Children develop division ideas naturally before they begin elementary school as they learn to take turns, divide snacks equally and do simple tasks such as setting the table (there are four spoons, and each person gets one). By third grade, they are learning complex methods, especially long division, to divide large quantities quickly. Helpful teaching strategies include focusing on mastery of multiplication, using manipulatives, estimating answers before dividing, using chants and acronyms and reading math picture books.
Multiplication is defined as a quick process for calculating multiple additions of the same number. So "3 X 9" is "9 + 9 + 9." It is much easier to move on to formal learning of division once children master the ideas and basic math facts (times tables) of multiplication. Knowing that "3 X 9 = 27" helps a student to see that 27 can be divided in three equal groups of nine or nine equal groups of three. Teachers often say that sometimes it is necessary to go slow in order to go fast. Spending extra time on multiplication can speed up learning of division.
Manipulatives are objects, large and small, that students can touch, move, and group to solve math problems. They make math processes more concrete. For example, a student can count a handful of dry lima beans, then divide them evenly into a number of empty margarine tubs. In another demonstration of the grouping idea, children are the manipulatives. The teacher tells the students how many children are in class that day, then directs them to line up in pairs. The class then discusses how many groups of two were made and whether anyone was left without a partner.
Before beginning the multi-step process of long division, teachers should focus on how to guess reasonable answers. The estimation process involves rounding divisors and dividends so they are easier to compute. A problem such as "72 divided by 8" is easier to estimate if students think about how many groups of 10 are in 70. The Math and Reading Help website notes that skill at estimation gives students a sense of what size of answer to expect and gives them "more control over mistakes."
Chants and Acronyms
Math chants and acronyms help remind students of processes such as the steps in long division. Students can easily remember D-M-S-B (Dad, Mom, Sister, Brother) and its meaning (Divide, Multiply, Subtract, Bring down). A simple chant to reinforce this would be something like "Listen to me, D-M-S-B. Dad, mom, sister, brother. Do it again! Divide, multiply, subtract, bring down the number. Do it again! D-M-S-B, listen to me." Another good idea is to add gestures and movement, such as crossing arms in an "X" for "multiply" and jumping at the phrase "Do it again!"
Read-alouds of colourful math picture books are always a wise investment of class time. "Remainder of One" by Elinor J. Pinczes focuses on Joe, a beetle who wants to march in an orderly insect parade with even rows. Joe perseveres in rearranging his squadron until he is not odd bug out but part of a harmonious configuration with evenly divided rows.
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