Single Strategy for Adding and Subtracting Mixed Numbers
Students will be able to add and subtract mixed numbers by converting them into improper fractions and back again.
- Show your class two examples:
- a whole piece of fruit and ¼ slice to represent 1 ¼,
- another model of 1 and ¼ of fruit, where the whole has been partitioned into ¼ pieces.
- Ask your class which would be easier to subtract ¾ from and why. Have your students turn to a neighbor and share their thoughts.
- Allow students to share out to the whole class and tease out the notion that it's easier to subtract from whole items already in a group of like pieces.
- Share that today's lesson uses a strategy for adding and subtracting mixed numbers by first making them improper fractions, or as a group of like or same-sized pieces.
- Point out to your students that mixed numbers are different from improper fractions in that they include a whole number and a proper fraction (where the numerator is less than the denominator).
Explicit Instruction/Teacher modeling(10 minutes)
- Show your class the following expression: 1 ⅖ + 3 ⅘.
- Explain that there is a three-step sequence that will always work when adding or subtracting mixed numbers:
- Step one: convert the mixed number to an improper fraction.
- Step two: perform the operation.
- Step three: convert the improper fraction back to a mixed number.
- Review converting a mixed number to an improper fraction, and vice versa, as needed. (This is not the focus of this lesson, but these skills are required to proceed.)
- Take your class through the three-step sequence for adding and subtracting mixed numbers for the following: 1 ⅖ + 3 ⅘.
- Step one: convert the mixed numbers to improper fractions: 7/5 + 19/5.
- Step two: perform the addition. The sum is 26/5.
- Step three: convert the improper fraction: 26/5 becomes 5 ⅕.
Guided Practice(5 minutes)
- Repeat the three-step sequence for 3 ⅘ – 1 ⅖, calling on various students for each step. Answer clarifying questions students may have.
- Tell your students to take out their math journals and list the three-step sequence for adding and subtracting mixed numbers.
- Post the following expression and perform the three-step sequence with the expression 1 6/8 + 8 2/8. Ensure students label the three steps in their solutions.
- Answer any clarifying questions and post the following exercise problems:
- 3 ⅝ + 1 ⅜
- 4 ¼ – 1 ¾
- 6 ⅚ + 3 ⅙
- 5 ⅕ – 3 ⅘
- 7 ⅓ – 2 ⅔
Independent working time(15 minutes)
- Instruct your class to copy and complete the exercise problems in their math journals.
- For review on converting mixed numbers to improper fractions or converting improper fractions to mixed numbers, see the Related Media section for videos for each procedure.
- Print the the three-step sequence for adding and subtracting mixed numbers in advance. Print five to a page and tear off in strips for students to place in their math journals.
- Students can add an extra addend as an addition challenge. For a subtraction challenge, have students design a subtraction expression that uses two subtrahends and works!
- Use an interactive whiteboard to demonstrate the processes involved when converting mixed numbers to improper fractions and back again.
- Assign exercise problems in your Google Classroom application for student reference and as a repository for their solutions.
- Show students a mixed number subtraction expression with two potential answers.
- Ask students to select the correct answer, including details for each of the three steps that yield the answer.
- Repeat for a mixed number addition expression.
Review and closing(15 minutes)
- Review exercises by having students share out their answers with details of each stage in the three-step solution sequence.
- Allow for students to "phone a friend" for assistance if they get stuck to take over their explanation.
- Discuss the following question, "How efficient is this strategy and how does it compare to others?"
- Post key learnings and comments on a poster for future reference.