Example Use mental math and a pattern. Multiply. 50 8,000. ALGEBRA Lesson 1.5
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1 Name Multiplication Patterns Essential Question How can you use a basic fact and a pattern to multiply by a 2-digit number? ALGEBRA Lesson 1.5 Number and Operations in Base Ten 5.NBT.A.2 MATHEMATICAL PRACTICES MP3, MP8 Unlock the Problem How close have you been to a bumblebee? The actual length of a queen bumblebee is about 20 millimeters. The photograph shows part of a bee under a microscope, at 10 times its actual size. What would the length of the bee appear to be at a magnification of 300 times its actual size? Use a basic fact and a pattern. Multiply = 6 basic fact 30 2 = ( 3 2 ) 10 1 = = ( 3 2 ) 10 2 = = ( 3 2 ) ( ) = = So, the length of the bee would appear to be about millimeters. Math Talk MATHEMATICAL PRACTICES 8 Generalize What pattern do you see in the number sentences and the exponents? Houghton Mifflin Harcourt Publishing Company Image Credits: (cr) Jude Gibbins/Alamy What would the length of the bee shown in the photograph appear to be if the microscope shows it at 10 times its actual size? Example Use mental math and a pattern. Multiply. 50 8, = 40 basic fact 5 80 = ( 5 8 ) 10 1 = = ( 5 8 ) 10 2 = = ( 5 8 ) ( ) = = 50 8,000 = ( 5 8 ) ( 10 1,000 ) = = Chapter 1 29
2 Share and Show MATH BOARD Use mental math and a pattern to find the product ,000 = What basic fact can you use to help you find 30 4,000? Use mental math to complete the pattern = = _ = _ = 56 ( 7 8 ) 10 1 = _ ( 7 8 ) 10 2 = _ = _ ( 6 5 ) _ = 300 ( 6 5 ) _ = 3, = _ On Your Own Use mental math to complete the pattern = 45 ( 7 8 ) 10 3 = _ = 21 Math Talk ( 6 5 ) _ = 30,000 MATHEMATICAL PRACTICES 3 Apply Explain Tell how how to to find find ,000 9,000 by by using using a basic basic fact fact and and pattern. pattern = _ ( 9 5 ) 10 1 = _ ( 9 5 ) 10 2 = _ ( 9 5 ) 10 3 = _ ( 3 7 ) 10 1 = _ ( 3 7 ) 10 2 = _ ( 3 7 ) 10 3 = _ ( 5 4 ) _ = 200 ( 5 4 ) _ = 2,000 ( 5 4 ) _ = 20,000 Use mental math and a pattern to find the product. 8. ( 6 6 ) 10 1 = _ 11. ( 4 3 ) 10 2 = _ 14. ( 6 5 ) 10 3 = _ 9. ( 7 4 ) 10 3 = _ 12. ( 2 5 ) 10 3 = _ 15. ( 8 8 ) 10 4 = _ 10. ( 9 8 ) 10 2 = _ 13. ( 2 8 ) 10 2 = _ 16. ( 7 8 ) 10 4 = _ 17. SMARTER What does the product of any whole-number factor multiplied by 100 always have? Explain. Houghton Mifflin Harcourt Publishing Company 30
3 Name Use mental math to complete the table roll = 50 dimes Think: 50 dimes per roll 20 rolls = ( 5 2 ) ( ) Rolls Dimes roll = 40 quarters Think: 40 quarters per roll 20 rolls = ( 4 2 ) ( ) Rolls Quarters , Houghton Mifflin Harcourt Publishing Company Image Credits: (cr) Graham Bailey/Alamy Use the table for What if you magnified the image of a cluster fly by ? What would the length appear to be? 23. DEEPER If you magnified the images of a fire ant by and a tree hopper by , which insect would appear longer? How much longer? 24. MATHEMATICAL PRACTICE 2 Reason Quantitatively John wants to magnify the image of a fire ant and a crab spider so they appear to be the same length. How many times their actual sizes would he need to magnify each image? Arthropod Lengths Arthropod Cluster Fly Crab Spider Fire Ant Tree Hopper Length (in millimeters) ers) WRITE Math Show Your Work Chapter 1 Lesson 5 31
4 MATHEMATICAL PRACTICES COMMUNICA E CONSTRUCT ARGUMENTS Blood Cells Single red blood cell Blood is necessary for all human life. It contains red blood cells and white blood cells that nourish and cleanse the body and platelets that stop bleeding. The average adult has about 5 liters of blood. White blood cell Platelet Use patterns and mental math to solve. 25. DEEPER A human body has about 30 times as many platelets as white blood cells. A small sample of blood has white blood cells. About how many platelets are in the sample? 26. Basophils and monocytes are types of white blood cells. A blood sample has about 5 times as many monocytes as basophils. If there are 60 basophils in the sample, about how many monocytes are there? 27. Lymphocytes and eosinophils are types of white blood cells. A blood sample has about 10 times as many lymphocytes as eosinophils. If there are eosinophils in the sample, about how many lymphocytes are there? 28. SMARTER An average person has times as many red blood cells as white blood cells. A small sample of blood has white blood cells. About how many red blood cells are in the sample? 29. SMARTER Kyle says 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? Houghton Mifflin Harcourt Publishing Company Image Credits: (t) Sciepro/Science Photo Library/Corbis 32
5 Name Multiplication Patterns Practice and Homework Lesson 1.5 COMMON CORE STANDARD 5.NBT.A.2 Understand the place value system. Use mental math to complete the pattern = 24 (8 3) 10 1 = 240 (8 3) 10 2 = 2,400 (8 3) 10 3 = 24, = (5 6) 10 1 = (5 6) 10 2 = (5 6) 10 3 = 3. 3 = 27 (3 9) 10 1 = (3 9) 10 2 = (3 9) 10 3 = 4. _ 4 = 28 (7 4) = 280 (7 4) = 2,800 (7 4) = 28, = (6 8) 10 2 = (6 8) 10 3 = (6 8) 10 4 = 6. 4 = 16 (4 4) 10 2 = (4 4) 10 3 = (4 4) 10 4 = Use mental math and a pattern to find the product. 7. (2 9) 10 2 = 8. (8 7) 10 2 = 9. (3 7) 10 3 = 10. (5 9) 10 4 = 11. (4 8) 10 4 = 12. (8 8) 10 3 = Problem Solving Houghton Mifflin Harcourt Publishing Company 13. The Florida Everglades welcomes about visitors per day. Based on this, about how many visitors come to the Everglades per week? 15. WRITE Math Do the products and have the same number of zeros? Explain. 14. The average person loses about strands of hair each day. About how many strands of hair would the average person lose in 9 days? Chapter 1 33
6 Lesson Check (5.NBT.A.2) 1. How many zeros are in the product (6 5) 10 3? 2. Addison studies a tarantula that is 30 millimeters long. Suppose she uses a microscope to magnify the spider by How long will the spider appear to be? Spiral Review (Reviews 4.OA.A.3, 4.NBT.B.5) 3. Hayden has 6 rolls of dimes. There are 50 dimes in each roll. How many dimes does he have altogether? 4. An adult ticket to the zoo costs $20 and a child s ticket costs $10. How much will it cost for Mr. and Mrs. Brown and their 4 children to get into the zoo? 5. At a museum, 100 posters are displayed in each of 4 rooms. Altogether, how many posters are displayed? A store sells a gallon of milk for $3. A baker buys 30 gallons of milk for his bakery. How much will he have to pay? FOR MORE PRACTICE GO TO THE Personal Math Trainer Houghton Mifflin Harcourt Publishing Company
One Way. Another Way Show partial products. Lesson
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