Sums of Tenths and Hundredths

10 min

Narrative

This Warm-up prompts students to carefully analyze and compare the features of four fractions. 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 characteristics of the items in comparison to one another. During the discussion, ask students to explain the meaning of any terms they use. They may consider size (of the fraction, the numerator, or the denominator), equivalence, relationship to benchmark numbers, and more. The reasoning here will be helpful later in the lesson, as students classify sums of fractions by their size and relationship to 1.

Launch

  • Groups of 2
  • Display the four expressions.
  • “Pick 3 fractions 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. 48100\displaystyle \frac{48}{100}
  2. 810\displaystyle \frac{8}{10}
  3. 120100\displaystyle \frac{120}{100}
  4. 70100\displaystyle \frac{70}{100}

Sample Response

Sample response:

A, B, and C go together because:

  • Their numerators are multiples of 4 or 8.

A, B, and D go together because:

  • They are all less than 1.

A, C, and D go together because:

  • They are all hundredths.
  • The denominator is 100.

B, C, and D go together because:

  • They can be written as equivalent tenths.
Activity Synthesis (Teacher Notes)
  • “Are any of these fractions equal to 1? How do you know?” (No, because none of them are 1010\frac{10}{10} or 100100\frac{100}{100}).
  • “Which of these fractions are greater than 1? How do you know?” (120100\frac{120}{100}, because it is greater than 100100\frac{100}{100}.)
  • "For Fractions B and D, how much more to equal 1?" (210\frac{2}{10}or an equivalent fraction, and 30100\frac{30}{100} or an equivalent 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.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.

20 min

15 min