Unit 1: Decimals Learning Goal: The student will be able to perform operations with decimals.

1. Unit 1: DecimalsLearning Goal: The student will be able to perform operations with decimals. Ms. Amanda G. Shaffer 6th Grade Math Palm Pointe Educational Research School @ Tradition

2. Scale

3. (0-2) Adding & Subtracting Decimals • In addition & subtraction, the decimal points must be lined up so that the same place values are lined up. • Use zeros as place holders. • Add & subtract from right to left, starting with the smallest place value.

4. (0-2) Adding & Subtracting Decimals • Complete each sample in your notebook. • 28.43 + 0.0972 + 15 • 97.2 – 16.437 • A big bend gecko is 16.8 centimeters long. A yellow-headed gecko is 8.9 centimeters long. How much longer is the big bend gecko? • One Western rattlesnake is 162.6 centimeters long. Another of the same species is 41.66 centimeters long. What is their combined length?

5. (0-2) Adding & Subtracting Decimals • Complete each sample in your notebook. (Answers) • 28.43 + 0.0972 + 15 = 28.4300 00.0972 +15.0000 ______________________ 43.5272 • 97.2 – 16.437 = 97.200 - 16.437 ___________________ 80.763

6. (0-2) Adding & Subtracting Decimals • Complete each sample in your notebook. (Answers) • A big bend gecko is 16.8 centimeters long. A yellow-headed gecko is 8.9 centimeters long. How much longer is the big bend gecko? 16.8 - 08.9 ____________ 7.9 inches longer • One Western rattlesnake is 162.6 centimeters long. Another of the same species is 41.66 centimeters long. What is their combined length? 162.60 + 41.66 ____________________ 204.26 cm.

7. Ch. 1 Math Vocabulary • compatible numbers – Numbers that are easy to divide mentally. • Example: 120 and 6 • decimal – A number that has a digit in the tenths place, hundredths place, and beyond. • Example: 1.67 • dividend – A number that is being divided. • Example: ; 429 is the dividend. • divisor – The number that divides the dividend. • Example: ; 3 is the divisor.

8. Ch. 1 Math Vocabulary • Factor – A number that is multiplied by another number. • Example: ; 3 and 4 are the factors. • Power of 10 – A number such as 10, 100, 1,000 and so on. It is the result of using only 10 as a factor. • Example: 101 = 10 and 102 = 100 • Product – The answer to a multiplication problem. • Example: ; 12 is the product.

9. Estimate Products (1-1A) • Remember the rules for rounding: • 5 and above, give it a shove. • 4 and below, let it go. • 6.8 = 7 • 3.2 = 3

10. Estimating Products (1-1A) • Draw a number line from 1-10 1 2 3 4 5 6 7 8 9 10 • Locate & label 1.5, 2.5, 3.5, and so on through 9.5. • Is 1.2 closer to 1 or 2? How can you tell? • Closer to 1; the distance between 1.2 and 1 is less than the distance between 1.2 and 2. • Is 4.75 closer to 4 or 5? How can you tell? • 5; The distance between 4.75 and 5 is less than the distance between 4.75 and 4. • Use the number line to round the following numbers to the nearest whole number. • 5.67 • 3.41 • 9.95

11. Estimating Products (1-1A) • Estimate Products Using Rounding • Estimate • Round to the nearest whole number to make it easy to compute mentally. 8.7 9 x 2.8 x 3 ______________ _________________ 27 • The product is about 27.

12. Estimating Products (1-1A) • Estimate each product.

13. Multiplying Decimals by Whole Numbers (1-1C)

14. Multiplying Decimals by Whole Numbers (1-1C)

15. Multiplying Decimals by Whole Numbers (1-1C)

16. Multiply Decimals by Decimals (1-1E) • When multiplying a decimal by a decimal, multiply like whole numbers. • To place the decimal point, find the sum of the number of decimal places in each factor. • The product has the same number of decimal places.

17. Example 1: Multiply Decimals • Find 4.2 x 6.7 1 1 4.2 1 decimal place X 6.7 1 decimal place ___________ 294 +2520 ___________ 28.14 2 decimal places

18. On your own! • 3.6 x 0.05 • 5.7 x 2.8 • 4.12 x 0.05 • 0.014 x 3.7

19. Ex. 2: Annex a Zero • Find 1.4 x 0.067 22 0.067 3 decimal places X 1.4 1 decimal place _________________ 268 + 670 _________________ 0.0938Annex a zero to make 4 decimal places

20. On your own! • 0.04 x 0.32 • 0.26 x 0.205 • 1.33 x 0.06

21. Ticket Out the Door • What do you know about multiplying a whole number by a decimal greater than 1? • What do you know about multiplying a whole number by a decimal between 0 and 1?

22. Estimating Quotients (1-2A) • To estimate quotients of decimals, use rounding and compatible numbers.

23. Estimating Quotients (1-2A) • Mario takes a trip. In 3 days he drives 923 miles. Each day he drives about the same distance. About how far does he drive each day? • Does this problem require an exact or estimated answer? Explain. • How can you use estimation to find about how far Mario drives each day?

24. Estimating Quotients (1-2A) • Suppose 3 friends order salads. The total cost of the salads is $15.75. They split the cost equally. How much does each person owe? • Does this problem require an exact or estimated answer? Explain.

25. Ex. 1: Estimate by Rounding Dividends 8.75 3. • Estimate 3 3 8.75 3 9

26. On your own! • Estimate the following: • 49.3 7 • 98.1 25

27. Ex. 2: Estimate by Rounding Divisors • Estimate 32 3.9 8 3.9 32 4 32

28. On your own! • 54 9.16 • 99 10.75

29. Divide Decimals by Whole Numbers (1-2C) • When dividing a decimal by a whole number, divide like whole numbers. • Place the decimal point in the quotient directly above its place in the dividend.

30. Ex. 1: Divide a Decimal by a 1-Digit Number • Find 6.8 2 3.4 2 6.8 - 6 _______________ 08 - 8 _________________ 0