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!
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!
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.
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