# 4. Understand dividing a whole number by a unit fraction (C)

teaches Common Core State Standards CCSS.Math.Content.5.NF.B.7b http://corestandards.org/Math/Content/5/NF/B/7/b
teaches Common Core State Standards CCSS.Math.Practice.MP2 http://corestandards.org/Math/Practice/MP2

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Lesson objective: Understand that the meaning of division does not change when the divisor is a fraction.

Students bring prior knowledge of division of unit fraction by a whole number from 5.NBT.6. This prior knowledge is extended to fractions as students represent and divide whole numbers by unit fractions. A conceptual challenge students may encounter is the meaning of each component in the division sentence. This lesson uses the idea of measurement division, with expressions such as $$4 \div \frac13$$ interpreted as "How many $$\frac13$$size pieces are in $$4$$?"

The concept is developed through work with number lines, which visually represent the number of fractional parts in a specified number of wholes.

This work helps students deepen their understanding of equivalence because it builds on the understanding that $$\frac55=1$$ whole, $$\frac{10}5=2$$ wholes, etc.

Students engage in Mathematical Practice 2 (reason abstractly and quantitatively) as they notice and model situations that show that the meaning of division is not changing simply because a fraction is now included as the divisor. The use of number lines help students to visually see how a whole number(s) can be divided into equal fractional parts.

Key vocabulary:

• divisor
• dividend
• quotient
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