Lesson 22

Divide Whole Numbers by 0.1 and 0.01

Warm-up: Number Talk: Remember Division of Unit Fractions (10 minutes)

Narrative

The purpose of this number talk is for students to divide a whole number by a tenth and a hundredth, presented both as fractions and as decimals. This prepares students to work with and understand quotients of whole numbers by decimals in this and future lessons.

Launch

  • Display one problem.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time

Activity

  • Record answers and strategy.
  • Keep problems and work displayed.
  • Repeat with each problem.

Student Facing

Find the value of each expression mentally.

  • \(1 \div \frac{1}{10}\)
  • \(2 \div \frac{1}{10}\)
  • \(1 \div 0.01\)
  • \(2 \div 0.01\)

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

  • “What is the same about these expressions? What is different?” (They all show a whole number divided by number less than 1. Some have decimals and some have fractions, but the decimals and fraction are all 1 of some unit. They all have a value that is a whole number.)

Activity 1: Patterns in Dividing by Decimal Units (15 minutes)

Narrative

The purpose of this activity is for students to divide a whole number by 0.1 or 0.01. Students may think about the quotients in different ways. Monitor for students who
  • use the hundredths grids to visualize the tenths and hundredths in 3 or 4 wholes
  • use their understanding of fractions or decimals to identify the number of tenths and hundredths in 1 whole and then multiply by the number of wholes
  • build on and solidify their reasoning from the warm-up

The work in this activity focusing on the tenths and hundredths in 3 or 4 wholes prepares students to generalize in the next activity where they explain how to find the number of tenths or hundredths in any whole number.

Representation: Internalize Comprehension. Begin by asking, “Does this problem/situation remind anyone of something we have seen/read/done before?”
Supports accessibility for: Memory, Attention

Required Materials

Materials to Copy

  • Small Grids

Launch

  • Groups of 2
  • Give students access to blackline masters with grids.

Activity

  • 1–2 minutes: quiet think time
  • 5–7 minutes: partner work time
  • Monitor for students who:
    • use fractions
    • use diagrams
    • use multiplication

Student Facing

  1. Find the value of each expression. Explain or show your reasoning. Use a diagram if it is helpful.

    1. \(3 \div 0.1\)
    2. \(3 \div 0.01\)
    3. \(4 \div 0.1\)
    4. \(4 \div 0.01\)
  2. What patterns do you notice?

Student Response

For access, consult one of our IM Certified Partners.

Advancing Student Thinking

If students do not find the value of \(3 \div 0.1\), ask, “How can you use a diagram to show \(1 \div 0.1\)? How can your diagram help you find the value of \(3 \div 0.1\)?”

Activity Synthesis

  • Ask previously selected students to share their strategies for finding the value of the division expressions.
  • “How do the different representations show that there are 10 tenths in 1 whole and 100 hundredths in 1 whole?” (With the diagram I can see each tenth and each hundredth in the whole. With fractions or decimals, I just know how many tenths or hundredths there are in 1 and can use that to figure out how many there are in 3 or 4.)
  • Display equations:
    \(3 \div 0.01 = 300\)
    \(4 \div 0.01 = 400\)
  • “What patterns do you notice?” (I notice that I multiply by 100 to find how many 0.01s there are in 3 or 4.)

Activity 2: Divide Whole Numbers by Decimals (20 minutes)

Narrative

The purpose of this activity is for students to describe the patterns they notice when they divide a whole number by one tenth and one hundredth (MP7). Students have the option of using a diagram recalling work from the previous activity. The reasoning students develop here prepares them to:

  • evaluate more complex quotients with decimals in future lessons.
  • observe patterns when multiplying or dividing by powers of 10 which will be a focus in the next unit.

This activity uses MLR1 Stronger and Clearer Each Time. Advances: Reading, Writing.

Required Materials

Materials to Copy

  • Small Grids

Launch

  • Groups of 2
  • Give students access to blackline masters with grids.
  • “You are going to use the patterns you noticed to explain how to divide any whole number by a tenth and a hundredth.”

Activity

  • 6–8 minutes: independent work time
  • Monitor for students who notice:
    • that when they divide a whole number by one tenth, the quotient is ten times larger than the whole number
    • that when they divide a whole number by one hundredth, the quotient is one hundred times larger than the whole number

Student Facing

  1. Describe how you can find the value of any whole number divided by 0.1. Use a diagram if it is helpful.
  2. Describe how you can find the value of any whole number divided by 0.01. Use a diagram if it is helpful.
Diagram, square. Length and width, 1. Partitioned into 10 rows of 10 of the same size squares. No squares shaded.
Diagram, square. Length and width, 1. Partitioned into 10 rows of 10 of the same size squares. No squares shaded.

Student Response

For access, consult one of our IM Certified Partners.

Advancing Student Thinking

If students do not describe how they could find the value of any whole number divided by 0.1 or 0.01, ask them to draw a diagram to show \(1 \div 0.1\) and ask, “How can you use this diagram to figure out the value of any whole number divided by one tenth?”

Activity Synthesis

MLR1 Stronger and Clearer Each Time
  • “Share with your partner your explanation of how you would find the value of
    • any whole number divided by one tenth
    • any whole number divided by one hundredth”
  • “Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
  • 2 minutes: structured partner discussion
  • Repeat with 2 different partners.
  • If needed, display question starters and prompts for feedback.
    • “Can you give an example to help show . . . ?”
    • “Can the examples we studied in the first activity fit in your explanation?”
  • “Revise your initial draft based on the feedback you got from your partners.”
  • 2–3 minutes: independent work time

Lesson Synthesis

Lesson Synthesis

“Today, we divided whole numbers by one tenth and one hundredth.”

Display expressions:

\(5 \div 0.1\)
\(5 \div 0.01\)

“Describe to your partner how to find the value of each of these expressions.” (To divide by 0.1 I just multiply by 10 so that's 50 and to divide by 0.01 I multiply by 100.)

“Now discuss with your partner why your strategy works.” (There are 10 tenths in 1 so that's \(5 \times 10\) or 50 in 5. There are 100 hundredths in 1 so that's \(5 \times 100\) or 500 in 5.)

Cool-down: Many Tenths and Hundredths (5 minutes)

Cool-Down

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