Lesson plan

Word Problems: Adding Mixed Number Fractions

Children often wonder if algorithms are practical. Using this lesson plan, your students will see how the standard algorithm for adding mixed numbers brings life to real world real-world situations.
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Students will be able to solve addition word problems that include mixed number fractions with unlike denominators.

(5 minutes)
  • Have one student stand at a corner of the room, another student stand in the middle of a wall (half way between corners) and hand one of them a marker.
  • Set the scene, "This will be a relay, a task where the activity is divided between’ participants. Everyone stand behind the starting student with the marker."
  • Tell the student holding the marker, "When you give the signal, to travel along the wall and hand off the marker to the next student, who will travel along the perimeter and hand the marker to you."
  • When everyone is clear on the instructions, announce the signal like "Go!"
  • Upon receiving the marker, ask your class, “How many walls did each student travel with the marker?” (Before it got to you, in a four-walled room, the answer should include two mixed numbers. Any combination like 1 1/2 + 2 1/2.)
  • Then ask your class, "How many walls did both students travel, all together?" The answer, for a typical four-walled room, will be four.
  • Highlight with your students how the relay was a demonstration of a sum of two mixed numbers (i.e 1 1/2 + 2 1/2) which is what today’s lesson will be about.
(10 minutes)
  • Pose the introductory demonstration as a number sentence (i.e. 1 1/2 + 2 1/2 = 4) and ask, "How does having common denominators make this an easier problem to solve?"
  • Allow for student responses, noting any academic terminology for future reference.
  • Noting how both mixed numbers contain a common denominator, ask your students rhetorically, "But what if they don’t have common denominators?"
  • Demonstrate the algorithm for establishing common denominators for mixed numbers with uncommon fractions, for a few problems with your class (see Resource section).
(10 minutes)
  • Pass out and preview the Swimming in Word Problems: Adding Mixed Number Fractions worksheet.
  • Solve the first problem from the worksheet as a class and answer any clarifying questions.
(15 minutes)
  • Have your students complete the remaining exercises.


  • For added algorithm practise, provide several exercises where students only convert unlike mixed numbers to ones with like denominators.
  • Do a Three Reads procedure with your class:
    • The first read is just to discover what it says.
    • The second read is to figure what is being asked.
    • The third read is to gather needed information to perform the ask - then do it!


  • Provide exercises with two-digit mixed number addends with unlike fractions.
  • Taking phone camera snapshots of lesson notes is a great way to integrate class notes electronically into computer generated documents such as:
    • Student portfolios
    • Newsletters
    • Study guides
(5 minutes)
  • Show students an exercise problem from the Swimming in Word Problems: Adding Mixed Number Fractions worksheet with omitted addends.
  • As an exit ticket, have your students input mixed number addends with unlike fractions of their choice and solve.
  • Collect and assess for student understanding to inform further instruction.
(10 minutes)
  • Review the Swimming in Word Problems: Adding Mixed Number Fractions worksheet.
  • Allow students to "phone a friend" to take over explanations, if they get stuck.
  • Discuss the following question, "How can word problems inform how we see fractions in the real world?"
  • Note important insights on poster paper for future reference.

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