True or False?

10 min

Narrative

The purpose of this True or False? is to elicit strategies students have for adding fractions with unlike denominators. The reasoning students do here helps to deepen their understanding of the properties of operations. It will be helpful later in this lesson when students develop their own True or False? activity.

In the Activity Synthesis, it is important to discuss things the writer had to pay attention to when they designed this activity.

Launch

  • Display one equation.
  • “Give me a signal when you know whether the equation is true and can explain how you know.”
  • 1 minute: quiet think time
Teacher Instructions
  • Share and record answers and strategies.
  • Repeat with each equation.

Student Task

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

  • 34+38=38+38\frac{3}{4}+\frac{3}{8} = \frac{3}{8}+\frac{3}{8}
  • 75+23=2115+815\frac{7}{5}+\frac{2}{3} = \frac{21}{15}+\frac{8}{15}
  • 89+512=3236+1536\frac{8}{9}+\frac{5}{12}=\frac{32}{36}+\frac{15}{36}

Sample Response

  • False: 34\frac{3}{4} is not equal to 38\frac{3}{8}.
  • False: 23=1015\frac{2}{3}=\frac{10}{15}.
  • True: 89=3236\frac{8}{9}=\frac{32}{36} and 512=1536\frac{5}{12}=\frac{15}{36}.
Activity Synthesis (Teacher Notes)
  • “What did the writer of this activity have to pay attention to when they designed this activity?” (Some equations are true, and some are false. Some terms on both sides are equal. Pay attention to the unlike and like denominators.)
  • “Where do we see those things in how the equations change during the True or False?” (The first two equations are false, but they use an appropriate common denominator.)
Standards
Addressing
  • 5.NF.1·Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. <em>For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)</em>
  • 5.NF.A.1·Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. <span>For example, <span class="math">\(2/3 + 5/4 = 8/12 + 15/12 = 23/12\)</span>. (In general, <span class="math">\(a/b + c/d = (ad + bc)/bd\)</span>.)</span>

15 min

15 min

15 min