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## Math 5 Multiplication : 3- digit x 2-digit

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**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 = 100 3 + 7 = 10 90 100 + 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 REVIEW**factors- numbers that are multiplied to get a product product - the number that is the result of multiplying two or more factors partial product - products found by breaking one of two factors into ones, tens, hundreds, and so on, to multiply each.**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? Let's underline the KEY QUESTION first.**Now let's circle the IMPORTANT NUMBERS to SOLVE the problem.**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 estimate to see what the answer will be close to**before we find the exact answer. MULTIPLY 17 x 242 We round #’s for estimating: 17 20 242 250 (using compatible numbers) Now we multiply 20 x 250! 2 x 25 = 50 20 x 250 = 5,000 The answer will be ~5,000!**STEP 1: Multiply by the ONES place.**• (partial product with ones factor) • MULTIPLY 17 x 242 242 • x 17 • 7x 2 = 14 ones • 7 x 40 = 28 + 1 zero = 280 • 7 x 200 = 14 + 2 zeros = 1400 • NOW 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 4 • 1, 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 242 242 • x 17 • 10 x 2 = 20 ones = 20 • 10 x 40 = 40 + 1zero = 400 • 10 x 200 = 20 + 2 zeros = 2000 • 2000 + 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 0 • 2, 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, 420 4, 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.**Guided Practice**• STEP 1: Multiply by the ONES place.(partial product with ones factor) 236 Remember the 3 steps! x 46 multiply 236x 46 6 x 6 ones = 36 6 x 3 tens(30) = 18 + 0 = 180 6 x 2 hundreds(200) = 12 + 00 = 1200 1200 + 180 + 36 = 1,416**Guided Practice**Line up the partial products to add. 6 x 6 ones = 36 6 x 3 tens(30) = 18 + 0 = 180 6 x 2 hundreds(200) = 12 + 00 = 1200 1 12 0 0 1 8 0 + 3 6 1, 4 1 6**Guided Practice**• STEP 2: Multiply by the TENS place. • (Regroup if needed.) 236 Remember the 3 steps! x 46 So we multiply 236 X 46 40 x 6 ones = 24 + 0 = 240 40 x 3 tens(30) = 12 + 0 = 120 40 x 2 hundreds(200) = 8 + 00 = 800 800 + 240 + 120 = 1,120**Guided Practice**Line up the partial products to add. 40 x 6 ones = 24 + 0 = 240 40 x 3 tens(30) = 120 + 0 = 1200 40 x 2 hundreds(200) = 80 + 00 = 8000 8000 + 240 + 1200 = 9,440 2 4 0 8 0 0 0 + 1 2 0 0 9, 4 4 0**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! 236 Remember the 3 steps! x 46 Easy as ....**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 = 12,500 236 Remember to Estimate! x 46**Guided Practice**Rounding up on both factors caused our estimated answer to be larger than the exact answer. 236 250 (compatible number) x 46 50 (rounding) 250x 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!**How do you multiply by 3-digit numbers?**REVIEW the STEPS Step 1: Multiply by the ONES place. Regroup if necessary.**How do you multiply by 3-digit numbers?**REVIEW the STEPS Step 2: Multiply by the TENS PLACE. Regroup.**How do you multiply by 3-digit numbers?**REVIEW the STEPS Step 3: Add the PARTIAL PRODUCTS. Easy as ....**Independent Practice**Find each product following the steps: 1. 244 2. 264 3. 177 4. 354 x 34 x 18 x 26 x 89 Easy as ....**Independent Practice**• Estimate first to see what the answer will be closest to! • 1. 244 2. 264 3. 177 4. 354 • x 34 x 18 x 26 x 89 • 250 2. 250 3. 200 4. 400 • x 30 x 20 x 25 x 90 • 750 5,000 5,000 36,000**Independent Practice**• How did you do? • 1. 244 2. 264 3. 177 4. 354 • x 34x 18 x26x 89 • 1976 2112 11062 31186 • + 7320 +2640 + 3 540+ 12 8 320 • 8,296 4,752 4,602 31,506**In your Math Notebook**Writing to explain: How does multiplying by 3 digits compare to multiplying by 2 digits? Math Notebook**In your Math Notebook**Quick Check Multiplying 3-digits is similar to multiplying by 2-digits because you use partial products. Writing to explain:**Good Work with this lesson.**Today you learned how to multiply 3 digits by digits.