Place Value Activities for Australian Teachers

Why Place Value Is the Foundation of Maths

Place value is arguably the most important concept in primary mathematics. It underpins everything students do with numbers — from counting and comparing in the early years through to multiplication, division, decimals, and fractions in the upper primary. When students truly understand that the value of a digit depends on its position in a number, they have a foundation that supports all future maths learning.

Yet place value is also one of the most commonly misunderstood concepts. Many students can read and write numbers correctly without understanding why the 3 in 35 represents thirty while the 3 in 53 represents three. Well-designed place value activities help students build genuine understanding, not just procedural knowledge.

Effective place value instruction moves through the same concrete-representational-abstract (CRA) progression as all good maths teaching. Activities at each stage play a different role.

Concrete — Hands-On Manipulation

Students first explore place value by physically grouping objects. Activities include:

• Bundling sticks or straws into groups of ten to see how ten ones become one ten
• Using base-10 blocks (MAB blocks) to build numbers and see the relationship between ones, tens, and hundreds
• Trading games where students exchange ten ones for one ten (and later, ten tens for one hundred)
• Place value cups or sliders that physically show how digits change when you add or subtract tens and ones

Representational — Visual Models

Once students understand place value with physical materials, they move to visual representations:

• Place value charts and mats where students draw or place digits in columns
• Number expanders that show how 347 expands to 300 + 40 + 7
• Arrow cards that layer hundreds, tens, and ones to build numbers visually
• Number lines that show how numbers relate to each other based on their place value

Abstract — Symbols and Reasoning

Finally, students work with numbers symbolically:

• Partitioning and recomposing numbers in different ways (e.g., 47 = 40 + 7 = 30 + 17)
• Comparing and ordering numbers using place value reasoning
• Rounding to the nearest ten, hundred, or thousand
• Applying place value to addition, subtraction, multiplication, and division strategies

Australian Curriculum Alignment

The Australian Curriculum v9 for Mathematics develops place value progressively:

• Foundation: Count to and from 20; subitise small collections; name, represent, and order numbers to 20
• Year 1: Count, order, read, and represent two-digit numbers; partition into tens and ones
• Year 2: Recognise, represent, and order numbers to at least 1000; group, partition, and rearrange collections of tens and ones
• Year 3: Recognise, represent, and order numbers to at least 10 000; apply place value to partition, rearrange, and regroup numbers
• Year 4: Recognise, represent, and order numbers to at least tens of thousands; use place value to round whole numbers
• Year 5: Interpret, compare, and order numbers with up to six digits; connect place value to decimals (tenths and hundredths)
• Year 6: Apply place value to operations with large numbers and decimals; solve problems involving place value patterns

1. Spend Longer on Concrete Materials Than You Think

Many teachers move to abstract number work too quickly. Students who can recite "the 4 in 43 is worth 40" without understanding why are not ready to move on. Extend the concrete phase until students can confidently explain what happens when they add a ten to a number using physical materials.

2. Use Non-Standard Partitioning

Most place value activities focus on standard partitioning (347 = 300 + 40 + 7). But students who can also partition non-standardly (347 = 200 + 140 + 7, or 300 + 30 + 17) have a much deeper understanding. Non-standard partitioning also directly supports mental computation strategies for addition and subtraction.

3. Make Trading Explicit

The concept of trading — exchanging ten ones for one ten, or ten tens for one hundred — is the heart of place value and the basis of regrouping in written algorithms. Use trading games regularly, and always connect the physical exchange to what happens symbolically.

4. Connect Place Value to Computation

Place value isn't a standalone topic — it's the reasoning that makes computation work. When teaching addition and subtraction, explicitly connect each step to place value understanding. "Why do we carry the one?" becomes "We've made ten ones, so we trade them for one ten."

5. Address Common Misconceptions

Watch for these common place value misconceptions:

• Treating digits independently: Thinking 35 means "a 3 and a 5" rather than "3 tens and 5 ones"
• Confusing face value and place value: Saying the 7 in 72 is worth 7 instead of 70
• Struggling with zero as a placeholder: Not understanding why 305 is different from 35
• Reversing digits: Writing 41 when they mean 14, indicating a lack of understanding about digit position

Foundation

Foundation students are developing number sense with numbers to 20. Place value activities at this level focus on one-to-one counting, recognising small collections without counting (subitising), and beginning to see that numbers are made up of parts (e.g., 5 is 3 and 2). While formal place value language isn't introduced yet, these early number sense activities lay the groundwork.

Year 1

Year 1 is when place value instruction begins in earnest. Students learn that two-digit numbers are made of tens and ones. Key activities include bundling objects into groups of ten, using base-10 blocks to represent numbers, and using place value mats. Students need extensive hands-on experience to internalise that ten ones is the same as one ten.

Year 2

In Year 2, place value extends to three-digit numbers (hundreds, tens, and ones) and numbers to at least 1000. Students practise grouping, partitioning, and rearranging numbers. Activities should include trading between place value columns and representing numbers on number lines. This is also when skip counting by 2s, 5s, and 10s reinforces place value patterns.

Year 3

Year 3 students work with numbers to at least 10 000. Place value activities include expanded notation, comparing and ordering four-digit numbers, and rounding to the nearest ten or hundred. Students begin to see how place value patterns extend — the relationship between ones, tens, hundreds, and thousands follows the same grouping-by-ten structure.

Year 4

By Year 4, students work with numbers to at least tens of thousands. Activities focus on rounding, estimating, and using place value for multiplication and division strategies (e.g., multiplying by 10 shifts digits one place to the left). Students begin to see place value in context — reading large numbers in real-world data, maps, and measurement.

Year 5 & Year 6

In the upper primary years, place value extends to decimals. Students learn that the base-10 system continues to the right of the decimal point, with tenths, hundredths, and thousandths. Activities connect place value to fractions, decimals, and percentages. Students also work with very large numbers and apply place value understanding to complex computation.