A fraction wall from one whole to twelfths, cut out or on the page

Why is 1/8 smaller than 1/4 when 8 is bigger than 4? Every child asks it, and no explanation works as well as laying an eighth strip on top of a quarter strip and seeing it. Fraction strips are the cheapest manipulative there is, if you can print them.

What the sheet looks like

The fraction strips generator prints six sheets. The fraction wall is a full page of rows, one whole at the top and then halves, thirds, fourths, fifths, sixths, eighths, tenths and twelfths, whichever rows you tick. Cut-out strips put the same rows on one or two sheets with cut lines. Fraction circles come 4 or 6 to a sheet. The equivalence chart adds dotted vertical lines at 1/4, 1/3, 1/2, 2/3 and 3/4 so the eye can follow 2/4 down to 4/8. A blank wall has the rows but no divisions, for the child to split and label.

Labels can be fractions, decimals, percents or blank. The fraction pizza is the odd one out: a pizza with toppings on some slices and questions like what fraction has pepperoni, with an answer key.

Why it works

• Comparing 1/8 to 1/4 by stacking strips makes the denominator rule visible before it is ever stated.
• Switching labels from fractions to decimals on the same wall shows that 0.5 and 1/2 are one thing. That connection often takes a year to land without it.
• Blank labels turn the manipulative into the worksheet. If a child can label the eighths row on their own, they understand eighths.

Who it suits

Grades 2 to 5. Halves, fourths and eighths with fraction labels suit second and third grade. Add thirds, sixths and twelfths and the equivalence chart in fourth. Decimal and percent labels are fifth-grade material, and the blank wall is a good test at any point. For a child who does not yet see that the parts have to be equal, start with the equal parts sheet, then come back.

Print the strips on colored paper, one color per row, and they stop getting mixed up.