# Integrated Math Online

Students will build mathematical skills that allow students to solve problems and reason logically. Students will be able to communicate their understanding by organizing, clarifying, and refining mathematical information for a given purpose. Students will use every day and mathematical language and notation in appropriate and efficient forms to clearly express or represent complex ideas and information. Prerequisite: Suggested that students have taken Pre-Algebra or equivalent.

## SEMESTER 1

### Unit 1: Number Sense

Number sense is our understanding of numbers that allows us to approach concepts, ideas and problems concerning numbers based on our backgrounds, experiences, and education. In this unit, students explore many types of numbers and learn to check their answers for reasonableness by using estimation.

- Whole Numbers
- Integers
- Fractions
- Decimals
- Exponents
- Introduction to Square Roots
- Rational Numbers
- Single-Step Estimation

### Unit 2: Operations

Learning to manipulate numbers gives us a more complete understanding of the order of things and allows us to make the best decisions. Students explore operations with the numbers that they studied in Unit 1. They learn to manipulate exponents, the order in which they solve basic calculations, and ratios and percents. They use estimation prior to solving problems and then self-check each problem.

- Operations
- Scientific Notation
- Order of Operations
- Estimation
- Ratio
- Number Sense Problem Solving

### Unit 3: Algebraic Sense

Algebra is a branch of mathematics in which letters are used to represent basic arithmetic relations. As in arithmetic, the basic operations of algebra are addition, subtraction, multiplication, division, and the extraction of roots. Arithmetic, however, cannot generalize such mathematical relations as the Pythagorean theorem, for example, which states that the sum of the squares of the sides of any right triangle is also a square. Arithmetic can produce specific instances of these relations, but algebra can make a purely general statement that fulfills the conditions of the theorem.

- Introduction to Algebraic Expressions
- Number Patterns
- Solving Single-Step Equations
- Solving Two-Step Equations
- Inequalities
- Graphing Equations and Inequalities
- Systems of Two Linear Equations with Two Variables

### Unit 4: Probability

What is a probability? In an event where the outcome is uncertain, such as the roll of a die, the amount of rain that we get tomorrow, or the state of the economy in one month, a probability is a numerical measure of the likelihood of the event. It is a number that we attach to an event, say the event that we'll get over an inch of rain tomorrow, which reflects the likelihood that we will get this much rain.

- Probability
- Theoretical Probability
- Experimental Probability
- Mean, Median, and Mode

## SEMESTER 2

### Unit 5: Geometric Figures

Students explore points, lines, planes, polygons—identifying figures and their characteristics. In a later unit, they will learn how to calculate perimeter and area of some of these figures.

- Points, Lines, and the Plane
- Geometric Figures
- Polygons
- Angles
- Parallel and Perpendicular Lines
- Triangles
- Prisms, Cones and Pyramids

### Unit 6: Geometric Figures

Points, Lines, Planes, Polygons - all of which you will learn about in this unit. We will explore figures and identify their characteristics. In a later unit, you will learn how to calculate perimeter and area of some of these figures.

- Identify collinear and coplanar points and lines.
- Identify various polygons.
- Identify and calculate sums of angles.
- Identify the various types of triangles and use the Pythagorean Theorem.
- Identify the characteristics of and draw prisms and pyramids.

### Unit 7: Geometric Movement

We are constantly measuring movement—the speed at which we drive, the direction that we hike, the angle that a ball is thrown. Movement is constantly changing—changing speed, direction, and angle. If you move all the points on a geometric figure (the "object") according to set rules ("transformation"), you get a new geometric figure (the "image"). Students learn three kinds of transformations: translations, reflections, and rotations.

- The Coordinate Plane
- Transformations
- Geometric Problem Solving

### Unit 8: Measurement

In order to measure accurately, measuring instruments must be carefully constructed and calibrated. However, all measurements have some degree of uncertainty associated with them. Students learn to use formulas, while drawing on previously learned mathematical topics.

- Metric Measurement
- Customary Measurement
- Perimeter
- Area of a Square
- Volume
- Measuring Time

### Unit 9: Probability 2

In the first semester, students studied the basics of probability. In this unit, they study permutations and combinations and how they are relevant to data collection.

- Permutations
- Combinations

Scatter Plots

- Permutations
- Combinations
- Scatter plots