Fraction Classroom · 2.4.0 · Student pages

Rebuild a missing whole from a known fraction

Use a labelled fragment to reconstruct its reference whole, then prove that the reconstructed whole gives the original fraction.

Anonymous group code: __________ Date: __________

The first three equal boxes represent the known 9 cm fragment. The fourth completes the same whole; it is the same size as the others.

Build the idea

Read the fraction as a relationship to the missing whole. The 9 cm fragment is three quarters, not the entire reference strip.
Draw three equal boxes for the known fragment and label their combined length 9 cm. Share that length across the boxes: each box represents 3 cm.
Add one more equal box to complete four quarters. Four copies of 3 cm produce a whole strip of 12 cm.
Check the reconstructed whole: splitting 12 cm into four equal parts gives 3 cm per quarter, and three quarters recover the original 9 cm fragment.

Worked example: 12 cm. The 9 cm fragment contains three equal quarter-parts, so each quarter is 3 cm. Four such parts make the whole.

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