Dissecting Decimals

Explicit Instruction/Teacher modeling

• Review the terms tenth, hundredth, thousandth, and number line with the students. Allow them to share their ideas and then have them repeat the meanings. Show students the fractional representation for tenth (1/10), hundredth (1/100) and thousandth (1/1000).
• Place a number to the tenths place (e.g., 10.7) on the number line from the Introduction section and then ask students to think about numbers that are closer to that number than the whole number (e.g., 10), such as 10.3. Then, ask students if there are numbers even closer to 10 they can find on the number line. (Tip: continue to refer to the fractional equivalent of the decimal number if students have a solid understanding of fractions.)
• Have students share their ideas with partners and allow them to find the number on the number line to confirm their answer.
• Ask students if there are numbers that are even closer to 10 but that they cannot find on the drawn number line. Choose students to share their ideas. They should understand that the thousandths place is not visible, but that the number 10.001 is even closer to 10.
• Have students talk to their elbow partner about a number that is closer to 11 this time. Have them find numbers closer to 11 little by little until they identify a closer number (e.g., 10.9).
• Ask students if there is a number closest to 11 that they cannot find on the number line (e.g., 10.999).
• Give students time to ask questions and give other students the opportunity to answer the question before answering it yourself.

Guided Practice

• Pose some questions that require students to make a choice:
  1. Is 4.56 closer to 5 than 4.506?
  2. Is 95.3 closer to 95 than 95.33?
  3. Can you think of a number in the tenths place that is closer to four than five?
• Pass out a whiteboard to each student to allow them to take notes or draw a number line to confirm their ideas. Answer the questions as a class.
• Provide the following sentence stems:
  • "I think ____ is closer to ____ because..."
  • "Also, ____ is close to ____."
  • "I agree with ____ because..."
  • "What about..."

Group work time

• Assign the Always, Sometimes, Never: Decimal Questions worksheet to partners.
• Explain to students that they need to read the cards to each other and determine if the statement is always true, sometimes true, or never true. Tell them to write an example to support their answers on the back of the card and then place the card in the corresponding column in the table.
• Ask partners to "correct" another partnership's answers. Have partners move to another partnership's table and review the card placements. Explain that if they disagree with the card placement, they should move them off the chart. When students come back to their table, ask them to review the disagreements and see if they have questions.
• Ask students to share if they had cards moved off of their table and then discuss the correct answer. ("Can you help me with card ____? I think the answer for card ____ is ____.") Correct misconceptions as necessary after students have tried to help partnerships correct their answer.
• Review the card placements on the chart and discuss the cards in detail that have the most debate between students.