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Big Ideas:
We can apply the associative property when multiplying fractions in the same way we apply it when multiplying whole numbers.
The task in this lesson will push students to think about the meaning of multiplication with a whole number and a fraction. Students will see that when multiplying whole numbers by fractions, they can employ their understandings of what multiplication means with whole numbers. For example, they will use a number line to think of 3 times two-fifths not only as 3 groups of two-fifths, but as the result of an amount (3 x 2) ÷ 5. Students will make a comparison to 1 times six-fifths. Exploring this relationship will help students realize the application of the associative property and see the analogy between fractions and whole numbers: 3 x ⅖ can be thought of as ⅖ +⅖ + ⅖ and as (3 x 2)/5. In this lesson, we also address the common misconception that you can multiply both the numerator and the denominator by the whole number to find the product. This is mostly a procedural misconception and precisely why we have used a conceptual approach that employs the number line as a tool.
Vocabulary: multiple, equation, factors, products, numerator, denominator, fraction, whole number
Special Materials:
Dry erase boards
Dry erase markers