Multiply With Place Value

Overview

Students use the standard written algorithm to multiply numbers up to four digits by one digit, then extend the method to multiply three-digit numbers by two-digit numbers. Explicit modelling connects each written step to place value and partial products, building on students’ prior understanding of multiplication facts, partitioning and regrouping.

Learning intentions

Students will:

• use the standard written algorithm to multiply up to four digits by one digit
• multiply a three-digit number by a two-digit number using partial products
• explain the value of each digit and regrouping in their calculation
• estimate and check whether an answer is reasonable.

Success criteria

• I can line up digits according to place value.
• I can multiply from the ones column, regrouping when needed.
• I can record and add partial products accurately.
• I can estimate and use an inverse operation to check my answer.

Curriculum links

• Multiplicative relations — select and apply strategies to solve multiplication problems.
• Number and place value — use place value and the role of zero to represent and partition numbers.
• Multiplicative relations — construct equivalent number sentences and apply efficient written strategies.

Lesson structure (60 minutes)

1. 0–5 min · Hook and diagnostic. Open with the estimation hook slide showing 398 × 6 and ask, “Is the answer closer to 240, 2,400 or 24,000? How do you know?” Students estimate on mini-whiteboards and explain their reasoning to a partner. Note misconceptions about place value, alignment and the size of the product.

2. 5–18 min · Model: four-digit by one-digit. Use the place-value modelling slides and model 2,347 × 6. First partition the number: (2,000 × 6) + (300 × 6) + (40 × 6) + (7 × 6). Then write the standard algorithm:

2,347
× 6
---------
14,082

Think aloud: “Six ones multiplied by seven ones is 42 ones. I write 2 ones and regroup 4 tens. Six tens multiplied by 4 tens is 24 tens, plus the 4 regrouped tens: 28 tens. I write 8 tens and regroup 2 hundreds.” Continue through hundreds and thousands. Emphasise that the small regrouped digit represents a place-value amount, not an extra number. Students track each step using place-value language and rehearse the explanation with a partner.

3. 18–28 min · Guided practice. Display the guided examples in the worked-example and guided-practice slides. Solve 1,206 × 4 and 3,482 × 7 together, pausing after each column for students to show the next digit on whiteboards. Ask: “What does the 2 in the regrouping space represent?” and “Why does the zero in 1,206 matter?” Students compare answers, correct errors and explain the role of zero. Confer with students who misalign columns or omit regrouping.

4. 28–40 min · Model and practise: three-digit by two-digit. Model 326 × 24. Explain that 24 is 20 + 4, so there are two partial products:

326
× 24
----------
1,304 (326 × 4)
6,520 (326 × 20)
----------
7,824

Explicitly place the second row one place to the left because it represents tens. Colour-code the ones and tens partial products. Students use grid paper or place-value columns to solve 214 × 13 with the teacher, then explain why the second row is shifted.

5. 40–53 min · Independent practice. Distribute the multiplication algorithm practice worksheet. Students complete a graduated set: four-digit × one-digit calculations, followed by three-digit × two-digit calculations and one word problem. Require an estimate beside each answer and one written check using multiplication or division. Students who need support begin with reduced-number entry tasks and may use a place-value chart, base-ten blocks or grid paper. Encourage partner rehearsal before recording an explanation. The teacher conferences strategically, checking alignment, regrouping and the tens partial product.

6. 53–60 min · Review and exit ticket. Use the checking and reflection slide to revisit the key steps. Students complete an exit ticket: (a) solve 2,406 × 3; (b) solve 315 × 22; (c) circle the error in a worked example where the tens partial product has not been shifted, and explain the correction. Collect tickets to group students for the next lesson.

Resources

• the multiplication modelling and practice deck
• the multiplication algorithm practice worksheet
• Mini-whiteboards and markers
• Place-value charts
• Base-ten blocks
• Grid paper
• Pencils, erasers and coloured pencils
• Calculators for checking only, after working is complete

Assessment

• Listen for accurate place-value language during modelling and partner rehearsal; check whiteboards after each guided calculation.
• During independent work, use a conference checklist: columns aligned, multiplication facts accurate, regrouping recorded and tens partial product shifted.
• Use the exit ticket to identify whether students can apply each algorithm independently and explain a common error.

Common misconceptions to address include adding regrouped digits instead of their place-value amounts, placing the second partial product directly under the first, forgetting a zero in the original number, and treating the zero in the tens row as optional without shifting the product. Ask students to estimate before recalculating so they notice unreasonable answers.

Differentiation

• Support learners with place-value charts, base-ten blocks, grid paper, colour-coded partial products and a step-by-step checklist: align, multiply ones, regroup, multiply next place, record the partial product, add and check.
• Provide reduced-number entry tasks, worked examples with selected steps completed, partner rehearsal and targeted teacher conferencing. Allow students to explain orally before writing; use clear vocabulary and visual gestures for ones, tens, hundreds and thousands to support EAL/D learners.
• Offer enlarged layout, extra writing space and a calculator for checking to support students with fine-motor, processing or working-memory needs, while retaining the requirement to show the algorithm.
• Advanced learners estimate using compatible numbers, check answers with an inverse operation, compare the standard algorithm with partitioning, and create a multiplication problem containing a deliberate error for a partner to analyse and correct.

Extension

• Create two different three-digit-by-two-digit calculations with the same product, then prove both answers are correct.
• Write an error-analysis problem in which a student forgets to shift the tens partial product. Include an explanation and corrected solution.
• Investigate how changing one digit in a factor affects the product and describe the pattern using place-value language.