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Fraction Classroom · 2.4.0 · Student pages

Measure a length when the ruler does not start at zero

Use quarter-inch intervals to read the distance between two marks, then record measurements independently of where an object starts.

Anonymous group code: __________   Date: __________

The highlighted interval begins at 1 1/4 inches and ends at 3 inches. The marks are spaced in quarters of an inch.11 1/41 1/21 3/422 1/42 1/22 3/43
The highlighted interval begins at 1 1/4 inches and ends at 3 inches. The marks are spaced in quarters of an inch.

Build the idea

model. A paper strip starts at the 1 1/4-inch mark and ends at the 3-inch mark. How long is it?

  1. Locate both ends of the strip. The left end sits at 1 1/4 inches, so the first 1 1/4 inches of the ruler are outside the strip.
  2. Count equal quarter-inch intervals from 1 1/4 to 3. Count the spaces traversed, not both endpoint marks as extra pieces.
  3. Group four quarter-inch intervals into one inch. The seven intervals give one inch and three quarters of another inch.
  4. Check by moving the strip's left end to zero on a drawing without stretching it. Its right end would be at 1 3/4, showing that changing the starting position does not change its length.

Worked example: 1 3/4 inches. Seven quarter-inch intervals connect the start to the end; the end reading alone is not the strip length.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. A strip begins at 1/2 inch and ends at 2 1/4 inches. Enter its length in inches.

p2. A strip begins at 2 inches and ends at 4 1/2 inches. Enter its length in inches.

p3. A strip begins at 3/4 inch and ends at 1 1/2 inches. Enter its length in inches.

e1. A strip begins at 1 3/4 inches and ends at 4 inches. Enter its length and explain your interval count.

Transfer the idea

transfer. An object measured from 2 inches to 5 inches is moved so its left end is at 1 inch. Where should its right end be?