1. FRACTION MULTIPLICATION AND THE PRODUCTS OF DECIMALS Lesson 6.2.11

2. ROUNDING DECIMALS - TENTHS Round each number to the nearest tenth  310.286  6.805  118.380  815.755  877.71  12.261

3. ROUNDING DECIMALS - HUNDREDTHS Round each number to the nearest hundredth.  487.362  22.700  159.410  2.190  58.139  10.886

4. APPLICATION PROBLEM  A tree grows 9.5 inches per year. If the tree continues to grow at this rate, how much will the tree grow in 3.5 years? Estimate to check whether your answer is reasonable.

5. APPLICATION PROBLEM SOLUTION 1  A tree grows 9.5 inches per year. If the tree continues to grow at this rate, how much will the tree grow in 3.5 years? Estimate to check whether your answer is reasonable. 9.5 in ? 9.5 in ÷ 2 = 4.75 in (9.5 x.5 = 4.75 in) 9.5 (3) + 4.75 = 9 (3) +.5 (3) + 4.75 = 27 + 1.5 + 4.75 = 33.25 inches Estimation: 10 x 4 = 40 (over estimate) or 10 x 3.5 = 35 The tree will grow 33.25 inches in 3.5 years.

6. APPLICATION PROBLEM SOLUTION 2  A tree grows 9.5 inches per year. If the tree continues to grow at this rate, how much will the tree grow in 3.5 years? Estimate to check whether your answer is reasonable. Year.511.522.533.5 Growth (in)4.759.514.2519.023.7528.533.25 The tree will grow 33.25 inches in 3.5 years.

7. EXPLORATORY CHALLENGE  Work in small groups to complete the two given problems.  Show all of your work that supports your solutions and the placement of the decimal in the product.  After finding each product, use previous knowledge to prove your product has the decimal in the correct location. Be prepared to present your proof to the class.

8. EXPLORATORY CHALLENGE 1

9. EXPLORATORY CHALLENGE 2

10. DISCUSSION  Do you see a connection between the number of decimal digits in the factors and the product?  In the first problem, there are two decimal digits in the first factor and one decimal digit in the second factor, which is a total of three decimal digits. The product has three decimal digits.  In the second problem, both factors have one decimal digit for a total of two decimal digits in the factors. The product also has two decimal digits.

11. PROBLEMS 1 - 4 1.Calculate the product..×..×.=,..×.=,. 2.Kevin spends $. on lunch every week during the school year. If there are. weeks during the school year, how much does Kevin spend on lunch over the entire school year? Remember to round to the nearest penny..×.=. ≅. Kevin would spend $. on lunch over the entire school year. 3.Gunnar’s car gets. miles per gallon, and his gas tank can hold. gallons of gas. How many miles can Gunnar travel if he uses all of the gas in the gas tank?.×.=. Gunnar can drive. miles on an entire tank of gas. 4.The principal of East High School wants to buy a new cover for the sand pit used in the long jump competition. He measured the sand pit and found that the length is. feet and the width is. feet. What will the area of the new cover be?.×.=. The cover should have an area of. square feet.

12. MATH TALK  Do you see a connection between the number of decimal digits in the factors and the product?  How can we use information about the factors to determine the largest place value of the product and the number of decimal digits in the product?

13. EXIT TICKET

14. ROUNDING DECIMALS - TENTHS  Round each number to the nearest tenth  310.286  6.805  118.380  815.755  877.71  12.261

15. ROUNDING DECIMALS - HUNDREDTHS  487.362  22.700  159.410  2.190  58.139  10.886