Let's take a look at the common core standards for long division
CCSS.Math.Content.4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
CCSS.Math.Content.5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
CCSS.Math.Content.6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm
There seems to be a lot about alternative strategies and using what kids know about place value and the relationship between multiplication and division to develop long division ideas. We have been committed to this idea in my school for the last 5-6 years. It has really helped kids understand division and be much better at estimating an answer and knowing when an answer is unreasonable. It took a lot of convincing but all the teachers in my school have now agreed that we do not teach the standard algorithm for long division until grade 6. Now the common core supports this as well.
So now in our school we start talking about partial quotients in grade 4. We use rectangular arrays and area models to support the development of this model and we get kids to a pretty good place by the end of grade 4. The best part is that kids can use numbers that are friendly and fluent to them to solve these problems.
So here is some evidence of this strategy at work from today's fourth grade math class. We got a new student last week who has no concept of division or any strategies for long division so when I do a booster group with them next week, I will post more ideas about how to develop the partial quotients using arrays and area models. But for now, here are the different ways kids used partial quotients to solve this problem.
|This student took more steps than any other student in the class. They did 5 partial quotients but used numbers that were very friendly known facts.|
|This is by far the most popular was this problem was solved today. Can you see how it leads right into the traditional algorithm?|
|Another very efficient strategy|
|This student used 4 partial quotients to solve the problem|