Area and Properties of Operations

10 min

Narrative

This Number Talk encourages students to think about equivalent expressions and to rely on the properties of operations to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students match diagrams to expressions.

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.

  • 5×(7+4)5 \times (7 + 4)
  • (5×7)+(5×4)(5 \times 7) + (5 \times 4)
  • (5×7)+(5×14)(5 \times 7) + (5 \times \frac{1}{4})
  • (5×7)−(5×14)(5 \times 7) - (5 \times \frac{1}{4})

Sample Response

  • 55: 5×11=555 \times 11 = 55
  • 55: 35+20=5535 + 20 = 55
  • 361436 \frac {1}{4}: 5×7=355 \times 7 = 35, 5×14=1145 \times \frac {1}{4} = 1\frac {1}{4}, and 35+114=361435 + 1 \frac{1}{4} = 36 \frac {1}{4}
  • 333433 \frac {3}{4}: 5×7=355 \times 7 = 35 and 5×14=1145 \times \frac {1}{4} = 1\frac {1}{4}, and 35−114=333435 - 1 \frac{1}{4} = 33 \frac {3}{4}

Synthesis

“What is the same about the last two expressions? What is different?” (They both have the same two products but one of them is the sum and the other is the difference.)
Standards
Addressing
  • 5.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • 5.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • 5.OA.1·Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
  • 5.OA.A.1·Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

20 min

15 min