Lesson 22

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.

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

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

• “What is the same about these expressions? What is different?” (They all show a whole number divided by a 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.)

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.

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

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

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 \(3 \div 0.1\)?”

• 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.)

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.

• 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.”

• 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

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?”

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