Multiply Larger Numbers

Overview

In this fifth lesson of “Build, Model, Solve,” students use place-value disks, partial-products mats, and area models to model two-digit-by-one-digit and two-digit-by-two-digit multiplication. They connect expanded notation to the standard algorithm, estimate products, and explain how each digit’s place value affects the calculation.

Learning intentions

Students will be able to:

• Use place-value understanding to multiply larger whole numbers.
• Represent multiplication with disks, partial-products mats, and area models.
• Connect expanded notation to the standard algorithm.
• Estimate products to check whether an answer is reasonable.
• Explain each step using equations and place-value language.

Success criteria

• I can break numbers apart by place value to find partial products.
• I can model multiplication with an area model or place-value disks.
• I can use the standard algorithm and explain what each digit represents.
• I can estimate and check whether my product is reasonable.

Curriculum links

• Number and Operations in Base Ten — multiply up to four-digit numbers by one digit and multiply two two-digit numbers using place value and properties of operations.
• Number and Operations in Base Ten — fluently add and subtract multi-digit whole numbers using the standard algorithm.
• Number and Operations in Base Ten — use place value to read, write, compare, and represent multi-digit numbers.
• Number and Operations in Base Ten — use place value to round multi-digit whole numbers.

Lesson structure (60 minutes)

1. 0–7 min · Estimate and notice. Open with the estimation hook and warm-up slides and display (38 \times 6) and (38 \times 26). Students estimate each product independently, discuss which factors they would round, and share how they know an estimate is reasonable. Briefly review expanded form: (38=30+8).

2. 7–18 min · Model two-digit by one-digit. Use the place-value model slides to model (38 \times 6) with place-value disks and a partial-products mat. Think aloud: (30 \times 6=180) and (8 \times 6=48), so (180+48=228). Students build the same example with disks, record the partial products, and explain why 3 tens multiplied by 6 produces 18 tens, or 180.

3. 18–30 min · Connect to the algorithm. Reveal the standard algorithm for (38 \times 6) on the expanded notation to algorithm slides. Relate each written step to the model: 6 ones times 8 ones is 48, regrouping 48 ones as 4 tens and 8 ones; then 6 times 3 tens is 18 tens, plus the regrouped 4 tens, giving 22 tens. Students annotate the algorithm on the multiplication modeling and practice worksheet and explain the regrouping to a partner.

4. 30–45 min · Build two-digit by two-digit. Model (38 \times 26) with an area model divided into 30 and 8 by 20 and 6. Students calculate and label (30 \times 20=600), (30 \times 6=180), (8 \times 20=160), and (8 \times 6=48), then add the partial products to find 988. Use the area-model activity slides for directions and discussion prompts. Pairs build the model with disks or sketch it, complete the corresponding worksheet problem, and compare their reasoning with another pair.

5. 45–54 min · Guided practice and error analysis. Display two problems from the guided-practice and error-analysis slides: (47 \times 3) and (24 \times 32). Students solve using an area model or partial-products mat, estimate first, and then use the standard algorithm. Invite students to analyze an incorrect solution, identify the place-value error, and revise the explanation. Circulate to check alignment, regrouping, and accurate addition of partial products.

6. 54–60 min · Exit check and reflection. Show the final prompt on the closing slides. Students complete the final section of the multiplication modeling and practice worksheet: solve (27 \times 14), estimate the product, and write one sentence explaining how the area model connects to the standard algorithm. Collect responses as students leave.

Resources

• the complete multiplication slide deck
• the multiplication modeling and practice worksheet
• Place-value disks or counters for pairs
• Partial-products mats
• Grid paper or blank paper
• Pencils, colored pencils, and erasers
• Document camera or interactive display
• Prepared error-analysis example

Assessment

• During modeling, ask students to explain what each digit represents and why regrouping is needed; listen for place-value language such as ones, tens, and hundreds.
• During pair work, check whether students create accurate area-model dimensions, calculate all partial products, and add them correctly.
• Use the exit response to assess multiplication accuracy, estimation, model-to-algorithm connections, and written explanation. Reteach with disks or an area model for students who confuse place values or omit a partial product.

Differentiation

• Support students with pre-labeled area-model sections, color-coded ones and tens, a place-value chart, and sentence starters such as “I multiplied ___ by ___ because…” and “The ___ represents…”
• Allow students who need additional support to complete the two-digit-by-one-digit example before attempting the two-digit-by-two-digit problem. Pair strategically and provide repeated modeling with concrete disks.
• For multilingual learners, explicitly model and display terms including factor, product, partial product, estimate, regroup, ones, tens, and hundreds; accept oral explanations before written responses.
• Extend ready students by asking them to solve a two-digit-by-two-digit problem in two methods, prove the methods agree, and explain which method makes their place-value thinking clearest.