An Assortment of Fractions

10 min

Narrative

This Warm-up prompts students to carefully analyze and compare fractions or expressions containing fractions. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminology students use to talk about the size of fractions, equivalence, mixed numbers, and addition of fractions. The reasoning also helps students to recall familiar relationships between fractions where one denominator is a factor or a multiple of the other. This awareness will be helpful later when students solve problems that involve combining quantities with different fractional parts.

Launch

  • Groups of 2
  • Display the numbers and expressions.
  • “Pick 3 expressions 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

112\displaystyle{1\frac{1}{2}}

B

44+24\displaystyle{\frac{4}{4} + \frac{2}{4}}

C

128\displaystyle{\frac{12}{8}}

D

46\displaystyle{\frac{4}{6} }

Sample Response

Sample responses:

A, B, and C go together because:

  • Their value is the same as 64\frac{6}{4}.
  • Their value is greater than 1.

A, B, and D go together because:

  •  They have single digit numerators.

A, C, and D go together because:

  •  They include just one fraction.

B, C, and D go together because:

  • They are written with only numerators and denominators.
Activity Synthesis (Teacher Notes)
  • “What are some fractions that are equivalent to the expressions in A, B, and C?” (32\frac{3}{2}, 64\frac{6}{4}, 96\frac{9}{6}, 1510\frac{15}{10}, 1812\frac{18}{12})
  • “What are some ways to decide if two fractions are equivalent?” (Think about the relationship of unit fractions—for instance, the number of one-eighths that are in one-fourth, compare the fractions to a benchmark—for instance, if one fraction is greater than 1 and the other less than 1, then they’re not equivalent, or see if the numerator and the denominator of one fraction could be multiplied by the same factor to get the other fraction.)
Standards
Building On
  • 4.NF.1·Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
  • 4.NF.3.c·Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
  • 4.NF.A.1·Explain why a fraction <span class="math">\(a/b\)</span> is equivalent to a fraction <span class="math">\((n \times a)/(n \times b)\)</span> by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
  • 4.NF.B.3.c·Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

15 min

20 min