4th Grade Multiplying Multi-Digit Numbers Lesson: Notes and Examples (Free PDF)

4th grade multi digit multiplication lesson – Maths PDF

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This 4th grade multi digit multiplication lesson covers multiplying multi-digit numbers (Common Core 4.NBT.B.5), with a free PDF to print.

Key takeaway: This lesson helps fourth grade students multiply whole numbers up to four digits by one digit, and two digit numbers by two digit numbers, using place value.

Topic: Multiplying Multi-Digit Numbers (4th grade)
Content: One-page lesson with a definition, a worked example and key facts
Standards: 4.NBT.B.5
Answers: Explanations included
Format: Free printable PDF, US Letter, black and white

To multiply multi-digit numbers, break a factor into place-value parts, multiply each part, and add the partial products. An area model draws this as a rectangle: 36 × 24 is 600 + 120 + 120 + 24 = 864. The distributive property allows the split. For multiples of 10, multiply the basic facts and attach the zeros.

This lesson helps fourth grade students multiply whole numbers up to four digits by one digit, and two digit numbers by two digit numbers, using place value. It builds from multiples of 10 to partial products and area models, so the standard steps come from ideas students can see.

Students learn to break a factor into tens and ones, find each partial product, and add them. Also, the lesson explains why 6 times 47 equals 6 times 40 plus 6 times 7, how a two digit by two digit problem makes four partial products, and how to estimate to check an answer. Then, plan about 25 minutes, and draw each area model on paper.

Grade 4 · Common Core State Standards: 4.NBT.B.5

Key facts in this 4th grade multi digit multiplication lesson

Key facts

Partial products are the answers to each smaller multiplication; add them for the final product.
Distributive property: 6 × 47 = 6 × 40 + 6 × 7.
A 2-digit by 2-digit problem has four partial products in an area model.
Then, for multiples of 10, multiply the basic facts and attach all the zeros: 30 × 40 = 1,200.
Estimate first by rounding to check that the product makes sense.

What is a partial product?

To multiply big numbers, break one number into place-value parts. Multiply each part, then add. Each answer you get along the way is a partial product.

Distributive property

The distributive property says you can split a factor and multiply each part: \(6 \times 47 = 6 \times 40 + 6 \times 7\). An area model draws this as a rectangle cut into parts.

47 × 6 splits into 40 × 6 = 240 and 7 × 6 = 42. Add: 240 + 42 = 282.

The rectangle is \(6\) units tall and \(47\) units wide. The two parts have areas 240 and 42, and they add to \(282\).

How do you multiply two 2-digit numbers?

Split both numbers. A 2-digit by 2-digit problem makes four partial products.

36 × 24 has four partial products: 600, 120, 120, and 24. Their sum is 864.

Split each factor into tens and ones: \(36 = 30 + 6\) and \(24 = 20 + 4\).
Multiply every part by every other part: \(30 \times 20 = 600\), \(6 \times 20 = 120\), \(30 \times 4 = 120\), \(6 \times 4 = 24\).
Add the four partial products: \(600 + 120 + 120 + 24 = 864\).

How do you multiply a 4-digit number by a 1-digit number?

Use the same idea. Split the big number by place value, multiply each part by the 1-digit number, then add.

2,438 × 4 = 8,000 + 1,600 + 120 + 32 = 9,752.

How can you multiply multiples of 10 in your head?

To multiply 30 × 40, multiply 3 × 4 and then attach the zeros.

Think of \(30 \times 40\) as 3 tens times 4 tens. The basic fact \(3 \times 4 = 12\) gives 12 hundreds, which is \(1,200\). Count the zeros in both factors and attach them all.

Which properties make multiplying easier?

Commutative: \(7 \times 12 = 12 \times 7\).
Associative: \(4 \times 17 \times 25 = (4 \times 25) \times 17 = 100 \times 17 = 1{,}700\).

Look for pairs that make friendly numbers, such as \(4 \times 25\) or \(5 \times 20\).

4th grade multi digit multiplication lesson: questions and answers

What is an area model for multiplication?

It is a rectangle cut into parts by place value. Each part shows one partial product, and the sum of the parts is the answer. For 47 × 6, the parts are 240 and 42, so the product is 282.

What are partial products?

Partial products are the products of each part of one factor with each part of the other. Add all of them to get the final product.

How do you multiply 30 × 40 in your head?

Multiply the basic fact 3 × 4 = 12, then attach the two zeros from the factors. The product is 1,200.

How many partial products does 36 × 24 have?

It has four: 30 × 20, 6 × 20, 30 × 4, and 6 × 4. They equal 600, 120, 120, and 24, and they add to 864.

How can I check a multiplication answer?

Estimate by rounding each factor. For 48 × 31, think 50 × 30 = 1,500. The exact product, 1,488, is close, so it makes sense.

Common mistakes with this 4th grade multi digit multiplication lesson

Students forget a zero when multiplying by tens. Thirty times four is 120, not 12, because 3 tens times 4 is 12 tens.
Students leave out a partial product in a two digit by two digit problem. Instead, four parts are needed: tens times tens, tens times ones, ones times tens, and ones times ones.
Students line up partial products carelessly when adding. Write them in a column by place value, so ones are under ones and tens are under tens.

How to study this chapter

Estimate first by rounding each factor. For 47 times 6, think 50 times 6 is 300, so the exact answer should be a bit less.
Draw a rectangle for every two digit problem and label each part. Also, an area model helps you see all four partial products.
Parents can ask the child to explain why 30 times 40 has three zeros in the answer, using the idea of 3 tens times 4 tens.

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