Lesson Plan: Multiplying Single Digits Using Partial Products

Partial products help students see what happens inside a multiplication calculation. Instead of treating a two-digit number as one large quantity, learners split it into tens and ones, multiply each part, and then combine the results. This makes place value visible and gives children a reliable strategy for checking their work.

This lesson suits Australian primary classrooms, tutoring sessions, homeschool routines, and small-group intervention. It can fit neatly into a 45–60-minute maths block during a school term and can be adapted for students working within the Australian Curriculum: Mathematics.

Learning Goal And Success Criteria

The focus is multiplying a two-digit number by a single digit using partitioning. For example, students solve 4 × 23 by calculating 4 × 20 and 4 × 3, then adding 80 + 12 to make 92. The language of “partial products” should be introduced alongside familiar terms such as tens, ones, groups, and total.

By the end of the lesson, students should be able to split a two-digit factor into tens and ones, record two smaller multiplication calculations, add the partial products accurately, and explain why the strategy works. A student-friendly success statement could be: “I can break apart a number, multiply each part, and combine the answers.”

Materials And Preparation

Prepare place-value charts, counters or bundled pop sticks, mini-whiteboards, pencils, and a set of printable multiplication questions. A classroom in Sydney, Brisbane, or Perth may use locally familiar contexts such as trays of lamingtons, teams at a weekend footy clinic, or boxes of mangoes at a market. These examples help children connect abstract calculations with quantities they recognise.

Display a worked example without filling in every step for students. Set out a small collection of differentiated tasks: two-digit numbers with no regrouping, examples requiring a larger ones product, and a few reasoning questions. For a movement-based activity, use multiplication task cards at stations around the room.

Warm-Up With Equal Groups

Begin with oral counting and quick multiplication facts. Ask students to represent 3 × 6 with counters, arrays, or drawings, then connect the model to repeated addition. Keep the warm-up short and purposeful so the class recalls that multiplication describes equal groups rather than simply a memorised answer.

Next, write 3 × 24 and ask students what they notice about the number 24. Guide them to identify 2 tens and 4 ones. Do not ask for the final answer immediately; invite estimates first. Students might predict an answer between 60 and 90, which creates a useful reasonableness check for the main strategy.

Model The Partial Products Strategy

Model 3 × 24 with a place-value chart. Partition 24 into 20 + 4, then write:

3 × 24 = 3 × (20 + 4)
3 × 20 = 60
3 × 4 = 12
60 + 12 = 72

Explain that 60 and 12 are partial products because they are the smaller products created from the two parts of 24. Use counters or an array to show that three groups of 20 and three groups of 4 make the same total as three groups of 24.

Repeat with 6 × 17 or 8 × 32, thinking aloud about each decision. Emphasise alignment when recording the addition and remind students that the single digit multiplies both the tens and the ones. If appropriate for older learners, explain that the distributive property is the formal name for breaking a factor into addends; this idea later supports future algebra connections.

Practise Together

Give pairs a calculation such as 5 × 26. Ask them to build it with materials, draw an area model, and write the matching number sentence. Partners should take turns as the explainer and checker. The checker can ask, “Did you multiply the single digit by both parts?” and “Does the answer seem reasonable?”

Move to examples such as 7 × 18, where the ones partial product is 56. This provides a natural opportunity to discuss regrouping when adding partial products. Encourage students to keep the multiplication stage and addition stage separate, as mixing the two operations can create avoidable errors.

Independent Differentiated Practice

For learners needing support, provide partitioned prompts such as 4 × 35 = 4 × 30 + 4 × 5. Include place-value mats, arrays, and a multiplication grid for fact support. The goal is to develop the structure of the method without allowing slow recall of basic facts to hide the student’s understanding.

On-level students can solve a collection of two-digit-by-one-digit calculations and explain one answer in words. Students ready for extension can compare two methods, such as partial products and a written vertical algorithm, then identify which method makes their thinking clearer. A short fact brag-tag system can celebrate fluency growth without turning the lesson into a speed contest.

Apply The Strategy To Problems

Present practical word problems connected with Australian life. For example: “A community garden in Adelaide plants 6 rows of 24 seedlings. How many seedlings are planted?” Another could involve 7 cartons with 18 juice boxes for a school sports day. Students should underline the important quantities, choose multiplication, and show the partial products before writing the answer.

Invite students to create their own problem using a local setting, such as a beach clean-up near Newcastle, a stall at a Perth community market, or seating at a Melbourne school performance. When students write the context themselves, listen for whether the numbers genuinely represent equal groups and whether the question can be solved with a single-digit multiplier.

Check Understanding And Extend Learning

Use an exit ticket with three parts: solve 4 × 27 using partial products, draw or describe a model, and explain what each partial product represents. Review responses for specific misconceptions, such as multiplying only the ones, forgetting the zero in a tens product, or adding the partial products incorrectly.

For follow-up lessons, connect the strategy to area models, expanded notation, and formal written multiplication. Students can sort correct and incorrect worked examples, explain the error, and repair it. In Australian classrooms, this makes a useful short activity for the next morning’s number routine or for targeted support during a maths rotation.

Print the practice pages, gather simple manipulatives, and begin with one accessible example before increasing the challenge. With repeated opportunities to model, explain, and apply partial products, students can build both multiplication fluency and a stronger understanding of place value.