Texas Math Models

Try “number line” or “4.5D”

Models & Strategies · Grades 3–4

Fraction Strips: One Whole, Cut Nine Ways

Every strip is the same whole. Only the number of equal parts changes, which is the whole idea behind comparing, ordering and finding equivalent fractions.

1 whole1 wholeGr 31212halvesGr 3131313thirdsGr 314141414fourthsGr 31515151515fifthsGr 4161616161616sixthsGr 31818181818181818eighthsGr 3110110110110110110110110110110tenthsGr 4112112112112112112112112112112112112twelfthsGr 4 the half-way line: halves, fourths, sixths, eighths, tenths and twelfths all have a cut here · thirds and fifths do not
Equivalent fractions; read DOWN a column. Any pieces whose right-hand edges line up are the same amount: 1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12, and 1/3 = 2/6 = 4/12.
Comparing: read ACROSS a column. The further down the wall you go, the more pieces the whole is cut into, and the smaller every one of those pieces gets: 1/12 < 1/10 < 1/8 < 1/6 < 1/5 < 1/4 < 1/3 < 1/2.
Making one whole; read along a ROW. Every row adds back up to exactly 1: 1/4 + 1/4 + 1/4 + 1/4 = 1, and 12/12 = 1. That is why a fraction with the same top and bottom number is always one whole.
Why these nine and no others. These are the denominators Texas actually tests. Grade 3 works with 2, 3, 4, 6 and 8 (TEKS 3.3A); Grade 4 adds 5, 10 and 12. Sevenths, ninths and elevenths appear on most fraction walls but are not tested in either grade, so they are left off: nothing here is padding.

seen one of these on a test? See it on a real question: TEKS 4.3D, comparing two fractions.