Use Expressions with the Same Value

10 min

Narrative

The purpose of this True or False? is for students to demonstrate the strategies they have for using equivalent fractions to add and subtract fractions with different denominators. These mental calculations prepare students for working with more complex common denominators during the lesson. 

Launch

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

Student Task

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

  • 14+24=34\frac{1}{4}+\frac{2}{4}=\frac{3}{4}
  • 12+14=24\frac{1}{2}+\frac{1}{4}=\frac{2}{4}
  • 34−12=24\frac{3}{4}-\frac{1}{2}=\frac{2}{4}

Sample Response

  • True: I just know it.
  • False: 24=12\frac{2}{4}=\frac{1}{2}, so 12+14\frac{1}{2}+\frac{1}{4} has to be more than 12\frac{1}{2}.
  • False: 34−14=24\frac{3}{4}-\frac{1}{4}=\frac{2}{4} and 12\frac{1}{2} is more than 14\frac{1}{4}.
Activity Synthesis (Teacher Notes)
  • “How can we find the correct value of 34−12\frac{3}{4}-\frac{1}{2}?” (12=24\frac{1}{2}=\frac{2}{4} so 34−24=14\frac{3}{4}-\frac{2}{4}=\frac{1}{4})
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