Fraction Classroom · 2.0.0 · Student pages

Count how many unit fractions fit

Measure a whole-number amount with a unit-fraction scoop and explain why the number of groups can exceed the starting number.

Anonymous group code: __________   Date: __________

Quick diagnosis

Try all three. Explain with words, a sketch, or objects.

d1. How many 1/2-liter bottles can be filled from 3 liters?

d2. A student says 2 ÷ 1/4 must be less than 2 because it is division. Explain using quarter-sized groups.

d3. Which equation describes “4 meters cut into 1/3-meter pieces”: 4 ÷ 1/3 or 1/3 ÷ 4? What does the answer count?

Worked examples

Study the example that matches the difficulty. Keep the other for a second session.

w1. How many 1/4-meter pieces can be cut from 3 meters of ribbon?

  1. Draw 0 to 3 meters with whole-meter landmarks.
  2. Divide each meter into four quarter-meter intervals.
  3. Count all twelve intervals as the pieces that fit.
  4. Check: 12 × 1/4 meter = 3 meters.

Worked example: 12 pieces.

w2. A 2-liter jug fills cups holding 1/6 liter each. How many full cups can it fill?

  1. One liter fills six cups of size 1/6 liter.
  2. Two liters contain two sets of six such cups.
  3. Count 2 × 6 = 12 cups.
  4. Check that twelve sixth-liters make 12/6 = 2 liters.

Worked example: 12 full cups.

Practice

For a short session, choose three tasks. Use the others for a second try or follow-up.

p1. How many 1/3-meter pieces fit in 2 meters? Write a multiplication check.

p2. Find 5 ÷ 1/2. Explain without using an invert-and-multiply rule.

p3. A tray holds 4 liters of soup. Each serving is 1/8 liter. How many servings are available?

p4. Which makes more pieces from the same 3-meter ribbon: pieces of size 1/4 meter or 1/6 meter? Give both counts.

p5. A student writes 3 ÷ 1/5 = 3/5. Check the proposed answer by multiplying it by 1/5, then repair it.

p6. Write a story for 2 ÷ 1/4. State what the 2, the 1/4, and the answer mean.

Transfer check

Try one independently. Save the other for a later check.

t1. A maker has 5 meters of wire and cuts 1/3-meter pieces with no waste. There must be at least 14 pieces. Is there enough wire? Explain with division and a multiplication check.

t2. Compare these stories: A shares 1/4 liter among 3 people. B pours 3 liters into 1/4-liter cups. Write both expressions and explain why their answers have different meanings.