teaching multi-digit multiplication with expanded form

When Year 5 students across Melbourne primary schools come across 47 × 23 in a maths lesson, many freeze. They have worked with two-digit by two-digit multiplication for weeks, yet the standard algorithm still feels mechanical and confusing. Expanded form offers a way back into sense-making. By breaking each factor into hundreds, tens, and ones, students lean on the place value they already know rather than memorising a sequence of moves.

This approach fits neatly with the Australian Curriculum Year 5 content descriptor on solving problems involving multiplication of large numbers. Children who start with expanded form tend to keep a deeper grip on what each digit is doing, so when they move to the algorithm in Year 6, they are transcribing understanding rather than copying procedure.

The method travels well across states, whether the setting is a small rural school in regional Queensland or a Year 4 maths group in Perth. It needs only a whiteboard, a pencil, and the confidence that comes from seeing the same idea carried across larger and larger numbers.

grounding the lesson in place value

Before any expanded form multiplication begins, students need to be rock-solid on what each digit in a number actually represents. In a Sydney Catholic primary classroom, teachers often open the term by reviewing place value using MAB blocks, arrow cards, and place value charts. The hundreds, tens, and ones columns become familiar territory well before formal multiplication starts.

Skip-counting quietly supports this stage. Counting by tens, fives, and twos helps students recognise multiples within larger numbers, which becomes important when expanded form asks them to multiply something like 30 × 4 or 200 × 6. A hundreds chart gives students a visual pattern they can fall back on whenever a multiplication feels abstract, so practising on one early in the term pays off well before multi-digit work begins.

Once place value feels sturdy, expanded form becomes a natural extension rather than a leap. The same number a student has written as 3 hundreds, 4 tens, and 7 ones on a chart now becomes 300 + 40 + 7 in working out, with the language shifting seamlessly between the two representations.

walking through the expanded form method

Take 47 × 23. The first move is to expand both factors: 47 becomes 40 + 7, and 23 becomes 20 + 3. Each piece is written clearly above or beside the original problem so students can see where the digits have come from. Students then multiply each part of the second factor by each part of the first, applying the distributive property without necessarily naming it.

The worked example usually reads 47 × 23 = (40 × 20) + (40 × 3) + (7 × 20) + (7 × 3), which simplifies to 800 + 120 + 140 + 21 and totals 1081. Walking students through this scaffolded version gives them room to slow down and notice which partial products come from which digits. Many Adelaide teachers colour-code each partial product to make the connection between place value and answer clearer, especially for visual learners.

The same routine extends to three-digit by two-digit questions such as 134 × 25, where the first factor expands to 100 + 30 + 4. Students who have practised the two-digit version rarely struggle once a third digit appears, because the pattern stays consistent.

real-world contexts make the method stick

Australian classrooms are goldmines of authentic contexts. A Year 5 class in Hobart might work out how many apples a school orchard produced over 23 days if it picked 47 each day. A Brisbane tutor could pose a question about cricket balls bowled across a school carnival. Numbers drawn from NAPLAN-style word problems feel most familiar because students recognise them from previous assessments.

Try framing a small part of a problem so the answer matters on its own. Asking how many students are in six Year 4 classes of 27 children each sounds like one giant multiplication, but splitting it into 20 × 6 and 7 × 6 brings the total within reach. Students see that 120 students sit in the hall and 42 stand along the wall, and the answer feels like an observation rather than a guess.

Currency tasks work well too, particularly when shopping or fundraising comes up. Multiplying $4.20 by 23 items uses the same expanded form approach, and a maths lesson at a fete stall suddenly has a real budget attached. These contexts help students remember both the method and the reason they learned it.

common stumbling blocks and how to address them

Place value errors are by far the most common slip. Students forget that the 4 in 47 stands for 40, not 4, and quietly write the partial product 4 × 20 as 80 instead of 200. Quick whiteboard checks during a lesson catch this early, and asking "what is the 4 really worth?" resets their thinking in seconds.

Misalignment of partial products is another stumbling block. When the four pieces of a question get jumbled on the page, students lose track of which is which. Numbering each partial product with a small label such as A, B, C, D lets students discuss their working out clearly with a partner and spot mistakes sooner.

A third hurdle is forgetting trailing zeros, particularly in problems like 30 × 40 where the answer is 1200, not 12. Counting the place value columns on a chart before multiplying helps anchor the size of each partial product, and that habit carries through into the standard algorithm later in the year.

making practice stick with printable worksheets

A strong introduction always needs reinforcement. Printable worksheets that move from guided examples to independent questions give students the repetition they need without becoming tedious. Gialdini Worksheets keeps a browsable library of multiplication materials, including expanded form exercises, multi-digit practice pages, and short quizzes that fit neatly into a single lesson.

Pair the worksheets with quick self-checks so students can spot their own slips. A simple answer column or a partner swap works in a busy classroom, and students catch errors like a dropped trailing zero much faster when they hunt for them on a peer's page. Regular, low-stakes practice builds the fluency that NAPLAN and everyday maths both expect.

Combine the worksheets with quick warm-up games, times-table chants, or a daily skip-counting routine, and expanded form multiplication stays fresh all term.

Browse the expanded form and multi-digit multiplication collection on Gialdini Worksheets and download a fresh set of printables for your next lesson. With the right scaffolding in place, every student in the room can grow into accurate, confident multi-digit multiplication by the end of term.