This page is designed to give you a refresher on various NUMBER OPERATIONS and maybe help teach you some strategies that you didn't already know. These tutorials will help you find a way to solve equations that is BEST for you! Watch the tutorials and try out the different strategies to see which algorithm (method) is the right one for you. Good luck and have fun!
Number Operation Strategies
Addition Strategies
Traditional Addition Algorithm
The Traditional Algorithm is the most commonly taught and used strategy. Here you add starting from the Ones column and moving up a column until you have your final answer.
Click here to watch the tutorial for the Traditional Algorithm.
Partial Sums Algorithm
The Partial Sums Algorithm shows you how to add all the digits in the same place value together, representing them separately, and then adding all those parts together for your final answer.
Click here to watch the tutorial for the Partial Sums Algorithm.
Incremental (Adding On) Algorithm
In the Incremental Algorithm, you start with one addend and add up the other addend in pieces by place value to get to your final answer.
Click here to watch the tutorial for the Incremental Algorithm.
Exploding Dot Algorithm
The Exploding Dot Algorithm is a very visual form of addition. It uses dots to represent each place value. By counting how many dots in each column, moving groups of ten to higher columns when necessary, the visual leads you to your final answer.
Click here to watch the tutorial for the Exploding Dots Algorithm.
Subtraction Strategies
Traditional Subtraction Algorithm
The Traditional Algorithm is the most commonly taught and used strategy. Here you subtract starting from the Ones column and borrowing from the next higher column until you have your final answer.
Click here to watch the tutorial for the Traditional Algorithm.
Remove in Chunks (Incremental) Algorithm
In the Removing in Chunks Algorithm, you take smaller, easier to subtract, "chunks" of your subtrahend (the number you're taking away) until you get to your final answer.
Click here to watch the tutorial for the Remove in Chunks Algorithm.
Adding Up Incremental Algorithm
In the Adding Up Incremental Algorithm, you start at the subtrahend and add up smaller parts until you get to your minuend (the number subtracted from). The number you added up is your difference (final answer).
Click here to watch the tutorial for the Adding Up Incremental Algorithm.
Exploding Dots Algorithm
The Exploding Dots Algorithm is a very visual form of subtraction. It uses dots and antidots to represent each place value for the minuend (dots) and subtrahend (antidots). By cancelling out antidots with solid dots, the visual leads you to your final answer.
Click here to watch the tutorial for the Exploding Dot Algorithm.
Multiplication Strategies
Traditional Multiplication Algorithm
The Traditional Algorithm is a commonly taught and used strategy. Here you multiply factors (the numbers being multiplied together) into parts to find the product (answer to a multiplication question).
Click here to watch the tutorial for the Traditional Multiplication Algorithm.
Partial Products Multiplication Algorithm
The Partial Products Algorithm is a strategy that is based on breaking larger factors into place values and then multiplying each place value by the smaller factor. The products are then added together to find the final product.
Click here to watch the tutorial for the Partial Products Algorithm.
Area Array Model for Multiplication
The Area Array model for multiplication is a visual way to represent partial products and is based on the area meaning of multiplication (length x width).
Click here to watch the tutorial for the Area Array Model for Multiplication.
Exploding Dots for Multiplication
Exploding Dots is a visual way to represent and solve multiplication equations that is based on place value.
Click here to watch the tutorial for Exploding Dots.
Division Strategies
Long Division (Sharing) Algorithm
The Long Division Algorithm is a commonly taught and used strategy. Here you take the dividend (the number you start with) and share it into equal parts using the divisor (the number you are dividing by or sharing the dividend by) to get the quotient (answer to a division question) and record if there are any remainders (leftover Ones pieces).
Click here to watch the tutorial for the Long Division Algorithm.
Partial Quotients Algorithm
The Partial Quotients Algorithm shows how to pull smaller quotients out of the dividend using easier multiplication that you already know and grouping those parts together to make the final quotient.
Click here to watch the tutorial for the Partial Quotients Algorithm.
Decomposition Algorithm
The Decomposition Algorithm is the breaking down of the dividend into "chunks" or parts we already know are divisible (can be shared equally) by the divisor to get the final answer with any leftover parts becoming the remainder.
Click here to watch the tutorial for the Decomposition Algorithm.
Exploding Dot Algorithm
The Exploding Dot Algorithm is a very visual form of division. It uses dots to represent each place value for the dividend. Starting at the largest place value, you make groups of what the divisor is, and any leftover dots "explode" into the lower place value, which you will do the same groupings with until you are in the lowest place value spot. The groupings you made lead to your final quotient and any dots that can't make groups become your remainder.
Click here to watch the tutorial for the Exploding Dots Algorithm.