1: Number and Computation

1.1: The student demonstrates number sense for rational numbers, the irrational number pi, and simple algebraic expressions in one variable 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; integer bases with whole number exponents; positive rational numbers written in scientific notation with positive integer exponents; time; and money, e.g., 253,000 is equivalent to 2.53 x 10 to the 5th power or x + 5x is equivalent to 6x.

Dividing Mixed Numbers
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Estimating Sums and Differences
Exponents and Power Rules
Fraction Garden (Comparing Fractions)
Improper Fractions and Mixed Numbers
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
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
Toy Factory (Set Models of Fractions)
Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

1.1.2: compares and orders rational numbers and the irrational number pi.

Circumference and Area of Circles
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 and between rational numbers and the irrational number pi.

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

1.3: The student uses computational estimation with rational numbers and the irrational number pi in a variety of situations.

1.3.2: uses various estimation strategies and explains how they were used to estimate rational number quantities and the irrational number pi.

Estimating Sums and Differences

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

1.4.1: computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.

Estimating Sums and Differences
Improper Fractions and Mixed Numbers
Sums and Differences with Decimals

1.4.2: performs and explains these computational procedures:

1.4.2.d: adds, subtracts, multiplies, and divides fractions and expresses answers in simplest form;

Fractions with Unlike Denominators

1.4.2.f: uses 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) using whole numbers;

Order of Operations

1.4.4: finds prime factors, greatest common factor, multiples, and the least common multiple.

Finding Factors with Area Models

1.4.5: finds percentages of rational numbers, e.g., 12.5% x $40.25 = n or 150% of 90 is what number? (For the purposes of assessment, percents will not be between 0 and 1.)

Percent of Change
Percents and Proportions

2: Algebra

2.1: The student recognizes, describes, extends, develops, and explains the general rule of a pattern in 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, or graph), verbal (oral description), kinesthetic (action), and written using these attributes:

2.1.1.e: things related to daily life, e.g., tide, moon cycle, or temperature.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

2.1.3: extends a pattern when given a rule of one or two simultaneous changes (addition, subtraction, multiplication, division) between consecutive terms, e.g., find the next three numbers in a pattern that starts with 3, where you double and add 1 to get the next number; the next three numbers are 7, 15, and 31.

Finding Patterns
Function Machines 1 (Functions and Tables)

2.2: The student uses variables, symbols, rational numbers, and simple algebraic expressions in one variable to solve linear equations and inequalities in a variety of situations.

2.2.1: knows and explains that a variable can represent a single quantity that changes, e.g., daily temperature.

Using Algebraic Expressions

2.2.2: knows, explains, and uses equivalent representations for the same simple algebraic expressions, e.g., x + y + 5x is the same as 6x + y.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Expressions

2.2.4: explains the difference between an equation and an expression.

Compound Interest
Solving Equations on the Number Line
Using Algebraic Equations

2.2.5: solves:

2.2.5.a: one-step linear equations in one variable with positive rational coefficients and solutions, e.g., 7x = 28 or x + 3/ = 7 or x/3 = 5;

Solving Algebraic Equations II

2.2.6: explains and uses the equality and inequality symbols (=, not equal to, <, less than or equal to, >, greater than or equal to) and corresponding meanings (is equal to, is not equal to, is less than, is less than or equal to, is greater than, is greater than or equal to) to represent mathematical relationships with rational numbers.

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

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

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

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

2.3.2: finds the values and determines the rule through two operations using a function table (input/output machine, T-table).

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

2.3.3: demonstrates mathematical relationships using ordered pairs in all four quadrants of a coordinate plane.

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

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

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

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
Fraction Garden (Comparing Fractions)
Toy Factory (Set Models of Fractions)

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

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Linear Functions
Linear Inequalities in Two Variables
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Using Algebraic Equations

2.4.1.f: function tables to model numerical and algebraic relationships; - factor trees to find least common multiple and greatest common factor and to model prime factorization;

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

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

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) to model perimeter, area, volume, and surface area, and properties of two- and three-dimensional; - function tables to model numerical and algebraic relationships;

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.i: geometric models (spinners, targets, or number cubes), process models (coins, pictures, or diagrams), and tree diagrams to model probability; - coordinate planes to model relationships between ordered pairs and linear equations;

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

2.4.1.j: frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single stem-and-leaf plots, scatter plots, and box-and-whisker plots to organize and display data; - two- and three-dimensional geometric models (geoboards, dot paper, nets or solids) to model perimeter, area, volume, and surface area, and properties of two- and three-dimensional;

Box-and-Whisker Plots
Compound Inequalities
Correlation
Describing Data Using Statistics
Distance-Time Graphs
Elevator Operator (Line Graphs)
Graphing Skills
Histograms
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (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
Similar Figures
Special Parallelograms

3.1.3: identifies angle and side properties of triangles and quadrilaterals:

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

Isosceles and Equilateral Triangles
Polygon Angle Sum
Triangle Angle Sum

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

Polygon Angle Sum

3.1.3.c: parallelograms have opposite sides that are parallel and congruent;

Classifying Quadrilaterals
Special Parallelograms

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

Classifying Quadrilaterals
Perimeter and Area of Rectangles
Special Parallelograms

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

Classifying Quadrilaterals
Special Parallelograms

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

Classifying Quadrilaterals
Perimeter and Area of Rectangles
Special Parallelograms

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

Classifying Quadrilaterals

3.1.4: identifies and describes:

3.1.4.a: the altitude and base of a rectangular prism and triangular prism,

Surface and Lateral Areas of Prisms and Cylinders

3.1.5: identifies corresponding parts of similar and congruent triangles and quadrilaterals.

