Introduction to Decimal Fractions

Materials

• A decimal board: a sheet of paper turned sideways and ruled into four columns labeled UNITS, TENTHS, HUNDREDTHS, THOUSANDTHS, with a large bold dot drawn between units and tenths
• Small counters in four colors — dark green for units, pale blue for tenths, pink for hundredths, pale green for thousandths (buttons, beads, or colored paper squares work; if you cannot match the colors, four clearly labeled cups do the job)
• Four small cups or dishes to hold each supply of counters
• Slips of paper with decimal numbers written on them, such as 0.3, 2.47, and 1.359
• Pencil and paper for writing the numbers your child builds

No materials at home? Use the virtual Decimal Board.

Before this lesson

• Adding & Subtracting Fractions
• The Large Bead Frame

Aims

Presentation

1. 1 Sit beside your child with the board and the four cups of counters. Point to the units column and recall the familiar pattern from the golden beads: ten units made a ten, ten tens made a hundred.You know that ten of something always trades for one of the next bigger place. Today we go the other direction — smaller than one.
2. 2 Place one dark green counter in the units column.This is one whole unit.
3. 3 Point to the big dot drawn between the units and tenths columns, tracing it with a finger.This dot is the decimal point. Everything on the other side of it is smaller than one whole.
4. 4 Place one pale blue counter in the tenths column.If we cut one unit into ten equal pieces, each piece is one tenth. Ten tenths make one whole unit.
5. 5 Count ten pale blue counters into the tenths column, one at a time, then trade them all for one green unit, sweeping your hand left across the decimal point as you do.Ten tenths — trade! — one unit. The rule is the same as always.
6. 6 Introduce the pink counter in the hundredths column the same way, and let your child do the ten-for-one trade into tenths themselves.If we cut a tenth into ten pieces, each piece is one hundredth. Ten hundredths make one tenth.
7. 7 Introduce the pale green thousandth last, and have your child say the trading rule before making the trade.Ten thousandths make one hundredth. This is the smallest piece on our board.
8. 8 Build a number together: place 2 units, 4 tenths, and 7 hundredths, then read the board from left to right while pointing at each column.Two units, four tenths, seven hundredths — we read it “two point four seven,” or “two and forty-seven hundredths.”
9. 9 Take turns with the problem slips: you read a number aloud and your child builds it, then your child builds a secret number and you read it. Include a number with an empty place, like 2.05.Can you build one point three five nine?
10. 10 Show how to record a built number: write one digit for each column in order, copying the decimal point between the units and tenths digits. Have your child write the last few themselves.We write exactly what the board shows — one digit for every column, and the point right after the units.

Points of interest

• The pattern never breaks: ten of anything, anywhere on the board, trade for one of the next place to the left
• The pale colors are a mirror of the strong ones — pale blue tenths echo the blue tens, pale rose hundredths echo the red hundreds, pale green thousandths echo the green thousands
• A number with a hole in it, like 2.05, needs a zero to hold the empty place
• Reading the same number two ways: “two point four seven” and “two and forty-seven hundredths”

Control of error

• Ten or more counters never stay in a column — a waiting trade means the number cannot be read yet
• The written number must match the board digit for digit; pointing at each column while reading aloud catches mismatches
• On the virtual board, the value readout and the Make-the-number check mark every column ✓ or ✗, so the child sees exactly which place to recount

Vocabulary

• decimal point
• decimal fraction
• tenth
• hundredth
• thousandth
• place value
• exchange

Variations

• Build numbers with an empty middle place (2.05, 3.007) and talk about why the zero must be written
• Say quantities in fraction words first — “four tenths and seven hundredths” — and let your child work out the digits
• Connect to money: dimes are tenths of a dollar and pennies are hundredths, so $2.47 is a decimal your child already knows

Extensions

• Bring back the fraction circles and show that the 1/10 piece and one pale blue tenth counter name the very same idea
• Draw a long place-value chart from thousands to thousandths and let your child write numbers that stretch across the decimal point
• Play the mistake game: build a number with one deliberate error and have your child find and fix the wrong column

Follow-up work (pencil & paper)

• Print a decimal place-value worksheet — reading, writing, and building numbers to thousandths — and have your child work it in pencil at the table, building only the ones they doubt on the board.Printable: Decimal Fractions
• Dictation: say six decimal numbers aloud (“three point zero five”) and have your child write each one in pencil; then trade roles and let them dictate numbers for you to write — with an occasional deliberate mistake for them to catch.
• Expanded form on paper: your child writes a handful of decimals the long way, one place per term — 2.47 = 2 + 0.4 + 0.07 — and reads each line aloud.

What comes next

When your child builds and reads decimal numbers confidently — including trading ten tenths for a unit and breaking a unit back into tenths — move on to Decimal Operations, where the same board compares decimal quantities and carries addition and subtraction across the decimal point.

Next in this strand: Decimal Operations