Why U

Material for mathematics courses on the K-12 and college levels

by AMMA · Published 31 de Março de 2015 · Updated 12 de Junho de 2023

Why U animated videos are designed as collateral material for mathematics courses on the K-12 and college levels, and as a resource for informal independent study. Rather than focusing on procedural problem solving, the objective is to give insight into the concepts on which the rules of mathematics are based.

Why U creators are currently working on the series of animated lectures entitled “Algebra”. This series examines the concepts on which Algebra, as well as higher mathematics, is based. The goal of these lectures is to explore these fundamental concepts more precisely and in greater depth than is currently possible in most high-school and college-level algebra courses.

Why U is funded by the Goldman Charitable Foundation in partnership with the University of Central Florida. Your comments, ideas, and contributions are appreciated. Thank you for helping us to continue this important work.

Fonte: https://www.whyu.org/

Pre-Algebra

Pre-Algebra

Pre-Algebra 3 - Decimal, Binary, Octal & Hexadecimal

Our modern decimal number system is base-10. Other number systems used in fields like computer engineering are base-2 (binary), base-8 (octal) and base-16 (hexadecimal). NOTE: The latest version of this video can be viewed on YouTube at https://youtu.be/CVcAz6LnTGE . That revision corrects a mistake at 8:42 where the number 1,000,000 was incorrectly converted to binary.

Autor: MyWhyU

Publicado: September 13, 2011, 7:06 pm

Pre-Algebra 14 - Creating Common Denominators

Addition and subtraction of fractions with different denominators requires creating a "common" denominator. Using the number line, this mysterious process can be easily visualized.

Autor: MyWhyU

Publicado: July 29, 2011, 9:21 pm

Pre-Algebra 15 - Least Common Denominators

Sometimes when finding a common denominator we create an unnecessarily large common denominator. This chapter explains how to find the smallest possible common denominator.

Autor: MyWhyU

Publicado: July 29, 2011, 9:17 pm

Pre-Algebra 13 - Reciprocals and Division with Fractions

When working with fractions, division can be converted to multiplication by the divisor's reciprocal. This chapter explains why.

Autor: MyWhyU

Publicado: July 29, 2011, 9:16 pm

Pre-Algebra 11 - Fractions and Rational Numbers

The first fractions used by ancient civilizations were "unit fractions". Later, numerators other than one were added, creating "vulgar fractions" which became our modern fractions. Together, fractions and integers form the "rational numbers".

Autor: MyWhyU

Publicado: July 29, 2011, 9:12 pm

Pre-Algebra 12 - Arithmetic Operations with Fractions

Arithmetic operations with fractions can be visualized using the number line. This chapter starts by adding fractions with the same denominators and explains the logic behind multiplication of fractions.

Autor: MyWhyU

Publicado: July 29, 2011, 9:09 pm

Pre-Algebra 9 - Division and Prime Numbers

The building blocks of all natural numbers are the prime numbers. The early Greeks invented the system still used today for separating natural numbers into prime and composite numbers.

Autor: MyWhyU

Publicado: July 29, 2011, 9:04 pm

Pre-Algebra 10 - Factoring

Any natural number can be decomposed into a product of prime factors. Prime factorization is fundamental to many arithmetic operations involving fractions.

Autor: MyWhyU

Publicado: July 29, 2011, 9:03 pm

Pre-Algebra 8 - Multiplying Negative Numbers

When number systems were expanded to include negative numbers, rules had to be formulated so that multiplication would be consistent regardless of the sign of the operands.

Autor: MyWhyU

Publicado: July 29, 2011, 8:59 pm

Pre-Algebra 6 - Commutative Property of Multiplication

The commutative property is common to the operations of both addition and multiplication and is an important property of many mathematical systems.

Autor: MyWhyU

Publicado: July 29, 2011, 8:56 pm

Pre-Algebra 7 - Associative & Distributive Properties of Multiplication

A look at the logic behind the associative and distributive properties of multiplication.

Autor: MyWhyU

Publicado: July 29, 2011, 8:53 pm

Pre-Algebra 5 - Commutative & Associative Properties of Addition

A look behind the fundamental properties of the most basic arithmetic operation, addition.

Autor: MyWhyU

Publicado: July 29, 2011, 5:49 pm

Pre-Algebra 4 - Whole Numbers, Integers, and the Number Line

Number systems evolved from the natural "counting" numbers, to whole numbers (with the addition of zero), to integers (with the addition of negative numbers), and beyond. These number systems are easily understood using the number line.

Autor: MyWhyU

Publicado: July 29, 2011, 5:46 pm

Pre-Algebra 2 - Roman Numerals: Sign-Value vs Positional Notation

Roman numerals are an ancient base-10 natural number system. Understanding Roman numerals (a sign-value notation) can shed light on our modern number system which uses positional notation. NOTE: Please see corrected revision: https://youtu.be/bqD2wDCiBv0

Autor: MyWhyU

Publicado: July 29, 2011, 3:54 pm

Pre-Algebra 1 - The Dawn of Numbers

A humorous look at early attempts at creating number systems, leading up to our modern base-10 decimal number system which uses "positional notation". The story takes place on the fictitious island of Cocoloco.

