2. Objective The learner will determine appropriate measuring tools, units, and scales The learner will determine appropriate measuring tools, units, and scales

3. The Metric System Length = Meters Length = Meters Capacity = Liters Capacity = Liters Weight = Grams Weight = Grams King Harry Died Drinking Chocolate Milk King Harry Died Drinking Chocolate Milk  Kilo, Hecto, Deka, Deci, Centi, Milli

4. The Customary System Length Length 12 inches (in)=1 foot (ft) 3 ft=1 yard (yd) 5,280 ft=1 mile (mi) Capacity Capacity 8 fluid ounces (oz)=1 cup (c) 2 c=1 pint (pt) 2 pt=1 quart (qt) 4 qt=1 gallon (gal) Weight Weight 16 dry ounces (oz)=1 pound (lb) 2,000 lb=1 ton (T)

5. Measurement Match Tell which metric & customary unit you would use to measure each item Length of house key Thickness of nickel Width of classroom Length of piece of chalk Height of pine tree Distance from Baton Rouge to Shreveport - centimeter, inch - millimeter, inch - meter, feet - centimeter, inch - meter, feet - meters, miles

6. Choose the Best Estimate Height of an average man Height of an average man A. 18 cm B. 1.8 m C. 6 km D. 36 mm Volume of a coffee cup Volume of a coffee cup A. 300 mL B. 20 L C. 5 L D. 1 kL Width of a math book Width of a math book A. 215 mm B. 75 cm C. 2 m D. 1.5 km Mass of an average man Mass of an average man A. 5 mg B. 15 cg C. 26 g D. 90 kg Mass of a dime Mass of a dime A. 3 g B. 30 g C. 10 cg D. 1 kg Length of a basketball court Length of a basketball court A. 1000 mm B. 250 cm C. 28 m D. 2 km

7. Measurement Match Tell which metric & customary unit you would use to measure each item Length of a book Contents of soda can A load of bricks Distance between 2 cities Water in a swimming pool Width of the letter A - centimeter, inch - milliliter, ounces - kilogram, pounds - kilometer,miles - kiloliter,gallons - millimeter, inch

8. Customary Conversion Review Decide if you multiply or divide, then complete the conversion 6000 lb = ___ T 8000 ft = ____ mi 10 gal = ____ pt 7 c = ____ pt 2 T = ____ lb 3.5 ft = ____ in 3, divide by 2000 1.51, divide by 5280 80, multiply by 8 3.5, divide by 2 4000, multiply by 2000 42, multiply by 12

9. Worksheet Choosing best measurement Choosing best measurement

10. Objective The learner will distinguish between precision & accuracy of measurements The learner will distinguish between precision & accuracy of measurements

11. Unit 7: Measurement Measuring means to compare something with a standard Measuring means to compare something with a standard Measuring requires an instrument Measuring requires an instrument

12. Measurements days old?months old?years old? Measurements Consists of two parts Consists of two parts  A Number  Unit Must have both parts Must have both parts  Ex: I have a cat that is 3

13. Ruler (Instrument of Measurement) Demonstrate how to use a ruler Demonstrate how to use a ruler Students measure using Customary Measurements worksheet Students measure using Customary Measurements worksheet

14. What is Accuracy? What does it mean to be accurate? What does it mean to be accurate? Accuracy tells us how CORRECT the measurement is. Accuracy tells us how CORRECT the measurement is. Accuracy is how CLOSE a number is to what it should be. Accuracy is how CLOSE a number is to what it should be. Accuracy is determined by comparing a number to a known or accepted value. Accuracy is determined by comparing a number to a known or accepted value.

15. What is Precision? What does it mean to be precise? What does it mean to be precise? Precision is the degree to which repeated readings agree. Precision is the degree to which repeated readings agree. Precision can be the number of decimal places assigned to the measurement. Precision can be the number of decimal places assigned to the measurement. The precision of an instrument reflects the number of digits in the reading. The precision of an instrument reflects the number of digits in the reading.

16. Accuracy and Precision Accuracy and precision can not be considered independently Accuracy and precision can not be considered independently A number can be accurate and not precise A number can be accurate and not precise A number can be precise and not accurate A number can be precise and not accurate The use of the number determines the relative need for accuracy and precision The use of the number determines the relative need for accuracy and precision

17. Example 1: How old are you? How old are you?  I am 16 years old  I am 15 years and 8 months old  I am 15years, 8 months, and 5 days old  I am 15 years, 8 months, 5 days, and 10 hours old

18. Accuracy vs. Precision for Example 1 Each of these statements is more accurate and more precise than the one before it. Each of these statements is more accurate and more precise than the one before it. Statement two is more accurate and more precise than statement one. Statement two is more accurate and more precise than statement one. Statement three is more accurate and more precise than statement two. Statement three is more accurate and more precise than statement two.

