Teaching Place Value: Tens, Ones and Beyond

Place value is the idea that a digit's value depends on its position: in 352, the 3 means three hundred, the 5 means fifty and the 2 means two. It's one of the most important ideas in math, because it underpins adding, subtracting, multiplying, rounding and decimals. Here's how to teach it with hands-on activities and games.

Why place value is tricky

Children see "35" and might think it's just a 3 and a 5. They need to understand it's 3 tens and 5 ones, or 35 ones. This takes lots of hands-on experience grouping and counting.

Step 1: Grouping in tens (ages 5–6)

• Bundle sticks: count out lolly sticks and bundle every ten with a rubber band.
• Tens frames: fill a 10-space frame with counters.
• Cups of ten: put ten beans in each cup.
• Count collections: count large collections by grouping in tens.

Step 2: Tens and ones (ages 6–7)

• Build numbers: use bundles or tens rods and loose ones to build numbers like 23 (2 tens, 3 ones).
• Place value mats: draw two columns labelled Tens and Ones.
• Expanded form: 47 = 40 + 7. Our place value worksheets include expanded form practice.
• Say it two ways: "4 tens and 7 ones is forty-seven."

Step 3: Hundreds (ages 7–8)

• Hundreds flats: 10 tens make 1 hundred.
• Build three-digit numbers: 352 = 3 hundreds, 5 tens and 2 ones.
• Zero as a placeholder: in 305, the zero shows there are no tens.

Step 4: Thousands and beyond (ages 8–10)

• Patterns: each place is 10 times bigger than the one to its right.
• Read and write large numbers.
• Rounding: round to the nearest 10, 100 and 1,000.

Step 5: Decimals (ages 9–11)

The same idea continues to the right of the decimal point: tenths, hundredths and thousandths. See our decimals worksheets.

Place value games

1. Biggest number. Roll dice and decide where to place each digit to make the biggest (or smallest) number.
2. Place value war. Each player draws cards to make a two- or three-digit number. Biggest wins.
3. Number of the day. Pick a number and show it in different ways: tens and ones, expanded form, on a number line, in words.
4. Bank game. Use play money with 1s, 10s and 100s. Roll dice to collect money, trading 10 ones for a ten.
5. Mystery number. "I have 3 tens and 4 ones. What am I?"
6. Hundred chart puzzles. Fill in missing numbers on a hundred chart.
7. Skip counting by tens. Count by 10s from any number: 7, 17, 27, 37. See skip counting worksheets.

Place value and other math

• Addition and subtraction: regrouping in column methods relies on place value. See addition strategies and subtraction strategies.
• Multiplying by 10: digits move one place to the left.
• Comparing numbers: compare the biggest place first. See comparing numbers.
• Money: dollars, dimes and cents work like hundreds, tens and ones.

Ideas by age

Ages 5–6: grouping objects in tens, tens frames and counting by tens.

Ages 6–7: tens and ones, expanded form, building two-digit numbers.

Ages 7–8: hundreds, three-digit numbers, zero as a placeholder.

Ages 8–10: thousands, rounding, and the ×10 pattern.

Ages 9–11: decimals and very large numbers.

Common mistakes to avoid

• Writing 305 as 3005. Show with blocks that there are 3 hundreds and 5 ones.
• Reversing digits. Practise reading numbers aloud.
• Skipping hands-on work. Objects make place value concrete.

Frequently asked questions

When do children learn place value?

Most begin with tens and ones in first grade, hundreds in second grade and larger numbers after that.

What is expanded form?

Writing a number as the sum of its place values: 352 = 300 + 50 + 2.

What does "regrouping" mean?

Trading 10 ones for 1 ten (or the reverse), used in addition and subtraction.

A place value checklist by grade

By the end of kindergarten: count to 100 by ones and tens; understand that 11–19 are ten and some more.

By the end of grade 1: understand two-digit numbers as tens and ones; compare two-digit numbers.

By the end of grade 2: understand three-digit numbers; skip count by 5s, 10s and 100s; read and write numbers to 1,000.

By the end of grade 3: round to the nearest 10 and 100.

By the end of grade 4: read, write and compare numbers to a million; round to any place.

Grade 5: decimals to thousandths.

These are general guides; check your local curriculum.

What materials help most?

Bundles of lolly sticks, base-ten blocks, place value charts, play money and hundred charts are all very effective.

Why do teen numbers confuse children?

In English, teen numbers don't follow the tens-and-ones pattern clearly (we say "fourteen," not "ten-four"). Practise building them with one ten and some ones.

What's a fun place value game for two?

Play "biggest number": roll dice, place digits on a tens-and-ones chart, and compare. The biggest number wins a point.