Autor: MyWhyU

Publicado: July 29, 2011, 3:49 pm

Algebra

Algebra

Algebra 99 Changing the Base of a Logarithm

Although the base of a logarithmic function can be any positive real number other than "one", the base values most commonly used for logarithms are base ten - otherwise known as the “common logarithm” and “base e” - the “natural logarithm”. Scientific calculators can typically calculate logarithms with a base of ten or e. However, we may want to find the log of that same number with a base other than ten or e. In that case, we can use what is called the "change of base" formula which can calculate the log of a number for any arbitrary base. In this lecture, we will see how to use this formula, to convert the base of any logarithm to any other base.

Autor: MyWhyU

Publicado: April 16, 2026, 9:30 pm

Algebra 97 - Introduction to Logarithmic Functions

Logarithmic functions are the inverse of exponential functions. Exponential and logarithmic functions both involve the same three quantities. The difference between an exponential function and a logarithmic function is which two quantities are given and which quantity must be determined. In an exponential function, the base and its exponent are given quantities and the resulting value must be calculated. On the other hand, in a logarithmic function, the base and resulting value are given quantities and the exponent that produced that value must be determined. Logarithmic scales are commonly used in many fields since they allow numerical data to be displayed over a very wide range of values in a compact way. Some examples of logarithmic scales are the decibel scale used as a measurement of signal or sound amplitude and the pH scale used in chemistry to measure the acidity of aqueous solutions.

Autor: MyWhyU

Publicado: March 4, 2025, 11:21 pm

Algebra 13 - Domain and Range of Binary Relations

Two sets which are of primary interest when studying binary relations are the domain and range of the relation.

Autor: MyWhyU

Publicado: January 30, 2013, 10:33 pm

Algebra 12 - Binary Relations

Fundamental to Algebra is the concept of a binary relation. This concept is closely related to the concept of a function.

Autor: MyWhyU

Publicado: January 25, 2013, 1:34 am

Algebra 11 - Cartesian Coordinates in Three Dimensions

Just as the Cartesian plane allows sets of ordered pairs to be graphically displayed as 2-dimensional objects, Cartesian space allows us to visualize sets of ordered triples in three dimensions.

Autor: MyWhyU

Publicado: January 25, 2013, 1:33 am

Algebra 10 - The Cartesian Coordinate System

The Cartesian coordinate system, formed from the Cartesian product of the real number line with itself, allows algebraic equations to be visualized as geometric shapes in two or three dimensions.

Autor: MyWhyU

Publicado: January 25, 2013, 1:33 am

Algebra 9 - Cartesian Products, Ordered Pairs and Triples

Cartesian products can create sets of ordered pairs which correspond to points in 2-dimensional space, or ordered triples which correspond to points in 3-dimensional space. These sets form the logical foundation of the Cartesian coordinate system.

Autor: MyWhyU

Publicado: January 25, 2013, 1:33 am

Algebra 8 - Unions of Intervals

Interval notation is often the simplest way to describe sets of real numbers as regions on the number line. Some sets which cannot be represented by a single interval can be written in interval notation as the union of two or more intervals.

Autor: MyWhyU

Publicado: August 17, 2012, 7:33 am

Algebra 7 - Bounded versus Unbounded Intervals

Bounded intervals may be either open or closed. Closed intervals contain a maximum and minimum number, but why is it impossible to find the maximum or minimum number in an open interval?

Autor: MyWhyU

Publicado: July 25, 2012, 5:00 am

Algebra 6 - Interval Notation and the Number Line

Although Venn diagrams are a useful way to visualize sets whose elements can be any type of object, interval notation and the number line are best suited for describing sets of real numbers used in Algebra.

Autor: MyWhyU

Publicado: June 29, 2012, 6:26 am

Algebra 5 - Symmetric Difference

The symmetric difference of two sets is the collection of elements which are members of either set but not both - in other words, the union of the sets excluding their intersection. Forming the symmetric difference of two sets is simple, but forming the symmetric difference of three sets is a bit trickier.

Autor: MyWhyU

Publicado: June 20, 2012, 6:44 am

Algebra 4 - Complement and Relative Complement

The complement of a set is the collection of all elements which are not members of that set. Although this operation appears to be straightforward, the way we define "all elements" can significantly change the results.

Autor: MyWhyU

Publicado: June 7, 2012, 7:30 am

Algebra 3 - Venn Diagrams, Unions, and Intersections

Venn diagrams are an important tool allowing relations between sets to be visualized graphically. This chapter introduces the use of Venn diagrams to visualize intersections and unions of sets, as well as subsets and supersets.

Autor: MyWhyU

Publicado: May 3, 2012, 4:31 pm

Algebra 2 - Set Equality and Subsets

Sets can be related to each other in different ways. This chapter describes the set relations of equality, subset, superset, proper subset, and proper superset.

Autor: MyWhyU

Publicado: April 27, 2012, 2:57 pm

Algebra 1 - Defining Sets

One of the most fundamental concepts in Algebra is the concept of a set. This video introduces the concept of a set and various methods for defining sets.

Autor: MyWhyU

Publicado: March 9, 2012, 7:05 pm

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