Grade 5: Decimals

Warm up with a quick recall on the board. Connect decimals to place value and money (tenths, hundredths), line up the decimal points, and use a number line to compare and round.

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. Model the method clearly, thinking aloud:

• 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.
• Extend the place-value chart rightwards: ones, then a decimal point, then tenths and hundredths.
• Use money constantly, cents are hundredths of a dollar, so $0.25 is 25 hundredths.
• Compare decimals by lining up the point and padding with zeros: 0.5 vs 0.45 becomes 0.50 vs 0.45.
• Add and subtract with the points lined up vertically, exactly like whole-number columns.

Do the first few questions of the practice worksheet together, one child explaining each step. Check for understanding before releasing the class to work alone.

Students complete the worksheet independently. Hand out the three difficulty levels below so every child works at the right stretch.

Circulate and look for these, they are the usual sticking points:

• 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).
• Thinking a longer decimal is larger (0.45 > 0.5), and mis-aligning place value when adding.

Pull the class back together. Ask one child to explain decimals in their own words, pose a single check question everyone answers on a mini whiteboard, and name what you will build on next lesson.

Use the independent worksheet as the evidence. A child who can complete it accurately and explain one answer has met the objective; anyone who cannot needs the easier level and a short reteach next session.