One of the main reasons that traditional long division is so hard to learn is that a correct answer depends on a memorized series of steps – divide, multiply, subtract, bring down. If a student forgets which step to do and when to do it, there is a very high chance that he will end up with an incorrect answer.

This is why it is ESSENTIAL to teach strategies, rather than steps.

Strategies encourage REAL UNDERSTANDING. This is such an important part of math. We want our students to really understand what they are doing, and to know that there are different ways to come up with a correct answer.

In this article, I’ll discuss three different alternatives to traditional long division. I encourage you to focus on the first two, as they are very mental math focused.

Ready to get serious about teaching multi-digit division? Check out the Long Division Station HERE.

The Box/Area Method

The Box Method or Area Model is a mental math based approach that will enhance number sense understanding. If you plan on teaching the Partial Quotients strategy (which I will discuss next), this is an excellent way to introduce it.

Students solve the equation by subtracting multiples until they get down to 0, or as close to 0 as possible. For example, in the example below we took out 100 groups of 3, then 50 groups of 3, and then 1 more group of 3 to make a total of 151 groups of 3 taken out of the dividend. Please head over to THIS POST for a very detailed explanation of this strategy, complete with pictures.

Partial Quotients

Partial Quotients is a “must-teach” strategy for multi-digit division. If you teach the Box/Area Method first, this is a very natural progression.

When we use the partial quotients strategy, we set up the equation similarly to how a traditional long division equation is set up. The difference here is that we take out multiples of the divisor until we get down to 0, or as close to 0 as we can. Please see THIS POST for a very detailed explanation of this strategy, complete with lots of pictures.

The Grid Method

The Grid method is NOT a mental math based approach. This means that if you have students who are struggling with multi-digit division, you should focus on the previous two strategies that I described rather than moving on to this one. The Grid Method can be used for students who are ready for a challenge, or as an introduction if you plan on teaching traditional long division. Some students will find the grid very helpful in organizing their thinking.

When we use the grid method we just organize the digits from the equation into a grid. For a complete, detailed explanation of how to perform the grid method, along with lots of pictures, please see THIS BLOG POST.

NEXT STEPS:

• Use Long Division Task Cards in your classroom to reinforce the strategies in isolation. Find the bundle HERE.
• Incorporate the self-paced, student-centered Long Division Station into your classroom to ensure that every student is working to his/her full potential.
• Read more about The Box Method, the Partial Quotients Method, and the Grid Method to develop a teaching plan.

The post Effective Alternatives for Long Division appeared first on Shelley Gray.

Long division is often considered one of the most challenging topics to teach. Luckily, there are strategies that we can teach to make multi-digit division easier to understand and perform.

The Grid method is one of these strategies.

The Grid Method is intended for those who plan to teach traditional long division. It follows the same steps as traditional long division, but uses a different method of organization. This makes traditional long division easier for some students.

The Grid Method is not a mental math based approach. If you are looking for a mental math approach to long division, be sure to check out my posts for the Box/Area Method and Partial Quotients. 

Let’s learn how to perform the Grid Method for long division!

Below, I have included both a video tutorial and step-by-step instructions.

VIDEO TUTORIAL:

STEP-BY-STEP INSTRUCTIONS

Suppose that we want to solve the equation 324÷2.

STEP 1:
First we draw a grid. The number of sections in the grid depends on the number of digits in our dividend. For this equation, our grid will have 3 sections. We write the digits from 324 inside the grid, and we write our divisor (2) on the left side.

STEP 2:
Now we ask ourselves, “How many times can 2 go into 3?” The answer is 1, so we write a 1 on top of the grid. We now multiply 1×2 to make 2, and take that 2 away from the 3. This leaves us with 1.

STEP 3:
Now we bring that 1 over to the tens place of the next section on the grid. This gives us a 12 in the next section.

Now we ask ourselves, “How many times does 2 go into 12?” The answer is 6, so we write a 6 on top of the grid. Now we multiply 6×2 to make 12, and take that 12 away from 12. This leaves us with 0.

STEP 4:
We carry that 0 over to the tens place of the next section on the grid. This doesn’t affect that number, so we still have 4 in the next section.

Now we ask ourselves, “How many times does 2 go into 4?” It goes 2 times, so we write a 2 on top of our grid. Now we multiply 2×2 to make 4, and take that 4 away from the 4. We are left with 0, which means that we have no remainder.

To find the final quotient, we simply list the digits from the top of the grid: 1, 6, 2. So 324÷2=162.

LET’S TRY ANOTHER EXAMPLE

This time we will try an example that has a remainder. It also has more digits that our last example. Notice that when we have more digits in our dividend, we simply extend our grid. Let’s solve 6542÷5.

Here are the steps that we followed to solve this equation:

• Section 1: First we knew that 5 goes into 6 one time, so we wrote a 1 on top. We multiplied 1×5 to make 5, and took that 5 away from the 6, leaving us with a 1. We carried that 1 over to the tens place of the next section. Now we have 15 in that section.
• Section 2: We know that 5 goes into 15 three times, so we wrote a 3 on top. We multiplied 3×5 to make 15 and took that 15 away from the 15, leaving us with 0. We carried that 0 over to the tens place of the next section.
• Section 3: 5 does not go into 4, so we write a 0 on top, multiply 0x5 to make 0, and take that 0 away from the 4. This leaves us with 4. We carry that 4 over to the tens place of the next section, giving us 42 in the final section.
• Section 4: 5 goes into 42 eight times, so we write an 8 on top of the grid. We multiply 8×5 to give us 40, and take that 40 away from the 42, leaving us with 2. This means that our remainder is 2.
• To find our final quotient, we list the numbers from the top of the grid: 1, 3, 0, 8, and then add our remainder of 2. So 6542÷5=1308 R2.

