Teaching multiplication before addition in primary maths

When students meet order of operations with multiplication and addition, many can calculate each part correctly yet still combine the answers in the wrong sequence. Effective worksheets therefore need to teach decision-making as well as arithmetic: which operation comes first, why it comes first, and how to record that reasoning.

Under the Australian Curriculum Mathematics sequence, these skills are commonly revisited in Years 5 and 6, although state, Catholic and independent schools and tutoring providers may sequence them differently. The aim is computational fluency with understanding, supported by compact practice that fits Australian classroom routines and busy home schedules.

Why the order matters

Multiplication and addition are both essential, but they do not carry equal priority in a number sentence. In a standard expression such as 6 + 2 × 3, the multiplication group is completed before addition. The answer is 12, because 2 × 3 means three groups of two.

Left-to-right calculation is appropriate only when all the operations have equal priority. Once multiplication is present, students need a clear reason for changing the order. Using brackets, such as (6 + 2) × 3, creates a different expression with the answer 24, showing why grouping symbols must be read first.

Start with equal groups

Begin with equal groups rather than a rule on a worksheet. Arrange six counters as two rows of three, then combine two separate groups of three. Ask students to describe what the expression 2 × 3 + 2 represents before they calculate it. This links symbols to quantity and makes the priority decision observable.

Arrays offer another useful bridge. Three rows of four counters can represent 3 × 4, while four additional counters can be placed apart to represent the addition. Students can cover the added counters, calculate the array, and then include them. That physical separation makes the two operations visible.

In Australian classrooms, counters, linking cubes and reused cardboard packaging are common, low-cost ways to model ideas before formal notation. Teachers often use the split strategy when explaining place value, and the same precise language can support later work with the distributive property and algebraic thinking.

Make the thinking visible

Give students stable language for each decision. “Multiply the groups first, then add the extra” is more useful than “do the hard one first”. Colouring, boxing or underlining can reinforce the same idea, provided every example shows the grouping before the answer. Keep the notation consistent so the code becomes familiar.

Think-alouds should expose meaning, not merely announce an answer. A student might say, “There are three groups of two, so the multiplication is six; now I add the six at the front.” Comparing two explanations helps the class see that correct arithmetic still needs correct order, and it supports students who are learning to articulate mathematical reasoning.

Move from guidance to independence

Use a gradual release sequence: model, practise together, then let students work independently. Put one worked example on the board with every stage labelled. Students then complete a similar problem beside it and finish with a mixed set. This prevents a worksheet from becoming a collection of disconnected calculations.

Mini-whiteboards, oral rehearsal or quick dry-bid games can check understanding before the written task. For example, ask pupils to hold up two, three or four fingers to show how many operations a sentence needs. The check takes seconds and reveals who is treating the whole expression as one left-to-right calculation.

Printable resources from Gialdini Worksheets work best when students have room to annotate. Leave space for the grouping step so a learner can circle 2 × 3, write 6 and then continue with the addition. These annotations act as a record of the strategy, giving feedback partners and tutors something specific to discuss beyond whether the final number was right.

Turn errors into teaching points

Error analysis turns common responses into teaching material. Compare 6 + 2 × 3 = 24 with 6 + (2 × 3) = 12. Ask which expression each answer belongs to and require an explanation. The contrast helps students notice that inserting brackets changes the grouping, while changing the sequence without brackets does not.

Watch for other misconceptions, including adding first because the number is written first or multiplying every number in the sentence. Use prompts such as, “What does this group represent?” and “Which operation changes the amount in each group?” Invite students to mark the priority operation before calculating any digits, and accept explanations that demonstrate the structure.

Add partner practice and purpose

Partner work can make the reasoning more accountable. One student reads the expression, the other records the grouping, and they swap roles for the next question. The multiplication tic-tac-toe boards offer a printable format for this partner practice, with games that reward correct evaluation rather than quick guessing.

Connect the symbols to familiar Australian purchasing. At a Coles or Woolworths checkout, three $4 multipacks and a $2 bag give 3 × 4 + 2 = $14. Prices in dollars and cents make multiplication meaningful, while the shopping context gives parents and tutors a natural way to discuss checking reasonableness.

Everyday routines work too: calculate the time needed for several homework sessions, combine ingredients for a batch of biscuits, or work out a total distance on a trip from Sydney to Melbourne. Keep these examples short, and use the relaxed language of “show your thinking” that many Australian classrooms encourage. A quick “good on ya” can acknowledge persistence without taking over the mathematical conversation.

Build a short home routine

At home, use three short rounds rather than one long sheet. Read one expression aloud, let the child explain the order and then complete a small set. Families who share a household printer can keep printable A4 pages in a folder, while others can display a downloaded version on a tablet and write on a separate sheet.

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End the routine by asking the learner to name one expression they found tricky and one method that helped. Revisit those examples after a few days, since spaced retrieval strengthens recall. Choose one printable lesson, print it and begin today: use the first three problems to check whether each learner multiplies before adding, then select the next practice set from their explanations.