Multiply Multi-Digit Numbers

Overview

In this fourth lesson of the Whole Number Operations unit, students use place-value reasoning and the standard algorithm to multiply multi-digit whole numbers. The lesson builds on earlier work with place value and partial products, then applies multiplication to zeros, reversed factors, and money situations such as $1.35 × 6.

Learning intentions

Students will be able to:

• Multiply multi-digit whole numbers using place-value strategies.
• Connect partial products to the standard multiplication algorithm.
• Explain why switching the order of factors does not change the product.
• Multiply a decimal amount by a whole number using place value.

Success criteria

• I can multiply a multi-digit number by a one- or two-digit number accurately.
• I can use partial products to explain each digit in my standard algorithm.
• I can solve multiplication problems involving zeros and explain my strategy.
• I can find the cost of several items and represent money amounts correctly.

Curriculum links

• Number and Operations in Base Ten — fluent multiplication of multi-digit whole numbers using the standard algorithm.
• Number and Operations in Base Ten — whole-number multiplication and division strategies based on place value and the relationship between operations.
• Number and Operations in Base Ten — understanding that a digit’s value changes by a factor of ten between adjacent places.
• Number and Operations in Base Ten — multiplying decimals to hundredths using place-value reasoning and written methods.

Lesson structure (45 minutes)

1. 0–5 min · Hook and retrieval. Teacher displays the opening comparison and retrieval prompt and asks, “Which is easier to solve: 6 × 135 or 135 × 6, and why?” Students solve mentally or with quick sketches, then explain how the factor order affects the work but not the product.

2. 5–13 min · Model place-value multiplication. Teacher models 324 × 26 using an area model or partial products: 324 × 20 = 6,480 and 324 × 6 = 1,944, then combines the products to make 8,424; teacher connects each part to the standard algorithm on the place-value model and algorithm slides. Students annotate the matching rows and identify the value represented by each digit.

3. 13–20 min · Guided practice and discussion. Teacher solves 47 × 302 with the student, emphasizing the zero in the tens place and asking, “Why does the second partial product have a zero?” Students use place-value language to explain that multiplying by 300 means multiplying by 3 hundreds, then complete 205 × 14 with prompts as needed.

4. 20–32 min · Independent practice. Teacher distributes the multi-digit multiplication practice worksheet and directs the student to complete the core problems, showing work and checking one answer with an estimate. Students solve problems including 238 × 7, 46 × 125, 307 × 24, and 509 × 30; they also solve a factor-order problem and write one explanation of a zero placeholder.

5. 32–39 min · Money application. Teacher displays the money application and discussion prompt and models $1.35 × 6 by treating $1.35 as 135 hundredths: 135 × 6 = 810 hundredths = $8.10. Students solve $2.45 × 4 and explain why the decimal point belongs in the answer, then discuss whether $1.35 × 6 and 6 × $1.35 represent the same situation.

6. 39–45 min · Check and exit ticket. Teacher asks the student to complete the final worksheet challenge and answer the exit prompt: “Solve 426 × 18. Show a place-value or partial-products explanation, then write the standard algorithm.” Student submits the response and states one strategy that helps prevent errors.

Resources

• the multi-digit multiplication slide deck
• the multi-digit multiplication practice worksheet
• Place-value chart
• Graph paper or lined paper
• Pencil and eraser
• Optional calculator for checking, after work is shown

Assessment

• During modeling, listen for whether the student connects each standard-algorithm row to the value of the multiplier digit, especially when a zero is needed.
• Review worksheet work for accurate regrouping, correct place alignment, reasonable estimates, and explanations using place-value language.
• Use the exit response to determine whether the student can independently connect partial products with the standard algorithm. Reteach with a place-value chart if the student misaligns rows or places the decimal incorrectly.

Differentiation

• For support, provide a place-value chart, graph paper for aligning digits, and the sentence frames “I multiplied ___ by ___ because…” and “The zero shows….” Model one problem with color-coded partial products.
• Reduce the initial practice set while requiring complete explanations; allow the student to use an area model before recording the standard algorithm.
• For the one-student setting, use frequent verbal checks and have the student explain each step aloud before moving to the next problem.
• For extension, ask the student to solve 1.25 × 24 in two ways—using hundredths and using the distributive property—and compare the methods.