NEXT STEPS:

I would love to help you teach the grid method and other division concepts in your classroom. You may find the following resources helpful:

GRID METHOD TASK CARDS

These task cards give students the opportunity to practice the grid method for long division in a variety of different ways. Students will calculate quotients, solve division problems, figure out missing dividends and divisors, think about how to efficiently solve an equation using the grid method, and more. See the Grid Method Task Cards HERE or the Big Bundle of Long Division Task Cards HERE.

THE LONG DIVISION STATION

The Long Division Station is a self-paced, student-centered math station for long division. Students gradually learn a variety of strategies for long division, the grid method being one of them. One of the greatest advantages to this Math Station is that is allows you to target every student and their unique abilities so that everyone is appropriately challenged. See The Long Division Station HERE.

OR SEE ALL RESOURCES HERE.

The post The Grid Method for Long Division appeared first on Shelley Gray.

Long division is often considered one of the most challenging topics to teach. Luckily, there are strategies that we can teach to make multi-digit division easier to understand and perform.

The Partial Quotients method is one of these strategies. It is a mental math based approach that will enhance number sense understanding. Students solve the equation by subtracting multiples until they get down to 0, or as close to 0 as possible.

If you would like to try this strategy in your classroom, you may want to start with the Box Method/Area Model, which you can read more about HERE. The Box Method uses the same approach as Partial Quotients, but is organized differently and works well as an introduction.

Let’s learn how to perform the Partial Quotients strategy for long division!

Below, I have included both a video tutorial and step-by-step instructions.

VIDEO TUTORIAL

STEP-BY-STEP INSTRUCTIONS

Suppose that we want to solve the equation 324÷2.

STEP 1:
Write the equation as shown below.

STEP 2:
Now it is time to start figuring out how many groups of 2 will fit into 324. We want to use numbers that are easy to work with, so we try to use friendly numbers like 10, 100, etc. We know that at least 100 groups of 2 fit into 324, so let’s start with that. We write x100 on the right side to symbolize that we are taking out 100 groups. 100 groups of 2 makes 200, so we subtract 200 from 324. This leaves us with 124.

STEP 3:
Now we need to figure out how many more groups of 2 we can make from 124. We know that we can make at least 50 more groups. We write x50 on the right side to symbolize the 50 groups of 2. 50 groups of 2 makes 100, so we take 100 away from 124 and we are left with 24.

STEP 4:
How many more groups of 2 can we make from 24? We know that we can make 12 more groups, so we write x12 on the right side. 12 groups of 2 makes 24, so we take away 24. We are left with 0, which means that we do not have a remainder.

STEP 4:
To find our quotient, we add up the three partial quotients. In this case, we add 100+50+12 to make 162. So 324÷2=162.

Here’s one more example. Let’s solve 679÷5:

We know that there are at least 100 groups of 5 in 679, so we wrote x100. We then subtract 100 groups of 5, or 500, from the 679, and we are left with 179.

We know that there are at least 30 more groups of 5 in 179. 30 groups of 5 makes 150, so we subtract 150 from 179 and are left with 29.

We know that there are at least 5 more groups of 5 in 29. 5 groups of 5 makes 25, so we subtract 25 from 29 and are left with 4.

We cannot make any more groups of 5 out of 4, so 4 is our remainder.

To find our quotient, we add the partial quotients (100+30+5) plus the remainder 4, to make 135 R4.

HELPFUL RESOURCES FOR THE PARTIAL QUOTIENTS STRATEGY FOR DIVISION

I would love to help you teach the partial quotients strategy for long division in your classroom. You may find the following resources helpful:

PARTIAL QUOTIENTS TASK CARDS

These task cards give students the opportunity to practice the partial quotients strategy for long division in a variety of different ways. Students will calculate quotients, solve division problems, figure out missing dividends and divisors, think about how to efficiently solve an equation using the partial quotients strategy, and more. See the Partial Quotients Task Cards HERE or the Big Bundle of Long Division Task Cards HERE.

THE LONG DIVISION STATION

The Long Division Station is a self-paced, student-centered math station for long division. Students gradually learn a variety of strategies for long division, the partial quotients strategy being one of them. One of the greatest advantages to this Math Station is that is allows you to target every student and their unique abilities so that everyone is appropriately challenged. See The Long Division Station HERE.

OR SEE ALL RESOURCES HERE.

The post Partial Quotients: an alternative for traditional long division appeared first on Shelley Gray.

Do you dread teaching long multiplication and division every year? Are you frustrated by the fact that very few of your students actually GET it?  What if you could teach your students strategies that would BOOST their conceptual understanding, as well as make multi-digit multiplication and division FUN to learn? Is that possible? Absolutely. Through a practical, strategic approach, we have the power to make a big impact on the success that our students experience with these operations.

Who is this mini course for?

• 4th-6th grade teachers teaching multi-digit multiplication and division
• 3rd grade teachers who have some students far above grade level and who need an extra challenge
• math intervention teachers
• parents who are interested in helping their child with multi-digit multiplication and division

Content

• “Old Math” vs “New Math” – MYTH BUSTED!
• The essential strategies that need to be taught BEFORE traditional methods for long multiplication and division
• A variety of approaches and which students should be using each one
• Q&A session
• Free resources for all attendees

See the full mini course schedule and get registered HERE.

Or read more about effective strategies for multi-digit multiplication HERE.

Can’t wait to connect with you,

Shelley

The post FREE MINI COURSE: Teaching Multi-Digit Multiplication and Division for REAL Understanding appeared first on Shelley Gray.