Multiplying Decimals Student Probe Find the product 3.7  4 Answer: 14.8 Lesson Description This lesson builds upon students’ understanding of whole number multiplication and estimation to develop the algorithm for multiplying decimals. The focus of the lesson is upon where to place the decimal point rather than the multiplication itself. Rationale Estimation plays a significant role in the development of the algorithm essential to multiplying decimals. Even though students will likely use a calculator when they encounter real world problems involving decimal multiplication, the use of estimation will help them as they think about the reasonableness of calculator answers. Preparation Have problems prepared to assign to students. At a Glance What: Multiplying decimals Common Core State Standard: CC.6.NS.3. Fluently add, subtract, multiply, and divide multi‐digit decimals using the standard algorithm for each operation. Mathematical Practices: Make sense of problems and persevere in solving them. Who: Students who cannot multiply decimals Grade Level: 6 Prerequisite Vocabulary: Estimate, round Prerequisite Skills: Multiplication of whole numbers, multiplication of fractions Delivery Format: Individual or Small Group Lesson Length: 15‐30 minutes Materials, Resources, Technology: calculators (optional) Student Worksheets: None Lesson The teacher says or does… 1.
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Expect students to say or do… If students do not, then the teacher says or does… Cartons of juice contain Model 3.7 on a number line to 3.7 ounces of juice. If you show it is closer to 4 than 3. buy 4 cartons, how many ounces of juice did you buy? Let’s estimate and use mental math. Is 3.7 ounces closer to 3 ounces 4 ounces or 4 ounces? About how many ounces would that be altogether? 16 ounces, because 4  4  16 . How do you know? Let’s multiply 37  4 . 148 Students may be allowed to use a calculator. You may use any method you want. Can we use repeated (Select a student to share addition? their strategy.) What do you notice about Answers may vary, but listen the problems 37  4 and for, “They have the same digits (numbers).” 3.7  4 ? So, if we multiply the numbers together we get 148, but our original problem was 3.7  4 . We need to find where to place the decimal. When we estimated we 14.8 got 16. Which is closer to 16: 148.0, 14.8, 1.48 or 0.148? So where should the Between the 4 and the 8. decimal point go? Let’s find some more 1512 Students may be allowed to decimal products. use a calculator. Find the product 24  63 . The teacher says or does… Expect students to say or do… If students do not, then the teacher says or does… Model the numbers 2.4 and 8. Without multiplying, what 6.3 on a number line. is 2.4  6.3 ? 2 Is 2.4 closer to 2 or to 3? 6 Is 6.3 closer to 6 or to 7? 12 What is 2  6? So our answer is near 12. 9. Which is closest to 12: 15.12 Model on a number line. 1512.0, 151.2, 15.12, 1.512, or 0.1512? 10. For 2.4 x 6.3 we are 1512/100 Refer to Multiplying Fractions. multiplying 24/10 x 63/10. What is the product? 11. How do we write 15.12 Refer to Decimal Place Value. 1512/100 as a decimal? 12. Without multiplying, what is 2.4  63 ? What numbers would you 2 and 60 use for this estimate? 2 is close to 2.4 and 60 is close Why? to 63. 13. What is your estimated 120, because 2  60  120 . answer? How did you get that? 14. What is the exact answer? 151.2 Which is closest to 120: 1512.0, 151.2, 15.12, 1.512, or 0.1512? 15. Without multiplying, what Refer to Equivalent Fractions. is 0.24  63 ? We know that we can use 60 as an estimate for 63. What can we use as an 1
estimate for 0.24? 4
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15 Refer to Multiplying Fractions. 16. What is of 60? 4
17. Which is closest to 15: 15.12 1512.0, 151.2, 15.12, 1.512, or 0.1512? 18. Repeat with additional problems if necessary. Teacher Notes: 1. Use a calculator to explore other products that are alike except for the decimals involved. The digits in the answer are always alike. 2. When finding the product of decimal numbers between 0 and 1, it is helpful to estimate 1 1 1 2 3
using benchmark fractions such as , , , , . 4 3 2 3 4
Variations None Formative Assessment Find the product: 8.5  6.5 . Answer: 55.25 Students should estimate 8  7  56 . Since 85  65  5525 , the exact answer is 55.25. References Russell Gersten, P. (n.d.). RTI and Mathematics IES Practice Guide ‐ Response to Intervention in Mathematics. Retrieved 2 25, 2011, from rti4sucess. Van De Walle, John A. Elementary and Middle School Mathematics: Teaching Developmentally. Boston: Allyn and Bacon, 2004. Print.