## Tutorial: Teaching Integer Division in Intuitive Phases

**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).

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**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.

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**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).