Thousandths in Expanded Form

10 min

Narrative

This Warm-up prompts students to carefully analyze and compare features of expressions. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminologies students know and how they talk about these features of expressions such as:

  • The operations
  • The values of the expressions
  • The types of numbers in the expressions (whole numbers versus decimals)

Students work in this lesson to express decimals in many different forms, and this Warm-up gives students some familiarity thinking about some of those different forms.

Launch

  • Groups of 2
  • Display the image.
  • “Pick 3 that go together. Be ready to share why they go together.”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 2–3 minutes: partner discussion
  • Share and record responses.

Student Task

Which 3 go together?

A

26÷10026\div100

B

0.260.26

C

26×0.00126 \times 0.001

D

(2×0.1)+(6×0.01)(2 \times 0.1) + (6 \times 0.01)

Sample Response

Sample responses:

A, B, and C go together because:

  • They have the digits 2 and 6 together.
  • They don’t have parentheses.

A, B, and D go together because:

  • Their value equals 0.26.

A, C, and D go together because:

  • They have operations.

B, C, and D go together because:

  • They have decimals in the expression.
Activity Synthesis (Teacher Notes)
  • Display the expression: (2×0.1)+(6×0.01)(2 \times 0.1 )+ (6 \times 0.01)
  • “What do you notice about the operations and types of numbers in this expression?” (It is written as a sum. The different place values are written separately.)
  • “Today we are going to represent decimal numbers in this way.”
Standards
Addressing
  • 5.OA.A·Write and interpret numerical expressions.
  • 5.OA.A·Write and interpret numerical expressions.
Building Toward
  • 5.NBT.3.a·Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
  • 5.NBT.A.3.a·Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., <span class="math">\(347.392 = 3 \times 100 + 4 \times 10 + 7 \times 1 + 3 \times (1/10) + 9 \times (1/100) + 2 \times (1/1000)\)</span>.

20 min

15 min