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Fraction strips

A fraction wall from halves to twelfths. Shade pieces to add them up, point at one to see what it equals, and print the strips to cut out.

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Fraction strips

Show these rows

US Letter, a whole and 11 rows as a wall, labelled with fractions, in colour

Tap pieces to shade them and add them up. Point at a piece, or move to it with the arrow keys, to see which pieces line up with it.

 

Nothing shaded yet.

Compare two fractions

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Fraction stripsstringmash.com/fraction-strips

Using the strips

Pick the rows first. Halves to twelfths gives the full wall of 12 rows, with the whole on top. The shorter sets keep to one family, such as halves, quarters and eighths, where every edge lines up with the row below. Tick or untick any row to make your own.

Tap a piece to shade it. The line under the wall adds up everything shaded, finds a common denominator when the rows differ, and gives the answer in lowest terms. Shade one third and one sixth and it reads 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2.

Point at a piece and every run that ends in the same place lights up. On a keyboard, tab to the wall and move with the arrow keys.

Printing gives the wall on its own, drawn to fill the page inside the margins. Strips to cut apart leaves a gap between rows for scissors. Labels can be fractions, decimals or percents, or left off so children can write their own. Leave A blank sheet too ticked and a second page prints with every piece empty and uncoloured.

Equivalent fractions

Two fractions are equivalent when they take up the same length of the strip. Line the half up against the rows below it and it matches 2/4, 3/6, 4/8, 5/10 and 6/12. That's six rows on the full wall, more than any other fraction.

Sevenths and elevenths are the loners. Their edges never meet another row's until the end of the whole, because 7 and 11 are prime and no other row is a multiple of them. Fifths only match tenths.

This is the picture Common Core asks for in Grade 3, where pupils explain why 1/2 = 2/4 and 4/6 = 2/3 'by using a visual fraction model', with denominators kept to 2, 3, 4, 6 and 8. The Grade 3 preset shows exactly those rows. In England, Year 3 pupils 'recognise and show, using diagrams, equivalent fractions with small denominators', and Year 4 moves on to families of them (DfE national curriculum).

Comparing fractions

Is 3/4 bigger than 2/3? Pick them in Compare two fractions and the two bars sit one above the other, both the same whole. The longer shaded part wins. Underneath, the tool writes both over a common denominator, 9/12 against 8/12, so the reason is there in numbers too.

Same denominator is the easy case, because more pieces of the same size is more. Same numerator catches children out. 1/3 is bigger than 1/4, since a whole cut into fewer pieces has bigger pieces, and a wall makes that plain at a glance.

Both bars measure the same whole. Grade 3 and Grade 4 both say comparisons only work 'when the two fractions refer to the same whole', and a strip of the same length is the easiest way to keep it so.

Adding with strips

With like denominators, adding is counting pieces. Shade two eighths and three eighths and you have five eighths, 2/8 + 3/8 = 5/8. Year 3 in England adds fractions with the same denominator within one whole; in the US it's Grade 4, 4.NF.B.3.

Unlike denominators need a row both fractions fit. To add 1/2 and 1/3, look for the row where both line up, sixths, and count 3/6 + 2/6 = 5/6. The sum line does this with the lowest common denominator every time. Common Core puts it in Grade 5, 5.NF.A.1, with the example 2/3 + 5/4 = 8/12 + 15/12 = 23/12.

Totals over one come out as mixed numbers. For longer sums with the working written out, the fraction calculator takes any denominators, and fraction worksheets give practice with an answer key.

Questions

What's the difference between fraction strips, fraction bars and a fraction wall?

Very little. Fraction strips or bars are the separate rows, often cut out so they can be moved and laid side by side. A fraction wall is the same rows stacked as one chart. Print as a wall for a chart, or as strips to cut apart.

Do the strips print the same size on every printer?

The sheet is drawn in millimetres to fit Letter or A4 inside the margins. Set the scale to 100% or Actual size in the print dialog. What matters most is that every row is the same length, and that holds at any scale.

Why do the decimals for thirds look wrong?

They're rounded. 1/3 is 0.333… forever, so it shows as 0.33, and three of them add up to 0.99 on paper. Thirds, sixths, sevenths, ninths, elevenths and twelfths all repeat. Halves, quarters, fifths, eighths and tenths come out exact.

Does the shading print?

No. The printed sheet is a clean wall so it can be used again. Use the blank sheet for children to shade by hand.

What age are fraction strips for?

Any age that's meeting fractions for the first time, and older pupils who need a picture again. Common Core starts unit fractions and equivalence in Grade 3 and adds unlike denominators in Grade 5. In England, Year 2 meets 1/3, 1/4, 2/4 and 3/4, and Years 3 and 4 work on equivalent fractions with diagrams.

Sources

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