Will It Always Work?

10 min

Narrative

The purpose of this True or False? is for students to demonstrate the strategies they have for comparing expressions. The reasoning students use here helps to deepen their understanding of the properties of operations. It also will be helpful later when students compare expressions and generalize their understanding of how the size of a number changes when multiplied by a fraction less than 1, a fraction equal to 1, and a fraction greater than 1.

Launch

  • Display the first equation.
  • “Give me a signal when you know whether or not the equation is true and can explain how you know.”
  • 1 minute: quiet think time
Teacher Instructions
  • Share and record students’ answers and strategies.
  • Repeat with each equation.

Student Task

Decide if each statement is true or false. Be prepared to explain your reasoning.

  • 34=1−14\frac{3}{4} = 1-\frac{1}{4}
  • (1−14)×9=9−(14×9)\left(1-\frac{1}{4}\right) \times 9 = 9 - \left(\frac{1}{4} \times 9\right)
  • (1+14)×7=(1×7)+14\left(1+\frac{1}{4}\right) \times 7 = (1 \times 7) + \frac{1}{4}

Sample Response

  • True: 1 is 4 fourths, so taking away 14\frac{1}{4} leaves 34\frac{3}{4}.
  • True: 1 is multiplied by 9, and I take away 14×9\frac{1}{4} \times 9.
  • False: The 1 is multiplied by 7, but the 14\frac{1}{4} is not.

Synthesis

  • Display the expression: (1+14)×7(1+\frac{1}{4})\times 7
  • “How can I rewrite this expression as a sum?” (Multiply 1 and 7 and that's 7, and then add 14×7\frac{1}{4} \times 7.)
  • Display equation: (1+14)×7=(1×7)+(14×7)\left(1+\frac{1}{4}\right) \times 7= (1 \times 7) + \left(\frac{1}{4} \times 7\right)
Standards
Addressing
  • 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