1: Number and Computation

1.1: The student demonstrates number sense for real numbers and simple algebraic expressions in a variety of situations.

1.1.1: knows, explains, and uses equivalent representations for rational numbers and simple algebraic expressions including integers, fractions, decimals, percents, and ratios; rational number bases with integer exponents; rational numbers written in scientific notation with integer exponents; time; and money.

Dividing Exponential Expressions
Dividing Mixed Numbers
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Estimating Sums and Differences
Exponents and Power Rules
Improper Fractions and Mixed Numbers
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

1.1.2: compares and orders rational numbers, the irrational number pi, and algebraic expressions, e.g., Which expression is greater -3n or 3n? It depends on the value of n. If n is positive, 3n is greater. If n is negative, -3n is greater. If n is zero, they are equal.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

1.1.3: explains the relative magnitude between rational numbers, the irrational number pi, and algebraic expressions.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

1.1.4: recognizes and describes irrational numbers, e.g., sqare root of 2 is a non-repeating, non-terminating decimal; or pi is a non-terminating decimal.

Square Roots

1.1.5: knows and explains what happens to the product or quotient when:

1.1.5.a: a positive number is multiplied or divided by a rational number greater than zero and less than one, e.g., if 24 is divided by 1/3, will the answer be larger than 24 or smaller than 24? Explain.

Adding and Subtracting Integers
Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

1.1.5.b: a positive number is multiplied or divided by a rational number greater than one,

Adding and Subtracting Integers
Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

1.2: The student demonstrates an understanding of the real number system; recognizes, applies, and explains their properties; and extends these properties to algebraic expressions.

1.2.3: names, uses, and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects:

1.2.3.a: commutative, associative, distributive, and substitution properties [commutative: a + b = b + a and ab = ba; associative: a + (b + c) = (a + b) + c and a(bc) = (ab)c; distributive: a(b + c) = ab + ac; substitution: if a = 2, then 3a = 3 x 2 = 6];

Adding and Subtracting Integers
Equivalent Algebraic Expressions I

1.2.3.b: identity properties for addition and multiplication and inverse properties of addition and multiplication (additive identity: a + 0 = a, multiplicative identity: a * 1 = a, additive inverse: +5 + -5 = 0, multiplicative inverse: 8 x 1/8 = 1);

Adding and Subtracting Integers

1.4: The student models, performs, and explains computation with rational numbers, the irrational number pi, and algebraic expressions in a variety of situations.

1.4.2: performs and explains these computational procedures with rational numbers:

1.4.2.a: addition, subtraction, multiplication, and division of integers;

Adding and Subtracting Integers
Adding on the Number Line

1.4.2.b: order of operations (evaluates within grouping symbols, evaluates powers to the second or third power, multiplies or divides in order from left to right, then adds or subtracts in order from left to right);

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations

1.4.2.c: approximation of roots of numbers using calculators;

Square Roots

1.4.2.d: multiplication or division to find:

1.4.2.d.i: a percent of a number, e.g., What is 0.5% of 10?;

Percents and Proportions

1.4.2.d.iii: percent one number is of another number, e.g., What percent of 80 is 120?;

Percents and Proportions
Percents, Fractions, and Decimals

1.4.2.d.iv: a number when a percent of the number is given, e.g., 15% of what number is 30?;

Percents and Proportions
Percents, Fractions, and Decimals

1.4.2.e: addition of polynomials, e.g., (3x – 5) + (2x + 8).

Addition and Subtraction of Functions
Addition of Polynomials

1.4.2.f: simplifies algebraic expressions in one variable by combining like terms or using the distributive property, e.g., –3(x – 4) is the same as –3x + 12.

Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions II

2: Algebra

2.1: The student recognizes, describes, extends, develops, and explains the general rule of a pattern from a variety of situations.

2.1.1: identifies, states, and continues a pattern presented in various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, graph), verbal (oral description), kinesthetic (action), and written using these attributes:

2.1.1.a: counting numbers including perfect squares, cubes, and factors and multiples with positive rational numbers (number theory).

Arithmetic Sequences
Finding Patterns
Geometric Sequences

2.1.1.c: geometric figures;

Arithmetic and Geometric Sequences
Finding Patterns

2.1.1.e: things related to daily life;

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

2.2: The student uses variables, symbols, real numbers, and algebraic expressions to solve equations and inequalities in a variety of situations.

2.2.2: simplifies algebraic expressions in one variable by combining like terms or using the distributive property, e.g., --3(x - 4) is the same as --3x + 12.

