5 th Grade Math Multiplication Unit

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1 5 th Grade Math Multiplication Unit Lessons/Learning Targets Multiplication Patterns o Use basic facts and patterns to multiply whole numbers by multiples of 10, 100, and 1000 Powers of 10 and Exponents o Use exponents to show powers of 10 Estimate Products o Estimate products of whole numbers Multiply by 1-Digit Numbers o Multiply multi-digit numbers by 1-digit factors Zeros in the Multiplicand o Multiply multi-digit numbers by 1-digit factors Multiply by 2-Digit Numbers o Multiply a whole number by 2-digit multiplier Multiply by 3-Digit Numbers o Multiply a whole number by 3-digit multiplier Zeros in the Multiplier o Multiply multi-digit whole numbers with zeros in the multiplier Name

3 Multiplication Patterns Use basic facts and patterns to multiply whole numbers by multiplies of 10, 100, and 1000 A data storage company uses computer servers to manage files for hundreds of small businesses. The company has 6 different rooms that each have 200 computer servers. How many servers does the company have? To solve, multiply 6 by 200. You can use patterns to help you multiply by multiples of 10, 100, and x 70 = x 70 = 1, x 50 = 2, x 70 = 56, x 70 = 14, x 50 = 20, x 70 = 560, x 70 = 140, x 50 = 200,000 To multiply a whole number by a multiple of 10, 100, or 1000: o Write the product of the nonzero digits o Count the number of zeros in the factors o Write the same number of zeros at the end of the product 500 x 3 = x 8000 two zeros 320,000 Multiply. 300 x 20 = 50 x 8,000 = 30 x 4,000 = 70 x 6 = 5,000 x 2 = 40 x 400 = 7 x 10 2 = 50 x 3 x 10 2 = 3 x 10 3 = Use mental math to complete the pattern. 7 x 8 = 56 (7 x 8) x 10 1 = (7 x 8) x 10 2 = (7 x 8) x 10 3 = 9 x 5 = 45 (9 x 5) x 10 1 = (9 x 5) x 10 2 = (9 x 5) x 10 3 = 4 x 5 = 45 (4 x 5) x = 200 (4 x 5) x = 2,000 (4 x 5) x 10 3 = 20,000

4 (7 x 4) x 10 3 = (8 x 8) x 10 4 = (9 x 8) x 10 2 = (2 x 5) x 10 3 = (2 x 8) x 10 2 = (7 x 8) x 10 4 = A 5 th grade class is learning about chemistry. To set up an experiment, a teacher places 30 marbles in each of 20 glass jars. How many marbles are needed for the experiment? Kyle says that 20 x 104 is the same as 20,000. He reasoned that since he saw 4 as the exponent he should write 4 zeros in his answer. Is Kyle correct?

5 Powers of 10 and Exponents Use exponents to show powers of 10 Expressions with repeated factors, such as 10 x 10 x 10, can be written by using a base with an exponent. The is the number that is used as the repeated factor. The is the number that tells how many times the base is used as a factor. 10 x 10 x 10 = 10 3 = 1,000 Numbers expressed using exponents can also be called. Numbers raised to the second or third power have special names. Exponent Form 2 5 Word Form EXAMPLE 1 Hummingbirds bear their wings very fast. The smaller the hummingbird is, the faster its wings beat. The average hummingbird beats its wings 3 x 10 3 times a minute. How many times a minute is that, written as a whole number? Multiply 3 by powers of ten. Look for a pattern. 3 x 10 0 = 3 x 1 = 3 x 10 1 = 3 x 10 = 3 x 10 2 = 3 x 10 x 10 = 3 x 10 3 = 3 x 10 x 10 x 10 = So, the average hummingbird beats its wings about times a minute. Write in exponent form and word form. 10 x x 10 x 10 x 10 Exponent form: Word form: Exponent form: Word form:

