Introduction to Addition Algorithms

10 min

Narrative

This Warm-up prompts students to compare three expressions and one three-digit number. In making comparisons, students have a reason to use language precisely (MP6). During the discussion, ask students to explain the meaning of any terms they use, such as “the value of each expression,” and the different ways that place value was used to write the number 247.

Launch

  • Groups of 2
  • Display the expressions and the number.
  • “Pick 3 representations 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.  200+30+17200 + 30 + 17

B.  247

C.  200+47+10200 + 47 + 10

D.  100+140+7100 + 140 + 7

Solution Steps (5)
  1. 1
    Evaluate A: 200 + 30 + 17
    →200 + 30 + 17 = 247 (30+17 = 47, so 200+47=247)
  2. 2
    Evaluate B: 247
    →247 (standard numeral)
  3. 3
    Evaluate C: 200 + 47 + 10
    →200 + 47 + 10 = 257 (not 247)
  4. 4
    Evaluate D: 100 + 140 + 7
    →100 + 140 + 7 = 247 (100+140=240, 240+7=247)
  5. 5
    Identify which 3 have value 247
    →A, B, D all equal 247

Sample Response

Sample responses:

A, B, and C go together because:
  • They have the digit 2 in them to show 2 hundreds.
A, B, and D go together because:
  • They have a value of 247.
A, C, and D go together because:
  • They are expressions.
B, C, and D go together because:
  • They have the digit 4 in them to show 4 tens. 
Activity Synthesis (Teacher Notes)
  • “How did you know that A and D were equal to 247?” (In A, there were 2 hundreds, 4 tens, and 7 ones, but 1 ten was with the ones. In D, there were 2 hundreds, 4 tens, and 7 ones, but 1 hundred was with the tens.)
Standards
Addressing
  • 3.NBT.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
  • 3.NBT.A.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

15 min

20 min