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 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.

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Sorry, this mini course is no longer available. However, I have a wealth of information on my website about teaching the basic multiplication facts. Start HERE with effective strategies for basic multiplication.

The post Free Mini Course: Basic Multiplication and Division – Mastery for ALL Students appeared first on Shelley Gray.

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I am a HUGE fan of using games to teach and reinforce math concepts. One of the biggest misconceptions that I hear is that math is boring. With the addition of math games into the regular classroom routine, math can be engaging, exciting, and fun.

With a simple deck of cards and a few dice, you can play many different kinds of games to reinforce many different topics. In the past I’ve even given students a few dice or a deck of cards and had them make up their own math game!

A few ways that you can use dice/cards quickly and easily in the classroom to reinforce basic math facts include:

• Have students roll two dice and add them up to make a sum (alternatively subtract to make a difference, or multiply to make a product). This is SO much more fun that simply completing a worksheet for basic facts, and can be done with no preparation. I like to have 20-sided dice on hand for higher level equations.
  • Here’s a little freebie that provides a graph that students can use during a roll and add activity.
• Practice Doubles facts with dice and have students graph their progress. I wrote a blog post about this activity HERE.
• Salute is a fantastic game that can be played with three people and a deck of cards. My students could never get enough of this game! Read more about it HERE.

When should Math games be used in the classroom?

I prefer to use games as reinforcement. For example, you could teach a mini-lesson, allow some guided and independent practice, and then have students play a game to reinforce their new learning. I also like to use Math games as a center. Students can play in pairs or groups of three. In this case, the game is always one that they have played before (because of the independent nature of centers).

Basic facts are an ideal skill to practice during math games, because it’s a way to reinforce those facts all year long, even while you are focusing on other concepts in your classroom.

Other Resources

All of my Math Stations and Mental Math Strategy Units also contain math games that are sure to engage even your most un-motivated students! Please click on the hyperlinks below to access these resources:

Math Stations

• Click here to access all self-paced, student-centered Math Stations for addition, subtraction, multiplication, division, and fractions.

Mental Math Strategy Units

• Mental Math Strategy Units: the Complete Addition Collection
• Mental Math Strategy Units: the Complete Subtraction Collection

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