Subtract Fractions Flexibly

10 min

Narrative

This Warm-up prompts students to carefully analyze subtraction expressions containing two fractions or a whole number and a fraction. 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 these expressions. To compare the values of the expressions, students need to perform subtraction and apply their knowledge of equivalence. The reasoning here also will be helpful later as students reason about differences of two mixed numbers or a mixed number and a fraction.

Launch

  • Groups of 2
  • Display the 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?

  1. 2−35\displaystyle 2-\frac{3}{5}
  2. 105−35\displaystyle \frac{10}{5} - \frac{3}{5}
  3. 135−15\displaystyle 1\frac{3}{5}-\frac{1}{5}
  4. 105−1\displaystyle \frac{10}{5} - 1

Sample Response

  • A, B, and C go together because their value is 75\frac{7}{5}.
  • A, B, and D go together because the first number is equivalent to 2.
  • A, C, and D go together because they include whole numbers or mixed numbers.
  • B, C, and D go together because the first number is written as a fraction or a mixed number.
Activity Synthesis (Teacher Notes)
  • “Why do all 4 go together?” (All are subtraction expressions that have fractions, whole numbers, or mixed numbers. We had to find their values to compare them.)
  • "As you compared the expressions, what strategies did you use to find their values?"
Standards
Addressing
  • 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.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