, circumference, and volume.

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Circumference and Area of Circles
Perimeter and Area of Rectangles
Prisms and Cylinders

C.1.4.5: Construct two-dimensional patterns for three-dimensional models (e.g., cylinders, prisms, cones).

Surface and Lateral Areas of Prisms and Cylinders

D: Measurement

D.1: Students will understand measurement systems and applications.

D.1.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

D.1.1.1: Understand the concept of volume and use the appropriate units in common measuring systems (e.g., cubic centimeter, cubic inch, cubic yard) to compute the volume of rectangular solids.

Prisms and Cylinders
Pyramids and Cones

D.1.2: Apply appropriate techniques, tools, and formulas to determine measurements.

D.1.2.1: Use ratios and proportions to measure hard-to-measure objects.

Estimating Population Size

D.1.2.3: Use proportional relationships in similar shapes to find missing measurements.

Beam to Moon (Ratios and Proportions)

D.1.2.4: Apply strategies to determine the surface area and volume of prisms, pyramids, and cylinders.

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

D.1.2.5: Perform conversions with multiple terms between metric and U.S. standard measurement systems.

Unit Conversions

E: Data Analysis and Probability

E.1: Students will understand how to formulate questions, analyze data, and determine probabilities.

E.1.1: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

E.1.1.1: Represent two numerical variables on a plot, describe how the data points are distributed, and identify relationships that exist between the two variables.

Box-and-Whisker Plots
Describing Data Using Statistics
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram

E.1.1.2: Generate, organize, and interpret real numbers in a variety of situations.

Box-and-Whisker Plots
Describing Data Using Statistics
Stem-and-Leaf Plots

E.1.1.3: Organize, analyze, and display appropriate quantitative and qualitative data to address specific questions including:

E.1.1.3.b: plots

Box-and-Whisker Plots
Stem-and-Leaf Plots

E.1.1.3.c: histograms

Histograms
Real-Time Histogram
Stem-and-Leaf Plots

E.1.1.3.d: bar, line, and pie graphs

Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)

E.1.1.3.e: diagram and pictorial displays

Box-and-Whisker Plots
Correlation
Stem-and-Leaf Plots

E.1.1.3.f: charts and tables

Describing Data Using Statistics
Stem-and-Leaf Plots

E.1.1.4: Select the appropriate measure of central tendency to describe a set of data for a particular problem situation.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Stem-and-Leaf Plots

E.1.1.6: Develop an appropriate strategy using a variety of data from surveys, samplings, estimations, and inferences to address a specific problem.

Estimating Population Size
Estimating Sums and Differences
Polling: City

E.1.2: Select and use appropriate statistical methods to analyze data.

E.1.2.1: Use changes in scales, intervals, or categories to help support a particular interpretation of data.

Polling: City

E.1.2.2: Generate, organize, and interpret real number and other data in a variety of situations.

Box-and-Whisker Plots
Describing Data Using Statistics
Stem-and-Leaf Plots

E.1.2.3: Analyze data to make decisions and to develop convincing arguments from data displayed in a variety of formats that include:

E.1.2.3.a: plots

Box-and-Whisker Plots

E.1.2.3.b: distributions

Box-and-Whisker Plots
Describing Data Using Statistics
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram

E.1.2.3.d: scatter plots

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

E.1.2.3.e: diagrams

Box-and-Whisker Plots
Correlation
Stem-and-Leaf Plots

E.1.2.3.f: pictorial displays

Box-and-Whisker Plots
Correlation
Stem-and-Leaf Plots

E.1.2.3.h: Venn diagrams

Compound Inequalities

E.1.2.4: Interpret and analyze data from graphical representations and draw simple conclusions (e.g., line of best fit).

Box-and-Whisker Plots
Correlation
Stem-and-Leaf Plots

E.1.2.6: Use appropriate central tendency and spread as a means for effective decision-making in analyzing data and outliers.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

E.1.2.8: Use appropriate technology to display data as lists, tables, matrices, graphs, and plots and to analyze the relationships of variables in the data displayed.

Box-and-Whisker Plots
Correlation
Stem-and-Leaf Plots

E.1.3: Develop and evaluate inferences and predictions that are based on data.

E.1.3.2: Describe how reader bias, measurement errors, and display distortion can affect the interpretation of data, predictions, and inferences based on data.

Box-and-Whisker Plots
Polling: City
Polling: Neighborhood

E.1.3.3: Conduct simple experiments and/or simulations, record results in charts, tables, or graphs, and use the results to draw conclusions and make predictions.

Earthquakes 1 - Recording Station

E.1.4: Understand and apply basic concepts of probability.

E.1.4.2: Design and use an appropriate simulation to estimate the probability of a real-world event (e.g., disk toss, cube toss).

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

E.1.4.3: Explain the relationship between probability and odds and calculate the odds of a desired outcome in a simple experiment.

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

E.1.4.4: Use theoretical or experimental probability to make predictions about real-world events.

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

E.1.4.6: Understand that the probability of two unrelated events occurring is the sum of the two individual possibilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.

Independent and Dependent Events
Theoretical and Experimental Probability

E.1.4.1: Calculate the odds of a desired outcome in a simple experiment.

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

E.1.4.5: Use probability to generate convincing arguments, draw conclusions, and make decisions in a variety of situations.

Independent and Dependent Events

E.1.4.7: Describe the difference between independent and dependent events and identify situations involving independent or dependent events.

Independent and Dependent Events