Lesson plan

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