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Big Ideas:
Fraction parts can be counted in groups, similar to how we skip count whole numbers.
A non-unit fraction can be described as an accumulation of two or more of the unit fractions.
The task in this lesson requires students to interpret the meaning of multiplication beyond whole numbers. Specifically, students see that when multiplying whole numbers by fractions, they can call on their understanding of what multiplication means with whole numbers. For example, they will use a bar model to think of 24 times one-third not only as 24 groups of one-third, but as the result of an amount that is 24 times as much as one-third. They will extend this idea to 24 times two-thirds. Students will grapple with why the result of 24 × 1/3 is less than 24 × 2/3. The approach in this lesson is meant to address the common misconception of multiplying both the numerator and the denominator by the given whole number to find the product.
Vocabulary: multiple, factor, product, expression, equation, numerator, denominator, fraction, bar model, unit fraction
Special Materials:
Cuisenaire rods
grid paper