Addition and Subtraction of Functions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

2.2.3: solves:

2.2.3.a: one- and two-step linear equations in one variable with rational number coefficients and constants intuitively and/or analytically;

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Two-Step Equations

2.2.3.b: one-step linear inequalities in one variable with rational number coefficients and constants intuitively, analytically, and graphically;

Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Linear Inequalities in One Variable

2.2.3.c: systems of given linear equations with whole number coefficients and constants graphically.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)

2.3: The student recognizes, describes, and analyzes, constant, linear, and nonlinear relationships in a variety of situations.

2.3.1: recognizes and examines constant, linear, and nonlinear relationships using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or appropriate technology.

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

2.3.2: knows and describes the difference between constant, linear, and nonlinear relationships.

Absolute Value with Linear Functions
Linear Functions

2.3.3: explains the concepts of slope and x- and y-intercepts of a line.

Cat and Mouse (Modeling with Linear Systems)
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope
Slope-Intercept Form of a Line

2.3.4: recognizes and identifies the graphs of constant and linear functions.

Exponential Functions

2.3.5: identifies ordered pairs from a graph, and/or plots ordered pairs using a variety of scales for the x- and y-axis.

City Tour (Coordinates)
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

2.4: The student generates and uses mathematical models to represent and justify mathematical relationships found in a variety of situations.

2.4.1: knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include:

2.4.1.a: process models (concrete objects, pictures, diagrams, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate grids) to model computational procedures, algebraic relationships, and mathematical relationships and to solve equations

Chocomatic (Multiplication, Arrays, and Area)
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

2.4.1.b: place value models (place value mats, hundred charts, base ten blocks, or unifix cubes) to compare, order, and represent numerical quantities and to model computational procedures;

Comparing and Ordering Decimals

2.4.1.c: fraction and mixed number models (fraction strips or pattern blocks) and decimal and money models (base ten blocks or coins) to compare, order, and represent numerical quantities;

Adding Fractions (Fraction Tiles)
Comparing and Ordering Decimals

2.4.1.e: equations and inequalities to model numerical relationships;

Comparing and Ordering Decimals
Linear Functions

2.4.1.f: function tables to model numerical and algebraic relationships

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

2.4.1.g: coordinate planes to model relationships between ordered pairs and linear equations and inequalities;

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

2.4.1.h: two- and three-dimensional geometric models (geoboards, dot paper, nets, or solids) and real-world objects to model perimeter, area, volume, surface area, and properties of two-and three-dimensional figures;

Chocomatic (Multiplication, Arrays, and Area)
Perimeter and Area of Rectangles
Prisms and Cylinders
Pyramids and Cones
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

2.4.1.j: geometric models (spinners, targets, or number cubes), process models (coins, pictures, or diagrams), and tree diagrams to model probability;

Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

2.4.1.k: frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single and double stem-and-leaf plots, scatter plots, box-and-whisker plots, and histograms to organize and display data;

Box-and-Whisker Plots
Compound Inequalities
Correlation
Describing Data Using Statistics
Distance-Time Graphs
Histograms
Least-Squares Best Fit Lines
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

3: Geometry

3.1: The student recognizes geometric figures and compares their properties in a variety of situations.

3.1.1: recognizes and compares properties of two- and three-dimensional figures using concrete objects, constructions, drawings, appropriate terminology, and appropriate technology.

Classifying Quadrilaterals
Parallelogram Conditions
Similar Figures
Special Parallelograms

3.1.2: discusses properties of triangles and quadrilaterals related to:

3.1.2.a: sum of the interior angles of any triangle is 180°;

Isosceles and Equilateral Triangles
Polygon Angle Sum
Triangle Angle Sum

3.1.2.b: sum of the interior angles of any quadrilateral is 360°;

Classifying Quadrilaterals
Parallelogram Conditions
Polygon Angle Sum
Special Parallelograms
Triangle Angle Sum

3.1.2.c: parallelograms have opposite sides that are parallel and congruent, opposite angles are congruent;

Classifying Quadrilaterals
Parallelogram Conditions

3.1.2.d: rectangles have angles of 90°, sides may or may not be equal;

Classifying Quadrilaterals
Perimeter and Area of Rectangles
Special Parallelograms

3.1.2.e: rhombi have all sides equal in length, angles may or may not be equal;

Classifying Quadrilaterals

3.1.2.f: squares have angles of 90°, all sides congruent;

Classifying Quadrilaterals
Perimeter and Area of Rectangles
Special Parallelograms

3.1.2.g: trapezoids have one pair of opposite sides parallel and the other pair of opposites sides are not parallel;

Classifying Quadrilaterals

3.1.2.h: kites have two distinct pairs of adjacent congruent sides.

Classifying Quadrilaterals

3.1.3: recognizes and describes the rotational symmetries and line symmetries that exist in two-dimensional figures.

