A focused Grade 5 learning session for Multiplying Multi-Digit Whole Numbers using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can multiply multi-digit whole numbers accurately.
Multiplying Multi-Digit Whole Numbers is the Grade 5 skill of students fluently multiply multi-digit whole numbers using the standard algorithm. They apply this skill to problems involving two-digit by two-digit, three-digit by two-digit, and larger products.
Strong understanding comes from naming what the numbers, shapes, units, or data values represent, then showing the idea with a model or clear steps before solving.
The key to this topic is understanding the structure behind the work, not just following a rule. Students should be able to talk through what is happening, point to a model, and explain why the answer makes sense.
Question: This area model shows \(25 \times 13\) broken into four partial products. What is the total product?
| \(20 \times 10\) | \(5 \times 10\) |
| \(20 \times 3\) | \(5 \times 3\) |
| \(= 25 \times 13\) |
How the model helps: Add the four partial products: \((20 \times 10) + (5 \times 10) + (20 \times 3) + (5 \times 3) = 200 + 50 + 60 + 15 = 325\).
Question: This area model shows the partial products for \(27 \times 25\). What is the total?
| \(20 \times 20 = 400\) | \(7 \times 20 = 140\) |
| \(20 \times 5 = 100\) | \(7 \times 5 = 35\) |
Answer: 675
Question: Using the area model above, what is \(32 \times 15\)?
| \(32 \times 15\) | ||||
|---|---|---|---|---|
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Answer: 480
Question: A school bought 12 boxes of colored pencils. Each box contains 24 pencils. How many pencils did the school buy?
Answer: 288 pencils
Why it works: Multiply: \(12 \times 24 = 12 \times (20 + 4) = (12 \times 20) + (12 \times 4) = 240 + 48 = 288\) pencils.
Multiplying Multi-Digit Whole Numbers gets easier when students read the model, track what each number means, and explain why the answer fits the situation.
Understand the structure first, then solve, check, and explain why the answer makes sense.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
What is \(45 \times 7\)?
Answer B: 315
Break 45 into 40 and 5: \((40 \times 7) + (5 \times 7) = 280 + 35 = 315\).
What is \(24 \times 15\)?
Answer C: 360
Multiply: \(24 \times 15 = 24 \times (10+5) = 240 + 120 = 360\).
A school orders 132 boxes of pencils. Each box has 24 pencils. How many pencils are ordered in all?
Answer D: 3,168
Multiply: \(132 \times 24 = 132 \times (20+4) = 2{,}640 + 528 = 3{,}168\).
Estimate the product of \(23 \times 18\) by rounding each factor to the nearest ten, then multiply.
Answer D: 400
Round 23 to 20 and 18 to 20. Then \(20 \times 20 = 400\).
This area model shows \(25 \times 13\) broken into four partial products. What is the total product?
Answer B: 325
Add the four partial products: \((20 \times 10) + (5 \times 10) + (20 \times 3) + (5 \times 3) = 200 + 50 + 60 + 15 = 325\).
A school bought 12 boxes of colored pencils. Each box contains 24 pencils. How many pencils did the school buy?
Answer B: 288
Multiply: \(12 \times 24 = 12 \times (20 + 4) = (12 \times 20) + (12 \times 4) = 240 + 48 = 288\) pencils.
What is \(31 \times 7\)?
Answer D: 217
Multiply: \(31 \times 7 = (30 \times 7) + (1 \times 7) = 210 + 7 = 217\).
Answer A: Student A is correct.
Student A correctly applies the distributive property: \(14 \times 16 = 14 \times (10 + 6) = 140 + 84 = 224\). Student B made an error; the correct product is 224, not 124.
A theater has 4 sections with 112 seats in each section. Which place-value sum can be used to find the total number of seats?
Answer A: \(400+40+8\)
Use place value: \(112 \times 4 = (100 \times 4) + (10 \times 4) + (2 \times 4) = 400 + 40 + 8 = 448\) seats.
A farmer plants corn in rows. There are 15 rows, and each row has 23 corn plants. How many corn plants does the farmer have?
Answer B: 345
Multiply: \(15 \times 23 = 15 \times (20 + 3) = (15 \times 20) + (15 \times 3) = 300 + 45 = 345\) plants.
What is \(43 \times 6\)?
Answer D: 258
Multiply: \(43 \times 6 = (40 \times 6) + (3 \times 6) = 240 + 18 = 258\).
