Lesson 12: Dividing Numbers that Result in a Decimal

Dividing Numbers that Result in a Decimal

5 min

Teacher Prep

Setup

Display one problem at a time. Allow 30 seconds of quiet think time per problem, followed by a whole-class discussion.

Narrative

This Math Talk focuses on division of multi-digit numbers by a single-digit divisor. It encourages students to think about place value and to rely on what they know about base-ten numbers and properties of operations to mentally solve problems. The reasoning elicited here will be helpful later in the lesson when students use long division to divide decimals by whole numbers.

To find the value of the last two expressions, students need to look for and make use of structure (MP7). In explaining their reasoning, students need to be precise in their word choice and use of language (MP6).

Launch

Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:

Give students quiet think time, and ask them to give a signal when they have an answer and a strategy.
Invite students to share their strategies, and record and display their responses for all to see.
Use the questions in the Activity Synthesis to involve more students in the conversation before moving to the next problem.

Keep all previous problems and work displayed throughout the talk.

Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

Find the value of each quotient mentally.

$80 \div 4$
$12 \div 4$
$1.2 \div 4$
$81.2 \div 4$

Sample Response

20. Sample reasoning:
- $4 \boldcdot 20$ is 80.
- $8 \div 4 = 2$ , so $80 \div 4$ is 10 times 2, which is 20.
3. Sample reasoning:
- There are 3 groups of 4 in 12.
- $4 \boldcdot 3 = 12$
0.3. Sample reasoning:
- 1.2 is a tenth of 12, so the quotient is a tenth of 3.
- $4 \boldcdot (0.3) = 1.2$
20.3. Sample reasoning:
- 81.2 is a sum of 80 and 1.2. We know $80 \div 4 = 20$ and $1.2 \div 4 = 0.3$ so $81.2 \div 4$ is $20 + 0.3$ .

Activity Synthesis (Teacher Notes)

To involve more students in the conversation, consider asking:

“Who can restate $\underline{\hspace{.5in}}$ ’s reasoning in a different way?”
“Did anyone use the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to $\underline{\hspace{.5in}}$ ’s strategy?”
“Do you agree or disagree? Why?”
“What connections to previous problems do you see?”

Highlight how partial quotients are used in finding $81.2 \div 4$ . Students recognized 81.2 as $80 + 1.2$ , so they added $80 \div 4$ and $1.2 \div 4$ to find $81.2 \div 4$ .

MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. For example, “First, I

\underline{\hspace{.5in}}

because . . . .” or “I noticed

\underline{\hspace{.5in}}

so I . . . .” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking, Representing

Standards

Building On

5.NBT.7·Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
5.NBT.B.7·Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Building Toward

6.EE.A·Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.A·Apply and extend previous understandings of arithmetic to algebraic expressions.

20 min

10 min

Knowledge Components

All skills for this lesson

No KCs tagged for this lesson

Dividing Numbers that Result in a Decimal

5 min

Teacher Prep

Setup

Display one problem at a time. Allow 30 seconds of quiet think time per problem, followed by a whole-class discussion.

Narrative

Launch

Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:

Give students quiet think time, and ask them to give a signal when they have an answer and a strategy.
Invite students to share their strategies, and record and display their responses for all to see.
Use the questions in the Activity Synthesis to involve more students in the conversation before moving to the next problem.

Keep all previous problems and work displayed throughout the talk.

Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

Find the value of each quotient mentally.

$80 \div 4$
$12 \div 4$
$1.2 \div 4$
$81.2 \div 4$

Sample Response

20. Sample reasoning:
- $4 \boldcdot 20$ is 80.
- $8 \div 4 = 2$ , so $80 \div 4$ is 10 times 2, which is 20.
3. Sample reasoning:
- There are 3 groups of 4 in 12.
- $4 \boldcdot 3 = 12$
0.3. Sample reasoning:
- 1.2 is a tenth of 12, so the quotient is a tenth of 3.
- $4 \boldcdot (0.3) = 1.2$
20.3. Sample reasoning:
- 81.2 is a sum of 80 and 1.2. We know $80 \div 4 = 20$ and $1.2 \div 4 = 0.3$ so $81.2 \div 4$ is $20 + 0.3$ .

Activity Synthesis (Teacher Notes)

To involve more students in the conversation, consider asking:

“Who can restate $\underline{\hspace{.5in}}$ ’s reasoning in a different way?”
“Did anyone use the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to $\underline{\hspace{.5in}}$ ’s strategy?”
“Do you agree or disagree? Why?”
“What connections to previous problems do you see?”

Highlight how partial quotients are used in finding $81.2 \div 4$ . Students recognized 81.2 as $80 + 1.2$ , so they added $80 \div 4$ and $1.2 \div 4$ to find $81.2 \div 4$ .

MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. For example, “First, I

\underline{\hspace{.5in}}

because . . . .” or “I noticed

\underline{\hspace{.5in}}

so I . . . .” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking, Representing

Standards

Building On

5.NBT.7·Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
5.NBT.B.7·Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Building Toward

6.EE.A·Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.A·Apply and extend previous understandings of arithmetic to algebraic expressions.

Dividing Numbers that Result in a Decimal

Warm-upMath Talk: Dividing by 45 minKCs

Setup

Narrative

Launch

Student Task

Sample Response

ActivityWhole Numbers No More20 minKCs

ActivityUsing Long Division to Divide Decimals10 minKCs

Knowledge Components

Dividing Numbers that Result in a Decimal

Warm-upMath Talk: Dividing by 45 minKCs

Setup

Narrative

Launch

Student Task

Sample Response

ActivityWhole Numbers No More20 minKCs

ActivityUsing Long Division to Divide Decimals10 minKCs

5 min

20 min

10 min

5 min

20 min

10 min