Decimals

Decimals are formally introduced in 4th grade, usually starting with tenths and hundredths and tied directly to fractions (0.3 is the same as 3/10). Fifth grade extends place value through thousandths and brings full operations: adding, subtracting, multiplying, and dividing decimals. Sixth grade builds on this for percent and ratio work, and 7th uses decimal fluency constantly in pre-algebra.

The conceptual heart of decimals is place value extended past the ones place. Each position to the right of the decimal point represents one-tenth the value of the position to its left, the same pattern as whole numbers but in the other direction. Students who understand this can reason about decimals; students who don't end up memorizing disconnected rules — line up the decimal points, count places when multiplying, move the decimal when dividing — that they later forget or misapply.

The two reliable trip-ups are decimal multiplication (why does 0.3 × 0.2 = 0.06, not 0.6) and comparing decimals (kids often think 0.45 is bigger than 0.5 because 45 is bigger than 5). Both are place-value problems. Spend time on base-ten blocks or money models — a dollar as the whole, a dime as a tenth, a penny as a hundredth — before any algorithm.

Useful approaches and tools:

• Money models for tenths and hundredths — kids already know $0.50 is half a dollar
• Decimal grids (10x10 squares) for visualizing tenths, hundredths, and decimal multiplication
• Always translating between decimal and fraction form so they stay connected
• Real-world practice: gas prices, race times, batting averages, measurement in centimeters

To check understanding, ask which is bigger, 0.7 or 0.65, and have your student explain why. The right answer with a wrong explanation (it has more digits) is still a problem. Make them justify with a model or a fraction equivalent until the reasoning is solid.