### Lesson plan

# Modeling Mixed Number Subtraction

#### Learning Objectives

Students will be able to model subtraction for mixed numbers with like denominators.

The adjustment to the whole group lesson is a modification to differentiate for children who are English learners.

#### Introduction

*(5 minutes)*

- 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**). 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.^{1}⁄_{4}− 1^{3}⁄_{4}

#### 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.

#### Differentiation

**Support:**

- Have students use the Mixed Numbers Subtraction Modeling Mat worksheet in small groups before illustrating their work.

**Enrichment:**

- Propose subtraction problems with larger subtrahend numerators than minuend numerators.

#### Technology Integration

- 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.

#### Assessment

*(5 minutes)*

- 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.