Special Parallelograms

3.1.10: describes the relationship between the diameter and the circumference of a circle.

Circumference and Area of Circles

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

3.2.1: determines and uses rational number approximations (estimations) for length, width, weight, volume, temperature, time, perimeter, and area using standard and nonstandard units of measure.

Fido's Flower Bed (Perimeter and Area)

3.2.2: selects and uses measurement tools, units of measure, and level of precision appropriate for a given situation to find accurate rational number representations for length, weight, volume, temperature, time, perimeter, area, and angle measurements.

Area of Triangles
Beam to Moon (Ratios and Proportions)
Fido's Flower Bed (Perimeter and Area)
Measuring Trees

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

Unit Conversions

3.2.4: knows and uses perimeter and area formulas for circles, squares, rectangles, triangles, and parallelograms;

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

3.2.5: finds perimeter and area of two-dimensional composite figures of circles, squares, rectangles, and triangles;

Fido's Flower Bed (Perimeter and Area)

3.2.7: finds surface area of rectangular prisms using concrete objects;

3.2.7.b: volume of rectangular prisms.

Prisms and Cylinders
Pyramids and Cones

3.2.8: uses appropriate units to describe rate as a unit of measure, e.g., miles per hour.

Household Energy Usage

3.2.9: finds missing angle measurements in triangles and quadrilaterals.

Classifying Quadrilaterals
Concurrent Lines, Medians, and Altitudes
Polygon Angle Sum
Similarity in Right Triangles
Triangle Angle Sum

3.3: The student recognizes and performs transformations on two- and three- dimensional 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

3.4: The student relates geometric concepts to a number line and a coordinate plane in a variety of situations.

3.4.1: finds the distance between the points on a number line by computing the absolute value of their difference.

Rational Numbers, Opposites, and Absolute Values

3.4.2: uses all four quadrants of a coordinate plane to:

3.4.2.a: identify in which quadrant or on which axis a point lies when given the coordinates of a point,

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

3.4.2.b: plot points,

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Point-Slope Form of a Line
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

3.4.2.c: identify points,

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Point-Slope Form of a Line
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

3.4.2.d: list through five ordered pairs of a given line.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points, Lines, and Equations
Slope

3.4.3: uses a given linear equation with whole number coefficients and constants and a whole number solution to find the ordered pairs, organize the ordered pairs using a T-table, and plot the ordered pairs on the 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: finds the probability of a compound event composed of two independent events in an experiment or simulation.

Independent and Dependent Events
Theoretical and Experimental Probability

4.1.2: explains and gives examples of simple or compound events in an experiment or simulation having probability of zero or one.

Independent and Dependent Events

4.1.3: uses a fraction, decimal, and percent to represent the probability of:

4.1.3.a: a simple event in an experiment or simulation;

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

4.1.3.b: a compound event composed of two independent events in an experiment or simulation.

Independent and Dependent Events
Theoretical and Experimental Probability

4.1.4: finds the probability of a simple event in an experiment or simulation using geometric models, e.g., Using spinners or dartboards, what is the probability of landing on 2? The answer is ¼,.25, or 25%.

Probability Simulations
Theoretical and Experimental Probability

4.2: The student collects, organizes, displays, and explains numerical (rational numbers) and non-numerical data sets in a variety of situations with a special emphasis on measures of central tendency.

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;

Elevator Operator (Line Graphs)
Graphing Skills
Reaction Time 1 (Graphs and Statistics)

4.2.1.d: charts and tables;

Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

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

Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

4.2.1.f: scatter plots;

Correlation
Graphing Skills
Solving Using Trend Lines
Trends in Scatter Plots

4.2.1.g: box-and-whiskers plots.

Box-and-Whisker Plots
Reaction Time 2 (Graphs and Statistics)

4.2.2: selects and justifies the choice of data collection techniques (observations, surveys, or interviews) and sampling techniques (random sampling, samples of convenience, or purposeful sampling) in a given situation.

Populations and Samples
Reaction Time 2 (Graphs and Statistics)

4.2.3: conducts experiments with sampling and describes the results.

Polling: City

4.2.5: identifies and determines the range and the quartiles of a rational number data set.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

4.2.6: identifies potential outliers within a set of data by inspection rather than formal calculation, e.g., consider the data set (1, 100, 101, 120, 140, 170); the outlier is 1.

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