Symmetry in Figures (Part 2)

10 min

Narrative

This Number Talk encourages students to think about place value and to rely on the structure of multi-digit numbers and properties of operations to mentally add multiple addends. The strategies elicited here help students develop fluency in adding multi-digit numbers. They will also be helpful when students reason about the perimeter and angles in line-symmetric figures.

Launch

  • Display one expression.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time
Teacher Instructions
  • Record answers and strategy.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally. 

  • 43+57+50+7+3+4043 + 57 + 50 + 7 + 3 + 40
  • 243+57+43+257243 + 57 + 43 + 257
  • 1,043+257+57+200+43+1,0001,043 + 257 + 57 + 200 + 43 + 1,000
  • 1,943+257+1+257+1,000+9431,943 + 257 + 1 + 257 + 1,000 + 943

Sample Response

  • 200: There are two sets of 43+5743 + 57, one of them is written in expanded form. 43+57=10043 + 57 = 100, because 40+50=9040 + 50 = 90, 7+3=107 + 3 = 10, and 90+10=10090 + 10 = 100. Two times 100 gives 200.
  • 600: 43+57=10043 + 57 = 100, so 243+257243 + 257 is 200+200+100200 + 200 + 100, which is 500. Adding another 43+5743 + 57 to 500 makes 600.
  • 2,600: 
    • The expression has two sets of 257+43257 + 43 (just written differently), plus two 1,000s. 257+43=300257 + 43 = 300, and twice 300 is 600. Adding the 2,000 and 600 makes 2,600.
    •  257+243=500257 + 243 = 500, 57+43=10057 + 43 = 100, and 1,000+1,000=2,0001,000 + 1,000 = 2,000, so 2,000+500+100=2,6002,000 + 500 + 100 = 2,600.
  • 4,401: 
    • The expression is symmetrical, with 1 in the middle and 1,943+2571,943 + 257 (written in different forms) on either side. We know that 43+257=30043 + 257 = 300, and 1,900+300=2,2001,900 + 300 = 2,200. Twice 2,200 is 4,400. Adding the middle 1 gives 4,401.
    • 943+257=1,200943 + 257 = 1,200, and 1,943+257=2,2001,943 + 257 = 2,200. Adding 1,200 and 2,200 gives 3,400. Adding 1,000+11,000 + 1 to 3,400 makes 4,401.

Synthesis

  • “How did you use the first expression to help solve the expressions that follow?” (43+57=10043 + 57 = 100, so anywhere we see numbers with that combination being added, we can add 100 instead.)
  • Consider asking:
    • “Who can restate _____’s reasoning in a different way?”
    • “Did anyone have the same strategy but would explain it differently?”
    • “Did anyone approach the expression in a different way?”
    • “Does anyone want to add on to _____’s strategy?”
Standards
Addressing
  • 4.NBT.B·Use place value understanding and properties of operations to perform multi-digit arithmetic.
  • 4.NBT.B·Use place value understanding and properties of operations to perform multi-digit arithmetic.

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