Art of Problem Solving
Dividing a Sum by a Number
Divide with sums. A video provides an explanation on whether it is possible to divide a sum by a number and a number by a sum by using the distributive property. Scholars see which procedure holds up under the rules of arithmetic and...
Art of Problem Solving
Subtraction and the Distributive Property
There's got to be a better way. Scholars learn that the distributive property does work with subtraction and not just addition. Using that fact, the video shows how to find the product of two numbers by rewriting a complicated number as...
Art of Problem Solving
Subtraction Problems
Subtraction does not work with the commutative property ... or does it? Confronted with a difficult problem, the narrator realizes that by writing the subtractions as adding a negative, he can rearrange the problem. Pupils learn that as...
Art of Problem Solving
Introduction to Division
Use reciprocals for the purpose of division. The video shows how to use reciprocals to rewrite division problems. Pupils see that the definition of division as the multiplication by the reciprocal works for all types of numbers.
Art of Problem Solving
What's a Reciprocal?
If there is something in addition to get to the identity, does the same exist for multiplication? Using negative numbers to talk about the identity of addition, the video asks the question whether something similar exists for...
Art of Problem Solving
Subtraction with Negatives Part 2
Dive deeper into subtraction. The presenter shows two more ways to use the definition of subtraction to solve subtraction problems. Using the distributive and commutative properties, pupils learn how to solve problems such as subtracting...
Art of Problem Solving
Subtraction with Negatives Part 1
What is the definition of subtraction when dealing with negatives? The short video provides the definition of subtraction. Scholars observe as the presenter applies the definition to examples with negative numbers.
Art of Problem Solving
Commutative Property of Addition
For a change, order does not matter. A short video provides a definition of the commutative property of addition. Pupils develop an understanding that—unlike some operations—order does not matter for addition problems.
Art of Problem Solving
Why Do People Say that Repeated Addition is Multiplication?
Is a repeated addition definition mathematically valid? Using mathematical properties, a video explains why, even though there is a connection between repeated addition and multiplication, it is not a good definition. The properties hold...
Art of Problem Solving
Associative Property of Addition
Groupings are the way to go! The short video provides a description of the associative property of addition and gives an example. Learners view how to write the property using variables.
Art of Problem Solving
Distributive Property
Here is a video that makes individuals feel comfortable with working with the distributive property.
Art of Problem Solving
Sum the Numbers from 1 to 100
When Gauss's teacher asked the class to find the sum of the numbers from 1 to 100, he quickly realized a relationship and discovered a formula that made finding the answer easy. Share this video with young mathematicians after...
Art of Problem Solving
Art of Problem Solving: Commutative Property of Addition
Video tutorial uses examples to explore the Commutative Property of addition. [2:03]
Art of Problem Solving
Art of Problem Solving: Distributive Property
Video tutorial uses examples to reinforce understanding of the Distributive Property. [4:30]
Art of Problem Solving
Art of Problem Solving: Associative Property of Addition
Video tutorial uses examples to reinforce understanding of the Associative Property of addition. [3:09]
Art of Problem Solving
Art of Problem Solving: Introduction to Circles
Video tutorial uses examples to introduce circles. [6:39]
Art of Problem Solving
Art of Problem Solving: Negative Exponents Introduction
Video tutorial uses examples to introduce negative exponents. [5:18]
Art of Problem Solving
Art of Problem Solving: Introduction to Division
Video tutorial uses examples to introduce division. [7:06]
Art of Problem Solving
Art of Problem Solving: What's a Reciprocal?
Video tutorial uses examples to reinforce understanding of how to find a reciprocal. [7:12]
Art of Problem Solving
Art of Problem Solving: Sum the Numbers From 1 to 100
Video tutorial uses examples to reinforce understanding of how to find the sum of the numbers from 1 to 100. [2:48]
Art of Problem Solving
Art of Problem Solving: Mixed Number Subtraction
Video tutorial uses examples to reinforce understanding of how to subtract mixed numbers. [6:39]
Art of Problem Solving
Art of Problem Solving: Fraction Division
Video tutorial uses examples to reinforce understanding of how to divide fractions. [4:24]
Art of Problem Solving
Art of Problem Solving: Mixed Number Multiplication and Division
Video tutorial uses examples to reinforce understanding of how to multiply and divide mixed numbers. [6:07]
Art of Problem Solving
Art of Problem Solving: Mixed Number Addition
Video tutorial uses examples to reinforce understanding of how to add mixed numbers. [4:03]