Step by Step Math Lessons

Our math lessons are designed to make math meaningful to the student. They will guide learners through mathematical concepts, breaking down each step in a clear and understandable manner. They provide a structured approach to learning math, ensuring comprehensive understanding and proficiency. Each math lesson provides in-depth instruction ideal for learners of all ages and abilities. Choose a topic below to start your adventure.

Arithmetic Sequence Formula	Linear Equations
Associative Property	Logic
Circumference and Area of Circles	Mean Absolute Deviation
Commutative Property	Mean Median Mode
Consumer Math	Percentages
Data and Graphs	Perimeter and Area
Decimals – Add and Subtract	Perpendicular Lines
Decimals – Multiply and Divide	Place Values
Decimals – How to Multiply	Point Slope Form
Distributive Property	Pre-Algebra
Elementary Math	Probability
Exponents	Pythagorean Identities
Equations – Solving Single and Double Steps	Pythagorean Theorem
Fractions Introduction	Rate of Change
Fractions and Mixed Numbers – Add and Subtract	Rounding
Fractions and Mixed Numbers – Multiply and Divide	Sets and Set Theory
Fractions – Adding Unlike Denominators	Special Right Triangle
Fractions – Improper Fractions	Volume of a Triangular Pyramid
Integer Properties	Z- Math Palindromes

The Universal Set

In previous lessons, we learned that a set is a group of objects, and that Venn diagrams can be used to illustrate both set relationships and logical relationships. Example 1: Given A = {1, 2, 5, 6} and B = {3, 9}, what is the relationship between these sets? A and B have no elements in common. This relationship is shown in the […]

Lesson on Subsets

Example 1: Given A = {1, 2, 4} and B = {1, 2, 3, 4, 5}, what is the relationship between these sets? We say that A is a subset of B, since every element of A is also in B. This is denoted by: A Venn diagram for the relationship between these sets is shown to the right. Answer: A is a subset of B. Another way to define […]

Venn Diagrams

Until now, we have examined sets using set notation. We know from previous lessons that the following conventions are used with sets: Capital letters are used to denote sets. Lowercase letters are used to denote elements of sets. Curly braces { } denote a list of elements in a set. Another way to look at […]

Equality

Problem 1: Mrs. Glosser asked her class to write the set of primary colors using roster notation. She received two different answers from two different students as shown below. Which student used the correct notation? Student Notation Eduardo X = {red, yellow, blue} Angie Y = {blue, red, yellow} Solution: Both students used the correct notation. The sets from […]

Types of Sets

Learn About Sets With The Following Examples And Interactive Exercises We learned how to write sets using roster notation, as shown in examples 1 and 2 below. Example 1: Let R be the set of all vowels in the English alphabet. Describe this set using roster notation. Solution: R = {a, e, i, o, u} Example 2: Let S be the set of […]

Basic Set Notation

Problem 1: Mrs. Glosser asked Kyesha, Angie and Eduardo to join the new math club. After school they signed up and became members. They wrote about it on the chalkboard using set notation: P = {Kyesha, Angie and Eduardo} When Angie’s mother came to pick her up, she looked at the chalkboard and asked: What does that mean? […]

Introductions to Sets

Set Theory Lesson and Examples: Introductions to Sets Use the following examples and interactive exercises to learn about Introductions to Sets. Example 1: Kyesha was in math class with her friend Angie. She whispered to Angie that she had just bought a set of winter clothes. The outerwear collection includes a coat, a hat, a scarf, […]

Challenge Exercises for Mathematical Logic

Directions: Read each question below. Create a truth table to help you answer each question. The answer choices provided correspond to the last column of the truth table for a given problem. Select your answer by clicking on its button. Feedback to your answer is provided in the RESULTS BOX. If you make a mistake, […]

Practice Exercises for Mathematical Logic

1. p q ~p pq pq pq T T T T T T F F T F F T T F T F F T F F Enter Clear Feedback 2. p q ~q pq (pq)~q T F T F T F F T F T F T F F T F […]

Equivalence

Example 1: Given: ~pq If I don’t study, then I fail. pq I study or I fail. Problem: Determine the truth values of the given statements. Solution: p q ~p ~pq pq T T F T T T F F T T F T T T T F F T F F In the truth […]