Zeros in the Standard Algorithm

10 min

Narrative

This Warm-up prompts students to carefully analyze and compare features of multi-digit numbers. In making comparisons, students have a reason to use language precisely (MP6), especially place value names. The activity also enables the teacher to hear how students talk about the meanings of non-zero digits in different places of a multi-digit number.

Students observations will support their reasoning in the next activity when they subtract a number with non-zero digits from the four numbers listed.

Launch

  • Groups of 2
  • Display numbers.
  • “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?

  1. 2,050
  2. 2,055
  3. 205.2
  4. 20,005

Sample Response

Sample responses:

  • A, B, and C go together because they have 4 digits.
  • A, B, and D go together because they are whole numbers.
  • A, C, and D go together because they only have one 5 as a digit.
  • B, C, and D go together because they have 5 in the ones place.
Activity Synthesis (Teacher Notes)
  • “What if we subtracted 44 from each whole number?” Record “– 44” under each whole number.
  • “Which number would it be easiest to subtract 44?” (2,055−44(2,055 - 44 because you don’t have to decompose units.)
  • “How could we subtract 44 from the other whole numbers?” (We would have to decompose other place values.)
Standards
Addressing
  • 4.NBT.2·Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
  • 4.NBT.A.2·Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using <span class="math">\(&gt;\)</span>, =, and <span class="math">\(&lt;\)</span> symbols to record the results of comparisons.

20 min

15 min