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Modeling Mixed Number Subtraction
Students will be able to model subtraction for mixed numbers with like denominators.
- Post a subtraction number sentence for all students to see. Then ask your students to name as many parts of the sentence as possible.
- Jot student answers for future reference, including the following terms: "minuend," "subtrahend," "subtraction sign," "equal sign," and "difference."
- Explain the names of three key parts of a subtraction expression:
- minuend: the amount being subtracted from
- subtrahend: the amount being subtracted
- difference: the answer to a subtraction expression
Explicit Instruction/Teacher modeling(10 minutes)
- Tell your students that they'll be learning to model mixed number subtraction with like denominators.
- Show the Mixed Number Subtraction Modeling Mat worksheet to your students and post the following expression: 3 5⁄9 − 1 2⁄9.
- Using the mat, model the minuend using markers (i.e., beads, cubes or even cutout dots) for 3 5⁄9 by placing:
- three markers in the whole number minuend circle,
- five markers in the numerator minuend circle,
- nine markers in the denominator circle.
- Subtract the subtrahend (1 2⁄9) into the section beyond the minuend circle for the whole number and the numerator by moving:
- one marker beyond the whole number minuend circle to the subtrahend area,
- two markers beyond the numerator minuend circle to the subtrahend area.
- Note the expression by filling in the sentence frame as, "This is a model of 3 5⁄9 − 1 2⁄9."
- Note the difference by filling in the sentence frame as, "The difference is 2 3⁄9."
- Point out to your students how the mat at this stage models the difference as well as the steps in solving the mixed number subtraction problem. Answer any clarifying questions.
Guided Practice(10 minutes)
- Hand out the Mixed Numbers Subtraction Models worksheet and the Mixed Numbers Subtraction Model Mat worksheet to your students.
- Lead your class through the instructions on the Mixed Numbers Subtraction Models worksheet.
- Model the illustrated example by selecting students for each step on their Mixed Numbers Subtraction Model Mat. Observe student models for accuracy.
- Have your class illustrate their procedure for the first exercise on their Mixed Numbers Subtraction Models worksheet and answer any clarifying questions.
- Provide another example in which students need to consider borrowing from the minuend to complete the problem (e.g., 4 1⁄4 − 1 3⁄4). Ask students, "How is this problem the same as the first exercise?" Encourage students to share aloud and ask a volunteer to model the process of borrowing, with help from peers.
Independent working time(15 minutes)
- Instruct your students to complete the remaining exercises:
- first by modeling their work with manipulatives on the Mixed Numbers Subtraction Modeling Mat,
- then by illustrating their work on the Mixed Numbers Subtraction Models worksheet.
- Have students use the Mixed Numbers Subtraction Modeling Mat worksheet in small groups before illustrating their work.
- Propose subtraction problems with larger subtrahend numerators than minuend numerators.
- Digital photographs of finished expression models can be integrated into Google or Word documents, which make for fine assessments or exercises.
- Student explanation recording postings into Google Classroom make excellent customized references for students to access when completing new exercises.
- Show an illustrated example of a completed mixed number subtraction problem.
- Have your students tell you the original subtraction expression of the illustrated difference.
Review and closing(10 minutes)
- Ask students, "What clues does a difference give about the minuend and subtrahend?"
- Student observations might include how the minuend and subtrahend are both less than the difference.
- Encourage clear explanations and assistance from other students whenever possible.