Ordering fractions and decimals

Ordering a mixed list is really a translation job. Fractions, decimals, and mixed numbers can only be lined up once they speak the same language, which at this level usually means decimals to the thousandths or a shared denominator.

The rows climb in difficulty. Row 1 sorts almost at a glance by whole parts. Row 3 asks your child to place 0.7140 just below 5/7, which is 0.714285 and keeps going. Row 6 sets 5.0003 next to 5 3/1000, which is 5.003, so the thousandths place decides.

Ordering rational numbers is 6.NS.C.7.

It rests on comparing decimals to thousandths, 5.NBT.A.3.b.

Every row starts with a direction, and half the trouble lives there. "Which way does this row go, up or down?" Have your child circle greatest or least before writing anything.

Row 7 deserves the slowest pace: 2 4/7, 15/6, 2.57, 2 3/7, 2.571. "What is 4/7 as a decimal, to four places?" At 2.5714 it edges past 2.571 by a hair.

Mixed numbers fool the eye when the whole parts match, because then the fraction part decides everything.

A note for parents on row 8: the answer page lists 1002/1000, 102/100, 1 1/1000, 1 1/100, but from least to greatest the order is 1 1/1000, 1002/1000, 1 1/100, 102/100, that is 1.001, 1.002, 1.01, 1.02.

Race results are a ready-made ordering problem. After a swim meet or a school race, write three times such as 12.5, 12 1/4, and 12.48 seconds, and let your child rank the finishers.

At the store, prices mix forms in your head: $2.50, two and a quarter dollars, $2.48. Which is cheapest, and how did your child decide?

The Grapes of Math by Greg Tang trains the same habit of seeing smart groups instead of counting one by one, and it makes a light follow-up.

Whichever row gave trouble, point out the habit that worked: "You put every number in the same form first." Fractions as division, in word problems, close the series.