Fractions as Sums

10 min

Narrative

The purpose of this Choral Count is to invite students to practice counting by 34\frac{3}{4} and to notice patterns in the count. The patterns they recognize here will be helpful when students decompose fractions into sums of 34\frac{3}{4}s in a problem later in the lesson. The exercise also draws students’ attention to multiples of 34\frac{3}{4} that are equivalent to whole numbers, which will be helpful as students compose and decompose mixed numbers.

Launch

  • “Count by 34\frac{3}{4}, starting at 34\frac{3}{4}.”
  • Record as students count.
  • Stop counting and recording at 484\frac{48}{4}.
Teacher Instructions
  • “What patterns do you see?” (The numerator is increasing by 3 each time. The numerators are multiples of 3. In every fourth fraction in the list, the numerator is a multiple of 4.)
  • 1–2 minutes: quiet think time
  • Record responses.

Sample Response

34 64 94 124\frac{3}{4} \ \quad \frac{6}{4} \ \quad \frac{9}{4} \ \quad \frac{12}{4}

154184214244\frac{15}{4} \quad \frac{18}{4} \quad \frac{21}{4} \quad \frac{24}{4}

274304334364\frac{27}{4} \quad \frac{30}{4} \quad \frac{33}{4} \quad \frac{36}{4}

394424454484\frac{39}{4} \quad \frac{42}{4} \quad \frac{45}{4} \quad \frac{48}{4}

Activity Synthesis (Teacher Notes)
  • “Which of these fractions are equivalent to whole numbers?” (124,244,364,484\frac{12}{4}, \frac{24}{4}, \frac{36}{4}, \frac{48}{4})
  • “To what whole numbers are they equivalent?” (3, 6, 9, 12)
  • “Why do you think these patterns are happening?” (The number of parts and the size of each part that is added stay the same each time, so the numerator always increases by 3 and the denominator always stays the same.)
Standards
Building On
  • 3.NF.1·Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
  • 3.NF.A.1·Understand a fraction <span class="math">\(1/b\)</span> as the quantity formed by 1 part when a whole is partitioned into <span class="math">\(b\)</span> equal parts; understand a fraction <span class="math">\(a/b\)</span> as the quantity formed by <span class="math">\(a\)</span> parts of size <span class="math">\(1/b\)</span>.
Building Toward
  • 4.NF.3·Understand a fraction a/b with a &gt; 1 as a sum of fractions 1/b.
  • 4.NF.B.3·Understand a fraction <span class="math">\(a/b\)</span> with <span class="math">\(a &gt; 1\)</span> as a sum of fractions <span class="math">\(1/b\)</span>.

20 min

15 min