Math is not about memorizing steps and procedures, it’s about developing a conceptual understanding. In division, this is incredibly important!

The traditional method of division, though it “works,” does not accurately represent whether or not a child has mastered the operation of division and frequently ignores the place values of the numbers involved. They might get the right answer by see how many times the number “goes into” another number, subtracting, and then bringing another number down, and repeating the process. However, if one of the steps is off, if the student makes one small arithmetic error, the entire problem can be considered wrong and they have no way of knowing where the problem lies. Most students today can do the correct procedure to solve a math problem, but don’t understand why they’re doing things or what’s going conceptually.

They need number sense! Approaching a division problem in a way other than the traditional method allows the child to use or develop his or her number sense and really understand the parts that go into those numbers.

Check out our Facebook Live broadcast to see these strategies in action using an actual 5th grader!

**Multiplying Up**

When multiplying, we talk about “groups of” a certain number. In this strategy, instead of breaking the dividend into small numbers that ignore their actual value and forcing the divisor into that misrepresented number, we use our knowledge of multiplication to tackle the dividend in its entirety. Start by picking a nice easy number (I recommend one of the decades – 10, 20, 30, etc.). Multiply the number by the divisor and see if there are more or less than that many groups of the divisor within the dividend. Subtract the resulting number from the dividend and see how many more groups of the divisor can be found. Continue until you’ve taken all the groups of the divisor out of the dividend that you can – add up the total number of groups, and you have your answer!

**Partial Quotients**

This strategy is most similar to the traditional method, but with one notable difference: the value of the dividend remains intact and it is treated as a whole number. As the name suggests, the goal here is to approach the problem as a series of small problems until there is no more of the dividend left. At that point, you can add all the partial quotients to get the final quotient and answer to the problem.

Tip: Use the place value discs to help kids develop a conceptual understanding of division! Watch the FB Live video for this process (Shannon demonstrates towards the end)!

Here’s a one-page handout with the division strategies: Division Strategies

Get all the strategies for addition, subtraction, multiplication and division in one document: Three Ways + The Traditional

Peggy Rowe says

I watched your division strategies FB Live video tonight and am so excited to take your strategies into my classroom tomorrow. We are starting multiplication and division in my 3rd grade class this week. Multiplying up builds on so well to their last unit on place value. The partial quotients strategy shows the whole numbers added together so that the students can see the actual place value. I will definitely be using both of these strategies. Thank you so much for your live videos. I attended your Math in the Mountains Workshop last year in Kalispell, Montana and use many of the strategies you taught us!

Strategic Intervention Solutions says

Hi Peggy, Thanks for your comment! You have won our contest for free merchandise from our store! Contact us at shannon@sis4teachers.org to claim your prize!