Understanding Algorithms

When looking at a new concept or operation for the first time, many students (and parents) become overwhelmed, especially when dealing with 3 or 4 digit numbers! Luckily, there are methods or algorithms designed to make solving these seemingly difficult problems much easier. When explained and modeled the right way, it can change a student's perspective on math! It will help save students a great deal of time and frustration.

Partial Sums is a method designed to teach addition of multi-digit numbers. At first, it might seem more confusing for you than traditional methods for addition, but once you get the hang of it, you will have that "ah-ha" moment! When we use partial sums to add, we are simply breaking down the numbers into parts based on their place value. For example, if we look at the number 45, we are simply breaking it down into two parts : 4(which is in the tens place) and 5(which is in the ones place). We would start by adding the tens column numbers together(the highest place value in the equation) and then the ones. So, when we add two numbers together, such as 45 + 36, it will look like this:

Jump Back Subtraction uses a number line for students to visualize the difference between two numbers. It is particularly helpful when teaching students subtraction because it begins with the larger number and works backward, using addition to find the difference. It begins at the same point on the number line as the problem reads, so for example if you are given 87-34= , you would start at the end of the number line (on 87) and "jump back" to the number 34. As you are moving back on the number line, you count each point until you reach 34, and add them up. Since this algorithm is done for the purpose of visualization, here is an example you may understand better:

Partial Products is similar to the partial sums method, which is used in addition. It is a place value model for multiplication, which is helpful for students to use when understanding multi-digit numbers. Each number is separated into different parts according to their place value. If we look at a problem like 82x3, we know that 8 is in the tens place, and 2 and 3 are in the ones place. A helpful way to teach this method to students is similar to the partial sums method, where we highlight each digit's place value first. When multiplying a 2-digit number by a 1-digit number, we can write out the equation like this:

We break the number 82 down and multiply the tens place (80) by 3, and then the ones place (2) by 3. Finally, these products are added together to make 246.

Partial Quotients looks a lot like long division, however it uses "friendly numbers" to help students. The purpose of using partial quotients is to use mental math in order to solve the problem more quickly. When dividing two numbers with the partial quotients method, you are also using multiplication to help solve the problem. This is a good strategy to use to reinforce multiplication while learning division. In the example below, you can see how we begin with asking how many times 13 can go into 483. Starting with a number like 10 is helpful, since it is easy to multiply by. 13x10 is 130, so we subtract that from 483. Next, we try multiplying 13 by 10 again, and we continue to do so until the number we get is smaller than 130, and then try a smaller number, like 5. We continue this process until we reach the number closest to 13. This method is helpful because it uses multiplication, subtraction, and addition to solve, building upon what students already know. You can see in the model below how we can solve the problem in a row going down.