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How to Teach Children Multiplicative Reasoning in Mathematics

Multiplicative reasoning is a mathematic skill that allows people to use proportions and basic reasoning to figure out a number that is not given. According to "Math Matters: Understanding the Math You Teach Grades K-8," by Suzanne H. Chapin, "Schooling builds on students' intuitive understanding of addition and subtraction by focusing on additive situations in the early grades and then introducing situations that can be addressed through multiplicative reasoning in the later grades." Typically a word or visual problem is set up, including two or more numbers that are used to create a proportion, thereby allowing someone to ascertain what the unnamed number would be.

Instructions

    • 1

      Create a word problem using two different forms of measurement. The problem should force a student to reason through proportion to arrive at the answer. For example: John is six boards tall and Cindy is four stars tall. If 1/2 star equals one board, how many boards tall is Cindy?

    • 2

      Set up a visual component to the problem. Draw out the stars and boards next to each figure so that students can see the proportion with their own eyes.

    • 3

      Print out the word problem and the visual representation. Distribute one to each student.

    • 4

      Run through an example problem with the students. Let them try it out loud as you draw it up on the board.

    • 5

      Allow them to try it on their own. Discuss their answers after they are finished. Show them how to set up a proportion and to use multiplicative reasoning if they don't already know how.

    • 6

      Incorporate a physical version of the problem for students who are struggling. Use dolls to represent the characters and blocks or other items to represent the proportions.

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