Lesson plan
Single Strategy for Adding and Subtracting Mixed Numbers
Learning Objectives
Students will be able to add and subtract mixed numbers by converting them into improper fractions and back again.
The adjustment to the whole group lesson is a modification to differentiate for children who are English learners.
Introduction
(5 minutes)- 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.
Differentiation
Support:
- 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.
Enrichment:
- 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!
Technology Integration
- 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.
Assessment
(5 minutes)- 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.
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