Math 5Multiplication: 3-digit x 2-

digit

Instructor: Mrs. Tew Turner

In this lesson we will how to multiply 3 digit numbers

by 2 digit numbers.

Math Warm-up

Figure out a way to do this problem mentally.

25 + 93 + 75 + 7 =

Math Warm-up

Figure out a way to do this problem mentally.

25 + 93 + 75 + 7 =

25 + 75 = 1003 + 7 = 1090100 + 90 + 10 = 200

In the last lesson you learned how to multiply 2 digits by 2 digits. In this lesson we will answer the question: How does multiplying by 3 digits compare to multiplying by 2 digits?

How do they compare?

Vocabulary REVIEWfactors - numbers that are multiplied to get a productproduct - the number that is the result of multiplying two or more factorspartial product - products found by breaking one of two factors into ones, tens, hundreds, and so on, to multiply each.

Let's look at this problem:The Level 5 class at Monticello School sold more bags of rice than any other class. They ordered 17 cases of rice. Each case had 242 bags. How many bags of rice did the class sell?Let's underline the KEY QUESTION first.

How do you multiply by 3-digit numbers?

Let's look at this problem:The Level 5 class at Monticello School sold more bags of rice than any other class. They ordered 17 cases of rice. Each case had 242 bags. How many bags of rice did the class sell?We need to MULTIPLY 17 x 242 to know the total amount of bags sold.Let’s estimate the answer first!

Now let's circle the IMPORTANT NUMBERS to SOLVE the problem.

MULTIPLY 17 x 242 We round #’s for estimating:17 20242 250 (using compatible numbers)Now we multiply 20 x 250!

2 x 25 = 5020 x 250 = 5,000

The answer will be ~5,000!

Now let's estimate to see what the answer will be close to before we find the exact answer.

STEP 1: Multiply by the ONES place.(partial product with ones factor)

MULTIPLY 17 x 242 242x

177 x 2 = 14 ones7 x 40 = 28 + 1 zero = 2807 x 200 = 14 + 2 zeros = 1400NOW we add 1400 + 280 +14 = ?(line them up by place value)

1400 + 280 +14 = (line them up by place value)

1 4 0 0 2 8 0+ 1 41, 6 9 4 is the multiplication by the ones factor. 242

x 17

1,694

STEP 2: Multiply by the TENS place.(partial product with tens factor)

MULTIPLY 17 x 242 242x

1710 x 2 = 20 ones = 2010 x 40 = 40 + 1 zero = 40010 x 200 = 20 + 2 zeros = 20002000 + 400 + 20 = (line them up by place value)

(line them up by place value)2000 + 400 + 20 = ?

2 0 0 0 4 0 0+ 2 02, 4 2 0 is the multiplication by the tens factor. 242

x 17

2,420

STEP 3: Add the partial products.242 x 17 11,1694+ 2, 4204, 114

How many bags of rice did the class sell?They sold 4,114 bags of rice. Our estimate of 5000 was more because we rounded UP on both factors.

1. 236 Remember the 3 steps!x 46

multiply 236 x 466 x 6 ones = 36 6 x 3 tens(30) = 18 + 0 = 1806 x 2 hundreds(200) = 12 + 00 = 12001200 + 180 + 36 = 1,416

Guided Practice

STEP 1: Multiply by the ONES place.(partial product with ones factor)

6 x 6 ones = 36 6 x 3 tens(30) = 18 + 0 = 1806 x 2 hundreds(200) = 12 + 00 = 1200

1 12 0 0 1 8 0+ 3 6 1, 4 1 6

Guided Practice

Line up the partial products to add.

1. 236 Remember the 3 steps!x 46 So we multiply 236X 4640 x 6 ones = 24 + 0 = 240 40 x 3 tens(30) = 12 + 0 = 12040 x 2 hundreds(200) = 8 + 00 = 800 800 + 240 + 120 = 1,120

Guided Practice

STEP 2: Multiply by the TENS place.(Regroup if needed.)

40 x 6 ones = 24 + 0 = 240 40 x 3 tens(30) = 120 + 0 = 120040 x 2 hundreds(200) = 80 + 00 = 8000 8000 + 240 + 1200 = 9,440

2 4 08 0 0 0+ 1 2 0 0 9, 4 4 0

Guided Practice

Line up the partial products to add.

1. 236 Remember the 3 steps!

x 46

Guided Practice

STEP 3: Add the partial products for the ones and the tens.

1, 4 1 6+ 9, 4 4 0 10, 8 5 6 is the product for 236 x 46!

Easy as ....

1. 236 Remember to Estimate!

x 46

Guided Practice

Round to the nearest 10, or 100, or use compatible numbers to find the closest estimate.

236 250 (compatible number) x 46 50 (rounding)

Now 250 x 50 = 125 + 2 zeros = 12,500

Rounding up on both factors causedour estimated answer to be larger thanthe exact answer. 236 250 (compatible number)x 46 50 (rounding)250 x 50 = 125 + 2 zeros = 12,500 about

1, 4 1 6+ 9, 4 4 0 10, 8 5 6 is the product for 236 x 46!

Guided Practice

REVIEW the STEPS

Step 1:

How do you multiply by 3-digit numbers?

Multiply by the ONES place. Regroup if necessary.

REVIEW the STEPS

Step 2:

How do you multiply by 3-digit numbers?

Multiply by the TENS PLACE. Regroup.

REVIEW the STEPS

Step 3:

How do you multiply by 3-digit numbers?

Add the PARTIAL PRODUCTS.

Easy as ....

Find each product following the steps:1. 244 2. 264 3. 177 4. 354x 34 x 18 x 26 x 89

Easy as ....

Independent Practice

Independent PracticeEstimate first to see what the answer will be closest to!1. 244 2. 264 3. 177 4. 354x 34 x 18 x 26 x 89

250 2. 250 3. 200 4. 400x 30 x 20 x 25 x 90 750 5,000 5,000 36,000

Independent PracticeHow did you do?

1. 244 2. 264 3. 177 4. 354x 34 x 18 x 26 x 89

1976 2112 11062 31186+ 7320 +2640 + 3 540 + 12 8 320 8,296 4,752 4,602 31,506

In your Math NotebookWriting to explain:How does multiplying by 3 digits compare to multiplying by 2 digits?

Math Notebook

Quick Check

Multiplying 3-digits is similar to multiplying by 2-digits because you use partial products.

In your Math Notebook

Writing to explain:

Today you learned how to multiply 3 digits by digits.

Good Work with this

lesson.