Build Multiplication Meaning

Overview

Students develop an initial understanding of multiplying a two-digit number by a one-digit number through equal groups, arrays, repeated addition and place value. They use materials and drawings before recording partitioned equations such as 4 × 23 = 4 × 20 + 4 × 3. The lesson is introductory and does not teach the compact written algorithm.

Learning intentions

• WALT represent multiplication using equal groups, arrays and repeated addition.
• WALT multiply a two-digit number by a one-digit number by partitioning into tens and ones.
• WALT explain how materials, drawings and equations show the same multiplication.
• WALT work collaboratively, take turns and explain our mathematical thinking.

Success criteria

• I can make equal groups or an array to represent a multiplication problem.
• I can partition a two-digit number into tens and ones.
• I can solve 3 × 12 and 4 × 23 using materials, drawings or repeated addition.
• I can explain why 4 × 23 is the same as 4 × 20 + 4 × 3.

Curriculum links

• Mathematics and Statistics — multiplication represented through grouping, repeated addition, known facts and arrays.
• Mathematics and Statistics — multiplying a one- or two-digit number by a one-digit number.
• Mathematical thinking, communicating and representing ideas.
• Key competencies: thinking, managing self, and relating to others.

Lesson structure (50 minutes)

1. 0–5 min · Hook and prior knowledge check. Display the opening multiplication question: “There are 3 bags with 12 counters in each. How could we find the total without counting every counter?” Students think quietly, then share with a partner; the teacher listens for counting in ones, repeated addition and equal groups. Ask students to show with fingers or a quick sketch what 3 × 4 could mean.

2. 5–13 min · Build equal groups and arrays. Give each pair counters and a small workspace. Teacher models 3 groups of 4, records 4 + 4 + 4 and 3 × 4, and turns the groups into an array. Students build an array for 3 × 12 using three rows of twelve, or three groups of twelve, then explain what the factors and total represent. Use the equal-groups and array examples to connect the models.

3. 13–23 min · Teacher modelling with place value. Use base-ten blocks or place-value equipment to model four groups of 23. Build each 23 as 2 tens and 3 ones, then combine: four groups of 20 make 80 and four groups of 3 make 12, giving 92. Record and read aloud: 4 × 23 = 4 × (20 + 3) = (4 × 20) + (4 × 3) = 80 + 12 = 92. Emphasise that 23 has not changed; it has been partitioned into 20 + 3. Students gesture “tens” with arms wide and “ones” with fingers, then rehearse the explanation with a partner.

4. 23–35 min · Guided partner practice. Distribute the multiplication representation worksheet. Complete the first example together using counters, a drawing and repeated addition. Pairs then solve 3 × 12, 2 × 14 and 4 × 23, choosing materials, an array or a drawn model; they must record the partitioned equation for at least one problem. Pause after each question for a movement reset: students stand, make equal “groups” of three or four, and return when the teacher says “multiply”. Confer with pairs and ask, “What does each group contain?” and “Where can you see the tens and ones?”

5. 35–44 min · Differentiated practice and explanation. Students continue with an appropriate worksheet pathway. Support learners use counters, pre-drawn arrays, a place-value mat and sentence frames: “___ groups of ___ make ” and “ × ___ = ___ + ___”. They may work with 2 × 12 and 3 × 13 first. Most learners solve two-digit by one-digit examples and show two representations. Advanced learners use the multiplication strategy cards as prompts to solve 5 × 24 or 3 × 32 in more than one way, compare strategies and explain why their answers are equivalent. Partners take turns as Builder, Recorder and Explainer.

6. 44–50 min · Plenary and exit check. Return to the final discussion and reflection slides. Invite two pairs to show different representations for 4 × 23 and discuss why both produce 92. Students complete an oral or written exit response: “Show or explain how to solve 3 × 12. What does 3 × 10 + 3 × 2 mean?” Finish with a quick self-rating using thumbs: “I can make groups”, “I can partition”, “I can explain”.

Resources

• Counters, linking cubes or small classroom objects
• Base-ten blocks or tens-and-ones place-value equipment
• Place-value mats and mini-whiteboards
• the multiplication introduction, modelling, practice and plenary deck
• the multiplication representation worksheet
• the multiplication strategy cards
• Pencils, paper and visual sentence frames

Assessment

• During the prior knowledge check, note whether students understand equal groups and the meaning of the multiplication symbol.
• Observe partner work for accurate grouping, place-value partitioning and explanations; record students needing further support with materials or counting.
• Use the exit response to identify whether students can connect a model to 3 × 12 and 3 × 10 + 3 × 2. Do not assess speed or memorised facts.

Differentiation

• Support learners with smaller numbers, concrete equipment, pre-drawn arrays, colour-coded tens and ones, repeated teacher modelling and a peer partner. Allow oral answers, pointing, drawing or scribing instead of extensive writing.
• For dyslexia-friendly access, read every instruction aloud, use a clear sans-serif font, large spacing, short lines, uncluttered pages and visual examples. Provide a printed or audio-read version of the worksheet and avoid requiring students to copy lengthy equations.
• Provide planned movement, standing workspaces and brief partner roles for students who wriggle or lose focus. Give one instruction at a time, use a visual timer and check understanding privately.
• Address misconceptions explicitly: multiplication is not just adding the two numbers; equal groups must contain the same amount; 4 × 23 does not mean 4 + 23; and partitioning 23 means 20 + 3, not 2 + 3. If students count inaccurately, rebuild one group and count tens before ones.

Next steps are to revisit any incomplete models with concrete materials, then connect partitioning to more examples such as 3 × 21 and 5 × 14. Once students can explain the structure confidently, introduce efficient mental recording strategies before considering any formal written method.