How to teach decimals

Grade 4 to Grade 6

Decimals extend place value to the right of the ones: tenths, hundredths, thousandths. 0.7 is seven tenths, the same value as 7/10. Money is the everyday model , $3.45 is 3 ones, 4 tenths (of a dollar) and 5 hundredths. Decimals let us write in-between amounts without fractions.

How to teach it

1. Anchor to fractions first: 0.1 IS one tenth. Show the same amount three ways: 1/10, 0.1, and one slice of a ten-strip.
2. Extend the place-value chart rightwards: ones, then a decimal point, then tenths and hundredths.
3. Use money constantly , cents are hundredths of a dollar, so $0.25 is 25 hundredths.
4. Compare decimals by lining up the point and padding with zeros: 0.5 vs 0.45 becomes 0.50 vs 0.45.
5. Add and subtract with the points lined up vertically, exactly like whole-number columns.

Common mistakes

• Reading 0.45 as 'bigger than 0.5 because 45 > 5' , the classic longer-is-larger error.
• Lining numbers up by their last digit instead of by the decimal point.
• Saying 'point four five' without ever naming it as tenths and hundredths, so place value never lands.
• Thinking multiplying always makes numbers bigger (0.5 × 8 = 4).