Mixed number builder

What the builder shows

An improper fraction such as 11/4 and a mixed number such as 2 3/4 are two ways of writing the same amount. This builder lets you make that amount out of fraction pieces. Choose a piece size from halves to eighths, then add pieces with the buttons or by tapping the circles or bars. When a shape fills, it turns green and counts as 1 whole, and a new empty shape appears. The readout shows the improper fraction and the mixed number side by side and explains how many pieces the wholes used and how many are left over.

Why building helps

The usual rule, divide the numerator by the denominator and keep the remainder, makes more sense once a child has seen it happen. With pieces, 11/4 is eleven fourths: four of them fill a whole, eight fill two wholes, and three are left. That is 2 3/4. Going back is just counting: 2 wholes of 4 pieces is 8 pieces, plus 3 more makes 11. Building numbers this way also shows that improper fractions are not wrong or unfinished, just another way to write an amount.

Common mix-ups

• Thinking an improper fraction is a mistake. 7/4 is a perfectly good number; it is just more than 1.
• Multiplying the wrong numbers. For 2 3/4 it is 2 × 4 + 3 = 11, not 2 × 3 + 4, because two wholes are 8 fourths.
• Changing the denominator when converting. 11/4 = 2 3/4, and the pieces are still fourths.
• Writing the leftover over the wrong number. In 11/4, the 3 pieces left over are fourths, so they go over 4, not over 11.

A 10-minute activity

• Minutes 1 to 3: choose fourths, press Start again and add one piece at a time. At 4/4, stop and ask what happened. Keep going to 11/4.
• Minutes 4 to 6: choose halves and build 3 1/2 with the whole and piece buttons. Ask how many halves it took.
• Minutes 7 to 8: switch to bars and build 13/6. Ask the child to say the mixed number before reading it.
• Minutes 9 to 10: press Challenge two or three times. During a challenge the readout only counts pieces, so the child does the converting.

Where it fits by grade

• Grade 3: whole numbers written as fractions and fractions equal to whole numbers, such as 4/4 = 1 and 6/2 = 3 (Common Core 3.NF.A.3c).
• Grade 4: a fraction such as 5/4 as a sum of unit fractions, 1/4 + 1/4 + 1/4 + 1/4 + 1/4 (4.NF.B.3), and adding and subtracting mixed numbers by replacing them with equivalent fractions (4.NF.B.3c).
• Grade 5: mixed numbers in adding, subtracting and multiplying fractions.
• England: Year 5 pupils recognize mixed numbers and improper fractions, convert from one form to the other, and write answers greater than 1 as mixed numbers, such as 2/5 + 4/5 = 6/5 = 1 1/5.

Learning more

Mixed numbers and improper fractions is a skill on Eurekami's skill map. Lessons draw fraction pieces from each question's numbers, and Daily Practice brings conversions back every so often, since they come up again in every later fraction topic.