Holiday Snowflake Designer
Quilting Bee (Symmetry)

3.1.5: knows and describes Triangle Inequality Theorem to determine if a triangle exists.

Triangle Inequalities

3.1.6: uses the Pythagorean theorem to:

3.1.6.a: determine if a triangle is a right triangle,

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

3.1.7: recognizes and compares the concepts of a point, line, and plane.

Parallel, Intersecting, and Skew Lines

3.1.9: describes and explains angle relationships:

3.1.9.a: when two lines intersect including vertical and supplementary angles;

Triangle Angle Sum

3.1.9.b: when formed by parallel lines cut by a transversal including corresponding, alternate interior, and alternate exterior angles.

Triangle Angle Sum

3.1.10: recognizes and describes arcs and semicircles as parts of a circle and uses the standard notation for arc and circle.

Chords and Arcs
Inscribed Angles

3.2: The student estimates, measures, and uses geometric formulas in a variety of situations.

3.2.3: converts within the customary system and within the metric system.

Unit Conversions

3.2.5: uses given measurement formulas to find:

3.2.5.a: area of parallelograms and trapezoids;

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles

3.2.5.b: surface area of rectangular prisms, triangular prisms, and cylinders;

Surface and Lateral Areas of Prisms and Cylinders

3.2.5.c: volume of rectangular prisms, triangular prisms, and cylinders;

Prisms and Cylinders
Pyramids and Cones

3.2.6: recognizes how ratios and proportions can be used to measure inaccessible objects, e.g., using shadows to measure the height of a flagpole.

Estimating Population Size

3.3: The student recognizes and applies transformations on geometric figures in a variety of situations.

3.3.1: identifies, describes, and performs single and multiple transformations [reflection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing)] on a two-dimensional figure.

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

3.3.2: describes a reflection of a given two-dimensional figure that moves it from its initial placement (preimage) to its final placement (image) in the coordinate plane over the x- and y-axis.

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

3.3.3: draws:

3.3.3.b: a scale drawing of a two-dimensional figure;

Dilations

3.3.3.c: a two-dimensional drawing of a three-dimensional figure.

Surface and Lateral Areas of Prisms and Cylinders

3.4: The student uses an algebraic perspective to examine the geometry of two-dimensional figures in a variety of situations.

3.4.1: uses the coordinate plane to:

3.4.1.a: list several ordered pairs on the graph of a line and finds the slope of the line;

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

3.4.1.e: solve simple systems of linear equations.

Solving Linear Systems (Matrices and Special Solutions)

3.4.2: uses a given linear equation with integer coefficients and constants and an integer solution to find the ordered pairs, organizes the ordered pairs using a T-table, and plots the ordered pairs on a coordinate plane.

Points, Lines, and Equations

4: Data

4.1: The student applies the concepts of probability to draw conclusions, generate convincing arguments, and make predictions and decisions including the use of concrete objects in a variety of situations.

4.1.1: knows and explains the difference between independent and dependent events in an experiment, simulation, or situation.

Independent and Dependent Events

4.1.2: identifies situations with independent or dependent events in an experiment, simulation, or situation, e.g., There are three marbles in a bag. If you draw one marble and give it to your brother, and another marble and give it to your sister, are these independent events or dependent events?

Independent and Dependent Events

4.1.3: finds the probability of a compound event composed of two independent events in an experiment, simulation, or situation, e.g., what is the probability of getting two heads, if you toss a dime and a quarter?

Independent and Dependent Events
Theoretical and Experimental Probability

4.1.4: finds the probability of simple and/or compound events using geometric models (spinners or dartboards).

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

4.2: The student collects, organizes, displays, explains, and interprets numerical (rational) and non-numerical data sets in a variety of situations.

4.2.1: organizes, displays and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays:

4.2.1.a: frequency tables;

Histograms

4.2.1.b: bar, line, and circle graphs;

Reaction Time 1 (Graphs and Statistics)

4.2.1.d: charts and tables;

Stem-and-Leaf Plots

4.2.1.e: stem-and-leaf plots (single and double);

Stem-and-Leaf Plots

4.2.1.f: scatter plots;

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

4.2.1.g: box-and-whiskers plots;

Box-and-Whisker Plots

4.2.1.h: histograms.

Histograms
Stem-and-Leaf Plots

4.2.2: recognizes valid and invalid data collection and sampling techniques.

Polling: City
Polling: Neighborhood
Populations and Samples

4.2.6: makes a scatter plot and draws a line that approximately represents the data, determines whether a correlation exists, and if that correlation is positive, negative, or that no correlation exists.

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