6 10 x 10 x x 10 x 10 x 10 x 10 Exponent form: Word form: Exponent form: Word form: Find the value = 4 x 10 2 = 7 x 10 3 = 10 4 = 2 x 10 3 = 6 x 10 4 = Complete the pattern. 12 x 10 0 = 12 x 1 = 12 x 10 1 = 12 x 10 = 12 x 10 2 = 12 x 100 = 12 x 10 3 = 12 x 1,000 = 12 x 10 4 = 12 x 10,000 = Explain how to write 50,000 using exponents. The Earth s diameter through the equator is about 8,000 miles. What is the Earth s estimated diameter written as a whole number multiplied by a power of 10? Peyton says 10 5 is the same as 50 because 10 x 5 equals 50. What was Peyton s mistake?

7 Estimate Products Estimate products of whole numbers When a problem asks for about how many, you can use estimation, rounding, and/or compatible numbers. numbers are numbers in a problem that are easy to compute mentally. Estimate by rounding: o Round each factor to its greatest place o Multiply the rounded factors EXAMPLE 1 A pet store has 12 gecko lizards for sale. Each gecko lizard costs $92. About how much money would the store make if it sells all 12 gecko lizards? Estimate the product of 92 and 12. One Way Round one factor. THINK It is easier to compute 92 x 10 than 90 x x 12 x 1 Round 12 to the nearest ten. Find 92 x 10 mentally. By rounding one factor, the estimate is. Another Way Round both factors Round 92 to the nearest ten. x 12 x 1 Round 12 to the nearest ten. Find 90 x 10 mentally. By rounding both factors, the estimate is.

8 Another Way Use compatible numbers. 92 Use numbers that are easy to multiply x 12 x 1 mentally such as 100 and 10. Find 100 x 10 mentally. By using compatible numbers, the estimate is. Estimate by rounding or using compatible numbers. Show how you estimated. Round both factors x 18 x 2 The product is about. Use compatible numbers. 98 x 83 x The product is about.

9 Estimate by rounding. Show how you estimated. 218 x 6» 68 x 7» 131 x 29» 61 x 68» 79 x 56» 392 x 46» In one week, a campground rented 18 cabins at $225 each. About how much did they collect in rent altogether? Show how you estimated. The average weight for a guinea pig is 2 pounds. The average weight for a pot belly pig is 45 times greater than the guinea pig. About how much does an average pot belly pig weigh. Show how you estimated.

10 Multiply by 1-Digit Numbers Multiply multi-digit numbers by 1-digit factors EXAMPLE 1 Grace and her three friends each paid $38 for an admission ticket to an amusement park. The total paid can be found by multiplying 4 and 38. Find 38 x 4. STEP 1 Estimate 38 x 4 Think: 40 x 4 = STEP 2 Multiply the ones. 8 ones x 4 = 32 ones 3 8 Regroup 32 ones as 3 tens and 2 ones. x 4 STEP 3 Multiply the tens. 3 tens x 4 = 12 tens Add any new tens. 12 tens + 3 tens = 15 tens So, the total amount paid for admission to an amusement park is. You can use an area model to check your answer

11 A commercial airline makes several flights each week from New York to Paris, France. If the airline serves 1,978 meals on its flights each day, how many meals are served for the entire week? To multiply a greater number by a 1-digit number, repeat the process of multiplying and regrouping until every place value is multiplied. Estimate 1,978 x 7 1,978 x 7 Think: 2,000 x 7 = So, in 1 week, meals are served on flights from New York to Paris. Estimate. Then find the product. Estimate: Estimate: Estimate: ,925 x 8 x 4 x 7 Estimate: Estimate: Estimate: ,431 x 3 x 6 x 7 One 747-airplane can carry 420 passengers. How many total passengers can three planes carry? Austin bought 14 cans of cat food. Each can weighs 8 ounces. How many total ounces of cat food did he buy?

