July 11, 2017
by Byron Delcomb

Lesson plan

When Having Like Denominators Isn’t Enough!

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Students will subtract mixed numbers where the larger fraction has a lesser numerator and a like denominator.

(5 minutes)
  • Write (or display) the following expressions on the board:
    • 5 1/4 - 2 3/4
    • 3 2/8 - 1 7/8
    • 9 2/4 - 3 3/4
  • Have students think, pair, and share their thoughts of a singular challenging trait these expressions have in common.
  • As students share out their ideas, write down any related academic language, terms, or ideas.
  • Point out how the minuend (the number being subtracted from) has a lesser numerator than the fraction in the subtrahend (the number being subtracted).
(10 minutes)
  • Explain that if we come across this situation, we know right away that we must subtract from improper fractions. The subtrahend and minuend must be converted to improper fractions to solve the expression.
  • Demonstrate how to convert mixed numbers to improper fractions using the Mixed and Improper Fractions strategy listed in the Materials and Preparation section and solve 5 1/5 - 2 3/5.
  • Review converting improper fractions to mixed numbers and convert the improper differences for 5 1/4 - 2 3/4.
(10 minutes)
  • Guide your students for each of the remaining opening exercises:
    • 3 2/8 - 1 7/8
    • 9 2/7 - 3 3/7
  • Answer any clarifying questions.
(15 minutes)
  • Issue the following exercises for students to solve on paper or in their math journals:
    • 4 1/5 - 1 3/5
    • 3 2/5 - 2 1/5
    • 6 3/4 - 2 4/4
    • 4 1/6 - 1 5/6
    • 7 2/7 - 2 5/7


  • Use unifix cubes or linking blocks to demonstrate subtraction of mixed numbers.
  • Demonstrate subtraction semi-concretely, using block notation to show mixed number to improper fractions conversions and subtraction.


  • Issue problems that have unlike mixed numbers and subtrahends with lesser numerators, (see resources for challenge problems.)
  • Slideshow applications are an excellent way to present exercises in succession text notation.
(5 minutes)
  • Show your students a subtraction expression with like mixed numbers and the minuend has a lesser numerator.
  • Offer three possible conversions and have your students select the proper one by a show of fingers, “one, two, or three,” along with an explanation of their choice.
(10 minutes)
  • Review the independent work time exercises by having students state their answers and explain their reasoning.
  • Discuss the question, "What kind of clues do differences give us about minuends and subtrahends?’

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