Why 0.35 looks bigger than 0.5 to a fourth grader, and what to print

Ask a fourth grader which is bigger, 0.5 or 0.35, and a surprising number say 0.35, because 35 is bigger than 5. They aren't being careless. They are applying everything they know about whole numbers to a place where it stops working, and the only fix is enough decimal problems for the new rules to take over.

What the sheet looks like

The decimals worksheet has five modes: Add, Subtract, Compare (< > =), Round, and Mixed. Decimal places are Tenths (0.x), Hundredths (0.xx) or Mixed. On a tenths-only Round sheet every problem rounds to the nearest whole; with hundredths, the problems alternate between the nearest whole and the nearest tenth so the child has to read which is being asked. Compare problems are written so that pairs like 0.5 and 0.50 turn up and have to be called equal. Pages hold 12 to 24 problems with an optional answer key.

Why it works

• Comparing with mixed places attacks the "longer is bigger" error head on. 0.5 against 0.35 has to be settled by place, not by length.
• Adding 3.4 to 2.75 is where column alignment breaks for the first time. Lining up the decimal point instead of the right-hand edge is a new habit and needs its own page.
• Rounding to the nearest tenth is the one most children haven't done before. Mixing it with rounding to the whole forces them to read the instruction every time.

Who it suits

Nine-year-olds start with Compare on Tenths, twelve problems. Twelve-year-olds can take Mixed on Hundredths with 24. The sheet assumes the child already knows what 0.3 means; if that is shaky, do tenths as fractions first, and make sure whole-number rounding is solid with the rounding worksheet before rounding decimals.

Money is the fastest bridge. 0.5 is fifty cents, 0.35 is thirty-five cents, and the argument is over.