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# 3-N-2-7

last edited by 6 years, 7 months ago

3.N.2.7 Recognize the relationship between multiplication and division to represent and solve real-world problems.

In a Nutshell

Students come to third grade with an understanding of fact families made up of addition and subtraction.  This objective will build upon that understanding by showing that multiplication and division are inverse operations and make fact families.  It will also show how and when to use each operation.

## Teacher Actions

• Demonstrate a flexible understanding when making connections between multiplication and division.

• Make generalizations about real life problems to determine when and how to use each operation. For example: Sally has 49 cookies. Her and her six friends are going to share them equally. How many do they each get? Students will divide 49 by 7 because they are sharing the cookies. They can use multiplication to solve the problem (7x__=49), but the context of the problem tells us we are dividing.

• Communicate mathematically with their peers by writing their own equations/stories to be solved by one or both operations.

• Model multiplication and division in ways to show the relationship between the two.

• Implement tasks that allow students to work in small groups and/or pairs to explore problems requiring multiplication and/or division to solve.

• Facilitate a mathematical discussion that allows students the opportunity to share and explain their work.

• Pose purposeful questions that spark students’ group and individual work. Questions may include: How do you know we are to multiply/divide in this problem? What clues help you decide? Can we use the other operation to help justify our solution? Which strategies could you use to solve this problem?

## Misconceptions

• Multiplication and division are reverse operation.

• That understanding one of the operations helps in understanding the other.

• There are real-world problems that can be solved using one or both operations.

• That when multiplying, the product will be larger than the factors, and the quotient will be smaller than the number being divided.

• that they have to learn a whole new set of facts for multiplication and division, rather than using those they already know.

• They have to multiply whenever they see the word “each”.

OKMath Framework Introduction