Teaching two-digit multiplication with the lattice method

Multiplying two-digit numbers can feel like a major step when students are secure with one-digit facts but have not connected those facts to place value. This lesson plan on multiplying two-digit numbers using the lattice method turns a calculation into four smaller products, then shows how diagonal totals form the final answer. At Gialdini Worksheets, it sits within a browsable collection of printable maths resources for teachers, parents, tutors and homeschool families.

The method is especially useful in Australian schools because it makes place-value reasoning visible without asking learners to memorise a new procedure. In Australian Curriculum Mathematics, this kind of work generally fits Years 5 and 6, depending on the cohort and task complexity. A composite class may include students working at different stages, so the lesson is designed around a clear example, guided practice, independent application and a short check for understanding.

Why the lattice method helps

The lattice offers a concrete structure for an abstract calculation. A two-digit number is split into tens and ones, and every row digit is paired with every column digit. For 23 × 14, the four inner products are 2 × 1, 2 × 4, 3 × 1 and 3 × 4. Recording these in a grid helps students see that regrouping is built into the method rather than added as an unexplained extra step.

It also provides a useful bridge to the standard algorithm. The partial products 92 and 230 correspond to multiplying by 4 and by 10, and the same place-value relationships can later be discussed in expanded form. Lattice multiplication should not replace explanation: students still need to explain what each digit means, read the diagonals from the correct direction and justify any carried value. Clear language prevents the grid from becoming a guessing game.

Goals, materials, and preparation

Learning intentions should state that students will multiply two-digit whole numbers with the lattice method, record partial products correctly and regroup diagonal totals. Success criteria can be phrased for pupils: “I can label the digits, calculate all four boxes, add along each diagonal and explain my answer.” A worthwhile final criterion is an estimate, such as 23 × 14 is close to 20 × 10, followed by an exact result of 322.

Prepare lattice templates on A4 or A3 paper, pencils, erasers, a visualiser and optional place-value blocks. A plain black-and-white template is often the most practical in Australian classrooms, where photocopied packs and mixed-year composite classes are common; pupils can use a coloured pencil at home if further marking is helpful. Before the lesson, cut enough templates for partners, model one on the visualiser and place the example 23 × 14 where every learner can see it.

A step-by-step teaching sequence

Begin with five minutes of retrieval. Ask pupils to recall selected times-table facts, including harder combinations such as 7 × 8, and to state the value of 3 tens and 4 ones. Set the purpose: today’s grid will show how tens and ones work together when both numbers have two digits. This activates the prerequisite knowledge without spending the main lesson on repetitive drill.

Model 23 × 14 slowly. Write 2 and 3 down the side for the first factor and 1 and 4 across the top for the second. Draw diagonal guide lines from the upper right towards the lower left. Fill the cells with 2, 8, 3 and 12. Read the lower-right diagonal first: write 2 from 12 and carry 1; then 8 + 3 + 1 gives 12, so write 2 and carry 1; the final diagonal gives 2 + 1 = 3. Reading the digits in place-value order gives 322.

Next, guide pupils through 24 × 13 with the visualiser, pausing after the products and again after the diagonal sums. Let students attempt 36 × 12 independently, using a checklist that includes labels, products, carries and an estimate. A familiar local context can follow: fourteen trays of twenty-three items for a Melbourne school fair create the same 23 × 14 calculation. Finish with an exit slip containing one grid and one sentence asking the pupil to explain a diagonal sum.

Supporting learners at different levels

Some pupils know the times tables but still lose track of diagonal direction. Give them a pre-drawn grid, a transparent strip to trace one diagonal and counters to represent regrouped tens. Work with a partner who can say, “Have a go and tell me what you know,” a common supportive phrase in Australian classrooms. If a factor contains zero, rehearse the zero products first; this keeps the procedure from masking gaps in one-digit multiplication.

For pupils ready to extend the task, invite them to multiply a three-digit number by a two-digit number, compare lattice with expanded form, or prove why the diagonal totals give the same result. Ask them to find and correct a deliberately faulty grid, then annotate every carry. Multilingual families can use an Arabic multiplication lesson overview as a complementary explanation. It is best used alongside the pupil’s own grid so terminology and number order are checked together.

Extending learning beyond the classroom

Learning continues outside the maths lesson. At home, pupils might calculate 14 packs of 23 badges for a Perth fundraiser and record the total cost in A$, or estimate how many items a class needs. Gialdini Worksheets provides printable quizzes, puzzles and practice activities that can extend the same ideas for different ability levels. Families can use a whiteboard version for quick practice, while teachers can assign one worksheet for independent follow-up.

Keep digital access purposeful. School-approved bookmarks and parent-selected sites are more dependable than broad search results, particularly when pupils are young. For example, a search may surface a no deposit bonus code, which is unrelated to mathematics and should not be treated as an educational resource. Teachers can show learners how to read the domain, question sponsored material and return to a trusted maths library.

Open the maths resources on Gialdini Worksheets, print a lattice template for each pair and keep the visualiser demonstration ready. Work through 23 × 14, release 36 × 12 for independent practice, then collect the exit slips. Use the completed grids to identify pupils who need another guided example and organise the next practice session around their needs.