Add and Subtract Fractions

10 min

Narrative

This Warm-up prompts students to compare four representations of fractions (fraction strips and number lines) that they have seen in an earlier course. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology to talk about the characteristics of the items in comparison to one another. During the discussion, ask students to explain the meanings of any terms they use, such as: equivalent fractions, thirds, sixths, twelfths, the whole. These representations will be useful to students in this lesson, and in future lessons, as they think about representing equivalent fractions.

Launch

  • Groups of 2
  • Display the image.
  • “Pick 3 representations that go together. Be ready to share why they go together.”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 2–3 minutes: partner discussion
  • Share and record responses.

Student Task

Which 3 go together?

A
Diagram. Two rectangles of equal length. Top rectangle, split into 3 equal parts, 2 parts shaded. Bottom rectangle, split into 6 equal parts, 4 shaded. Total length, 1.

B
<p>Two number lines of equal length.</p>
Two number lines of equal length. Top number line. From 0 to 6 thirds. Evenly spaced by thirds. Bottom number line. From 0 to 12 sixths. Even spaced by sixths. 

C
Diagram. Two rectangles of equal length.
Diagram. Two rectangles of equal length. Top rectangle split into three parts. Each labeled 1 third. First two parts shaded. Bottom rectangle split into 12 parts. Each labeled 1 twelfth. 8 shaded. 

D
<p>Number line. From 0 to 6 sixths. Evenly spaced by sixths. </p>

Sample Response

Sample responses:

A, B, and C go together because:

  • They show 2 representations of fractions.
  • They show thirds.

A, B, and D go together because:

  • They show sixths. 

A, C, and D go together because:

  • They stop at 1.

B, C, and D go together because:

  • They have labels that are fractions.
Activity Synthesis (Teacher Notes)
  • “How do Diagrams B and C help us see the relationship between thirds, sixths, and twelfths?” (We can see that 13=412\frac{1}{3}=\frac{4}{12} and 13=26\frac{1}{3}=\frac{2}{6}.)
Standards
Building Toward
  • 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

20 min