Lesson plan for the lattice method in multi-digit multiplication

The lattice method gives students a clear visual structure for multiplying larger numbers. By placing each partial product inside a grid and collecting the diagonal totals, learners can see how place value, regrouping and multiplication facts work together.

This lesson suits Australian primary classrooms, tutoring sessions and home learning. It is especially useful for students who know their times tables but lose track of columns when working with two-digit or three-digit factors.

The activities below can be adapted for Year 4, Year 5 or Year 6 learners, depending on their confidence with place value and written multiplication. Printable grid paper, worked examples and short practice sets help students build accuracy without making the page feel crowded.

What students should know first

Before introducing the lattice, revise multiplication facts, place value and partitioning. Ask students to explain that 23 means two tens and three ones, while 14 means one ten and four ones. This prepares them to understand why each small multiplication belongs in a particular part of the grid.

A quick warm-up might include products such as 3 × 4, 2 × 4, 3 × 1 and 2 × 1. Use mini-whiteboards or a short times-table quiz to identify gaps. Students do not need perfect recall of every fact, but they should have a reliable strategy for facts they cannot remember immediately.

Materials and lesson setup

Prepare squared paper, pencils, coloured markers and a multiplication worksheet with space for the lattice diagrams. Larger squares are helpful at first, particularly for students who have difficulty writing two-digit partial products neatly. A ruler can help learners draw straight diagonals and separate the cells.

Begin with a short teacher demonstration, followed by partner work and independent practice. In an Australian classroom, this format works well during a numeracy block, while at home it can be completed over two shorter sessions. Keep examples on an A4 page so they are easy to print and store in a maths folder.

Building the lattice step by step

Use 23 × 14 as the first example. Draw a two-by-two grid, place 2 and 3 across the top, and place 1 and 4 down the side. Divide every square with a diagonal line. Each cell represents one single-digit multiplication.

Multiply the digits at the top and side of each cell. Write 02 for 2 × 1, 03 for 3 × 1, 08 for 2 × 4 and 12 for 3 × 4, placing the tens digit above the diagonal and the ones digit below it. This preserves leading zeroes and reinforces the difference between tens and ones.

Add along the diagonals, starting at the bottom-right corner. The first diagonal gives 2. The next gives 3 + 8 = 11, so write 1 and carry 1 into the next diagonal. The following diagonal contains 0 + 12 + 1, making 13, and the final diagonal gives 0 + 1 = 1. Reading from left to right produces 322.

Guided practice and differentiation

Work through another example together, such as 36 × 24. Invite students to say each step aloud: draw the grid, label the factors, calculate each cell, add diagonally and manage regrouping. Verbal rehearsal helps learners follow the process rather than copying a pattern without understanding it.

For students who need support, provide pre-drawn grids and multiplication facts beside the worksheet. Let them use arrays, counters or a times-table chart while they focus on place value. Confident learners can solve three-digit by two-digit examples, estimate the answer first and compare the lattice with the standard vertical algorithm.

Common errors are useful teaching points. Students may reverse a factor, forget a diagonal carry or read the final digits in the wrong direction. Ask them to check the result with an estimate: 23 × 14 is close to 20 × 10, so an answer of 32 or 3,220 should immediately be questioned.

Australian classroom applications

Give the calculations a familiar purpose by using Australian dollars and everyday quantities. For example, ask students to find the cost of 23 packs of stickers at $14 each, or calculate the number of tiles needed for 24 rows of 36 tiles. These contexts connect written multiplication with shopping, building and measurement without requiring complicated financial calculations.

The lesson can also fit an Australian Curriculum sequence on number and algebra, with extension tasks linked to local places. Students might calculate seating arrangements for a school assembly in Melbourne, rows of plants in a community garden in Brisbane or packed boxes for a Sydney excursion. Use Australian spelling, kilometres and dollars consistently so the language feels natural.

When students search for online examples, remind them that a printable maths resource should be age-appropriate, accurate and easy to verify. Teachers can model safe source checking with adult-only examples, such as checking a site’s legitimacy, while keeping unrelated websites away from student devices and classroom tasks.

Assessment and follow-up

Use an exit ticket with two calculations and one explanation prompt. Students might solve 42 × 16 and describe what the diagonal sums represent. Their written explanation will reveal whether they understand the method or are simply following drawing instructions.

For ongoing assessment, collect one practice page and mark the grid, partial products, diagonal additions and final answer separately. This makes feedback specific. A student may have strong multiplication facts but need help with regrouping, while another may understand the diagonals but need further times-table practice.

Finish with a comparison task in which students solve the same problem using the lattice method and the conventional column method. Ask them to check that both answers match and to identify which method helps them organise their thinking. The lattice should become a useful strategy, rather than a compulsory replacement for every written calculation.

Print a small set of worked examples, blank grids and mixed practice questions for the next lesson. Encourage students to explain one example to a partner, parent or tutor, then revisit the method with larger factors when their accuracy is secure. Consistent practice with feedback will turn the visual grid into a dependable multi-digit multiplication tool.