Tutorial: Teaching Integer Division in Intuitive Phases


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Sep 14, 2012
This tutorial’s objective defines an intuitive teaching method for integer division. This tutorial defines an Intuitive teaching method for integer division from a very basic division problem to solve any division problems. What are the phases to teaching integer division? Teaching integer division in four phases makes it easier for students to grasp the subject matter. Partition the four phases across grades or combine multiple phases within a single grade depending on the curriculum requirements; it is important to maintain the four distinct phases. First, we need to define a terms dictionary-using example: 7 ÷ 3 = 2 1/3. Dividend: The divided number is the dividend: seven (7). Divisor: The dividing number is the divisor: three (3). Answer: The answer is the result of dividing the dividend by the divisor: two and one third (2 1/3). Remainder: The fractional part of the answer is the remainder: one-third (1/3).   A brief definition of each phase is as follows: First – divide two one-digit numbers. In parallel, show the reciprocal multiplication problem. Make sure students have a complete understanding of the first phase, because this will be starting point for individual student’s foundering in division. Second – divide a one one-digit number in to two-digit number. Third – divide two two-digit numbers. Fourth – divide two numbers each with a variable number of digits (minimum two-digits); if students can handle completion of this phase, they can solve any integer division problems.   Why are four phases important to teaching integer division in an intuitive manner? First requires dividing two – one-digit numbers. Alongside the division problem, show the reciprocal multiplication problem. The multiplication problem provides for visual comparison. Second requires dividing a one-digit number in to a two-digit number. Third requires dividing at least two two-digit numbers or more. Four requires dividing two variable – multi-digit numbers. Notice at each phase, we include more digits to the division learning process. The first phase is crucial. It is the students’ first introduction to division. The procedural thinking is very different from multiplication; failure to transition from multiplication to division will leave students confused. Let us further investigate teaching phase one in more detail; it is more complex than phase two and three. There are three reasons why this is true. The first phase is the transition from multiplication thinking to division thinking. We recommend teaching division together with the same multiplication problem. This puts students in a familiar comfort zone. The second phase requires phasing out the parallel multiplication problems. Phasing out showing multiplication depends on the learning curve of the class. The third phase shows division problems only – no multiplication. Phase four makes students apply all the skills and techniques they have learned in the previous phases. They now have the tools to solve any division problem. Math K-Plus (http://www.mathkplus.com) is a free website to use. It provides homework study tools to help children learn arithmetic. Our goal is to help students help themselves build a clear understanding of arithmetic. Come try our interactive division calculators. First phase starts here: Division Phase One (http://www.mathkplus.com/Integer-Math/Division/First-Grade-Division-Practice.aspx).