12 Zeros in the Multiplicand Multiply multi-digit numbers by 1-digit factors EXAMPLE 1 Each of the 3 classes uses 21,708 ml of distilled water in a science experiment. How much distilled water is used altogether by the three classes? o Estimate by rounding o 21,708 x 3 20,000 x 3 = 60,000 o Multiply to find the exact value multiplicand 21,708 multiplier x 3 product 65,124 Use rounding to estimate. Then multiply. The three classes use 65,124 ml of distilled water. Estimate: Estimate: Estimate: 3,302 6,011 62,090 x 7 x 8 x 3 Estimate: Estimate: Estimate: 5,209 83,806 5,004 x 2 x 5 x 7 Each of the four sides of a building contains 31,080 bricks. Each brick costs $2. What is the total cost of the bricks used for the building? Use an estimate to determine if your answer is reasonable.

13 Multiply by 2-Digit Numbers Multiply a whole number by 2-digit multiplier EXAMPLE 1 A tiger can eat as much as 40 pounds of food at a time but it may go for several days without eating anything. Suppose a Siberian tiger in the wild eats an average of 18 pounds of food per day. How much food will the tiger eat in 28 days if he eats that amount each day? Estimate 28 x 18 Think: 30 x 20 = 28 x 18 So on average, a Siberian tiger may eat pounds of food in 28 days. Complete to find the product. 6 4 x x x x + 64 x x Estimate. Then find the product. Estimate: Estimate: Estimate: x 15 x 63 x 45

14 Estimate: Estimate: Estimate: ,271 x 22 x 76 x 29 A delivery truck travels 278 miles each day. How far does it travel in 25 days? A musical theater sold 187 tickets on Friday and 238 tickets on Saturday. Tickets cost $12. Did the theater reach its goal of $5000 in ticket sales? Explain. Tickets to a museum cost $17 each. For a fieldtrip, the museum offers a $4 discount on each ticket. How much will tickets for 32 students cost?

15 Multiply by 3-Digit Numbers Multiply a whole number by a 3-digit multiplier EXAMPLE 1 A Siberian tiger was observed sleeping 1,287 minutes during the course of one day. If he slept for that long every day, how many minutes would he sleep in one year? (Assume there are 365 days in one year.) Estimate 1,287 x 365 Think: 1,000 x 400 = 1,287 x 365 Estimate. Then find the product. Estimate: Estimate: Estimate: ,537 x 387 x 271 x 242

16 Estimate: Estimate: Estimate: ,108 x 325 x 243 x 362 Emily is downloading photos from her memory card. She has 189 photos, and each photo uses 335 KB of memory. Estimate the total amount of memory used by the photos. How does your estimate compare to the exact value? A ticket to a football game costs $149. A season pass for all 16 games costs $2150. Explain whether a season pass is a good deal.

17 Zeros in the Multiplier Multiply multi-digit whole numbers with zeros in the multiplier EXAMPLE 1 Sullivan paints using pointillism, which is a technique that uses patterns of dots. The painting will have about 225 dots per square inch. If the painting is 208 square inches, how many dots are in the painting? Estimate 225 x 208 Think: 200 x 200 = 225 x 208 Estimate. Then find the product. Estimate: Estimate: Estimate: x 300 x 360 x 209

18 Estimate: Estimate: Estimate: ,409 x 900 x 805 x 306 Earth is approximately 585 times as far away from Mars as it is from the moon. If the distance from the Earth to the moon is 384,400 km, what is its distance to Mars?

Lesson 1.7. Multiply by Multi-Digit Numbers Essential Question How do you multiply by multi-digit numbers? Unlock the Problem. Name.

Lesson 1.7. Multiply by Multi-Digit Numbers Essential Question How do you multiply by multi-digit numbers? Unlock the Problem. Name. Name Multiply by Multi-Digit Numbers Essential Question How do you multiply by multi-digit numbers? Lesson 1.7 Number and Operations in Base Ten 5.NBT.B.5 MATHEMATICAL PRACTICES MP1, MP4, MP6 Unlock the