Multiply Larger Numbers

Overview

In Lesson 13 of 18 in Big Numbers, Time, and Data, students multiply a two- or three-digit whole number by a one-digit number. They connect base-ten models to partial products and the vertical algorithm, then use estimation to check whether an answer is reasonable.

Learning intentions

Students will be able to:

• Multiply a larger whole number by a one-digit number using a model.
• Explain how ones and tens are multiplied and regrouped.
• Use partial products and a vertical algorithm to solve multiplication problems.
• Check a product using estimation or a calculator.

Success criteria

• I can multiply each place value by the one-digit factor.
• I can regroup when a place has 10 or more units.
• I can use a model, partial products, or an algorithm to show my thinking.
• I can check whether my answer is reasonable.

Curriculum links

• Measurement and Data — use the four operations to solve problems involving measurement quantities and represent quantities with diagrams.
• Measurement and Data — express measurements in larger units in terms of smaller units and record equivalent quantities.
• Number and Operations in Base Ten — read, write, compare, and reason about multi-digit whole numbers using place value.
• Georgia Standards of Excellence, Grade 4 Mathematics — multi-digit multiplication, place-value reasoning, mathematical modeling, and justification of solutions.

Lesson structure (30 minutes)

1. 0–4 min · Hook and retrieval. Open with the multiplication hook and place-value warm-up. Display 20 × 3 and ask, “How could you find this without counting by ones?” Students solve mentally, share a strategy with a partner, and identify the factors and product. Briefly review the vocabulary: factor, product, array, regroup, ones, and tens.

2. 4–11 min · I do: model 23 × 3. Use the worked-example slides and physical base-ten blocks to build 23 as 2 tens and 3 ones, then make three equal groups. Teacher color-codes ones blue and tens green, models 3 × 3 ones and 3 × 2 tens, trades 10 ones for 1 ten when needed, and records the partial products 9 + 60 = 69 before showing the vertical algorithm. Read each step aloud and place each digit in a large boxed place-value column.

3. 11–17 min · We do: regroup together. Display a tens-and-ones place-value mat from the interactive regrouping slides. Students move tens and ones tiles on the smartboard as the teacher guides 27 × 3, first finding 21 ones, trading 20 ones for 2 tens, and combining the tens. Pause to ask, “Why did we regroup?” and “Where does the new ten belong?” Students explain the model, partial products, and algorithm to a partner.

4. 17–24 min · You do: supported practice. Distribute the larger-number multiplication practice sheet and provide each student with a place-value mat and base-ten blocks. Students solve 23 × 3 and 31 × 2, showing a model or partial products before recording a vertical algorithm. They circle the place where they regroup, then estimate to check each answer. Teacher works with a small group of students who need additional support, using one-digit factors and color-coded columns.

5. 24–27 min · Reasonableness check. Return to the error-analysis and estimation slide. Show a sample answer for 42 × 2 and ask students to decide whether it is reasonable, explaining their thinking with a partner. Students may use a calculator to verify after completing their own method, then correct any error in a different color.

6. 27–30 min · Exit assessment and closure. Students complete the five-question check on the five-question exit assessment independently: 20 × 3, 12 × 4, 30 × 2, 21 × 3, and 100 × 5. Close with the final reflection slide and ask students to finish the sentence, “When I multiply a larger number, I first….” Collect the assessment before students leave.

Resources

• the multiplication hook, modeling, practice, error-analysis, and reflection deck
• the larger-number multiplication practice sheet
• Base-ten blocks or tens and ones tiles
• Place-value mats with boxed ones and tens columns
• Smartboard or interactive display
• Pencils and two colored pencils
• Calculators for verification
• Multiplication fact chart
• Large visual vocabulary cards

Assessment

• During modeling, listen for students’ correct use of factor, product, place value, and regroup; ask individuals to explain why a trade is needed.
• During practice, check that students multiply each place, record partial products accurately, align digits, and use estimation to judge reasonableness.
• Use the five-question exit assessment to identify misconceptions: answers are B, B, B, A, and B respectively. Review errors in the next lesson’s warm-up.

Differentiation

• Support students with base-ten blocks, a place-value mat, color-coded ones and tens, partial-products boxes, a one-digit fact chart, and a large boxed algorithm. Keep factors to one digit and reduce the number of practice problems if needed.
• Read every direction and worked example aloud. Use short, numbered steps, uncluttered pages, clear sans-serif text, generous spacing, and no unnecessary decoration for dyslexia-friendly access.
• Provide sentence starters such as “I multiplied the ___ place by ___” and “I regrouped because ___.” Pair students strategically and allow students to explain orally or point to a model before writing.
• Extend ready students by asking them to solve 124 × 3 in two ways and explain how the partial products match the vertical algorithm. Students may use a calculator only after showing their reasoning.