Lesson plan: using area models to multiply two-digit numbers

An area model turns a two-digit multiplication problem into a picture of manageable parts. Instead of treating 23 × 14 as a mysterious written procedure, students see how tens and ones combine to create four partial products.

This lesson suits upper-primary learners who are developing multiplication strategies and beginning to connect visual representations with the standard algorithm. It can fit a Year 4 or Year 5 mathematics sequence aligned with the Australian Curriculum, particularly work involving multiplication, place value, partitioning and efficient calculation.

The activities use inexpensive classroom materials and printable practice pages, making them practical for teachers, tutors, parents and homeschoolers. The examples use centimetres and square centimetres, familiar units in Australian schools, and can be adjusted for learners in Sydney, Brisbane, Perth or regional communities.

Learning goals and preparation

Students will partition two-digit numbers into tens and ones, represent multiplication with a rectangular area, calculate four partial products, and combine those products accurately. By the end of the lesson, they should be able to explain why 23 × 14 equals 322 rather than simply recall an answer.

Prepare grid paper, pencils, coloured markers, rulers and a set of two-digit multiplication cards. A whiteboard or interactive display is useful for modelling. For a small group, square tiles or MAB blocks can make the tens-and-ones structure easier to handle.

Begin with a short review of place value. Ask students to represent 23 as 20 + 3 and 14 as 10 + 4. Emphasise that partitioning changes the way a number is shown, not its value.

Launch with a familiar array

Display a rectangle labelled 23 units long and 14 units wide. Explain that its total area can be found by splitting each side into a tens section and a ones section. The resulting four rectangles are 20 × 10, 20 × 4, 3 × 10 and 3 × 4.

A quick warm-up with equal groups can connect multiplication to earlier learning. Students may review number line multiplication before moving from repeated addition to a more efficient area representation. This helps learners who still rely on counting while showing why multiplication strategies become more useful with larger numbers.

Use a context that feels ordinary rather than abstract. For example, a community garden in Melbourne has 23 rows with 14 seedlings in each row. The exact story matters less than the structure: two groups of tens and ones must be multiplied systematically.

Build the area model

Draw a large rectangle and partition the horizontal side into 20 and 3. Partition the vertical side into 10 and 4. Label each region clearly, then calculate the four products:

• 20 × 10 = 200
• 20 × 4 = 80
• 3 × 10 = 30
• 3 × 4 = 12

Ask students to shade each region in a different colour. The completed model shows that 23 × 14 is the sum of 200 + 80 + 30 + 12, which equals 322.

Have students read the model aloud using complete mathematical sentences: “Twenty-three times fourteen is the area of the whole rectangle.” Then ask them to explain what each partial product represents. This verbal step is valuable because students can produce correct arithmetic while still misunderstanding place value.

If learners confuse 20 × 4 with 2 × 4, use base-ten blocks or expanded notation beside the drawing. Keep the zero visible in the written calculation and connect it to the size of the region, rather than presenting it as a rule to memorise.

Move from regions to the written method

Once students understand the picture, connect it to the distributive property:

23 × 14 = (20 + 3) × (10 + 4)

= 20 × 10 + 20 × 4 + 3 × 10 + 3 × 4

= 200 + 80 + 30 + 12

= 322

Model how the same four products appear in a partial-products calculation. This creates a bridge to the compact vertical method without asking students to abandon a strategy they understand. Explain that the written algorithm is a condensed record of the area model.

Use a second example, such as 36 × twenty? Need valid. 36 × 24 = 30×20 600, 30×4 120, 6×20 120, 6×4 24 =864. Ask students to predict which region will be largest before calculating. Their predictions reinforce the relationship between place value and product size.

Practise, differentiate and assess

Begin guided practice with examples such as 12 × 13, 21 × 32 and 42 × 15. Require students to draw or label an area model before using partial products. Circulate and check whether they have partitioned both factors, placed the tens and ones correctly, and included all four regions.

For students needing support, provide pre-drawn rectangles, colour-coded place-value labels or multiplication fact charts. Use smaller products first, then introduce numbers with less familiar facts. Pairing a confident calculator with a learner who needs language support can encourage mathematical discussion without turning the task into answer copying.

For extension, include products such as 47 × 28 or ask students to find two different rectangles with the same area. A learner might compare 24 × 13 with 26 × 12 and discuss why equal products are not guaranteed when dimensions change. Students can also estimate first, then decide whether their exact answer is reasonable.

Assess through observation and a short exit ticket. Give one problem, such as 34 × 22, and ask students to draw the model, calculate the partial products and write one sentence explaining the answer. Record whether each learner can partition, multiply, combine and justify.

Extend learning beyond the lesson

Connect the activity to measurement by designing a rectangular vegetable bed or floor space. Students can calculate area in square metres or square centimetres, then compare estimates with exact results. This suits an Australian classroom where metric measurement is used consistently and can link mathematics with gardening, design or sustainability projects.

A shopping context can make the lesson relevant to families comparing prices at Woolworths, Coles or a local market, although the focus should remain on arrays rather than money. For example, students could arrange 24 packets in each of 13 display rows and calculate the total stock. In a homeschool setting, graph paper and recycled cardboard provide an easy alternative to commercial manipulatives.

Finish with a strategy discussion. Invite students to compare an area model, partial products and the compact algorithm, identifying what each representation makes visible. Revisiting these connections during Australian school terms can strengthen multiplication fluency before more demanding multi-digit calculations.

Print a selection of two-digit multiplication worksheets, prepare coloured pencils and use the model as a reference while students practise. Consistent visual work, clear explanations and brief feedback will help learners build accuracy and confidence with multi-digit multiplication.