19. Example 2: How long is a piece of string? How long is a piece of string?  Johnny measures the string at 2.63 cm.  Using the same ruler, Fred measures the string at 1.98 cm.  Who is most precise?  Who is most accurate?

20. Accuracy vs. Precision for Example 2 The actual measurement is 2.65 cm. The actual measurement is 2.65 cm. Johnny is fairly accurate and also very precise. Johnny is fairly accurate and also very precise. Fred is very precise, however, he is not very accurate. His lack of accuracy is due to using the ruler incorrectly. Fred is very precise, however, he is not very accurate. His lack of accuracy is due to using the ruler incorrectly.

21. ACCURACY/PRECISION You can tell the precision of a number simply by looking at it. The number of decimal places gives the precision. You can tell the precision of a number simply by looking at it. The number of decimal places gives the precision. Accuracy on the other hand, depends on comparing a number to a known value. Therefore, you cannot simply look at a number and tell if it is accurate. Accuracy on the other hand, depends on comparing a number to a known value. Therefore, you cannot simply look at a number and tell if it is accurate.

22. Activity Lesson 1: Linear Measurement Lesson 1: Linear Measurement Unit 7: Activity 4 Unit 7: Activity 4

23. When Do We Need to Be Accurate & Precise?? Making Accurate Measurements Making Accurate Measurements Making Accurate Measurements Making Accurate Measurements Accuracy (Actual) & Precision (Predict) Accuracy (Actual) & Precision (Predict) Accuracy (Actual) & Precision (Predict) Accuracy (Actual) & Precision (Predict)

24. Target Examples Were we accurate or precise? This is a random- like pattern, neither precise nor accurate. The darts are not clustered together and are not near the bull’s eye.

25. Target Examples Were we accurate or precise? This is a precise pattern, but not accurate. The darts are clustered together but did not hit the intended mark.

26. Target Examples Were we accurate or precise? This is an accurate pattern, but not precise. The darts are not clustered, but their average position is the center of the bull’s eye.

27. Target Examples Were we accurate or precise? This pattern is both precise and accurate. The darts are tightly clustered and their average position is the center of the bull's eye.

28. Objective The learner will use significant digits in computational problems. The learner will use significant digits in computational problems.

29. Scientific Notation REMEMBER: Scientific Notation Used to deal with very small or very large numbers as powers of 10 Examples: 0.00002 is written as 2 x 10 -5 4,000,000 is written as 4 x 10 6 Note: a negative exponent just means it’s a number less than 1

30. Significant Digits Not every number your calculator gives you can be believed Every measurement has error in it so the calculations do too

31. Significant Digits Significant Digits - all digits in a number representing data or results that are known with certainty plus one uncertain digit.

32. The measuring device determines the number of significant digits a measurement has. The measuring device determines the number of significant digits a measurement has. In this section you will learn In this section you will learn  to determine the correct number of significant digits to record in a measurement  to count the number of significant digits in a recorded value  to determine the number of significant digits that should be retained in a calculation. Significant Digits

33. For example, if you measured the length, width, and height of a block you could calculate the volume of a block: For example, if you measured the length, width, and height of a block you could calculate the volume of a block: Length: 0.11 cm Width: 3.47 cm Height: 22.70 cm Volume = 0.11cm x 3.47cm x 22.70cm = 8.66459 cm 3 Where do you round off? = 8.66?= 8.7?8.66459? Volume = lwh

34. Significant Digits RECOGNITION OF SIGNIFICANT DIGITS All nonzero digits are significant. 3.51 has 3 significant digits The number of significant digits is independent of the position of the decimal point Zeros located between nonzero digits are significant 4055 has 4 significant digits

35. Significant Digits Zeros at the end of a number (trailing zeros) are significant if the number contains a decimal point. 5.7000 has 5 sig figs Trailing zeros are not significant if the number does not contain a decimal point 2000. versus 2000 Zeros to the left of the first nonzero integer are not significant. 0.00045 (note: 4.5 x 10 -4 )

36. Significant Digits How many significant figures are in the following? 7.500 2009 600. 0.003050 80.0330 4 4 3 4 6

37. Significant Digits 2.30900 0.00040 30.07 300 0.033 6 2 4 1 2

38. Significant Digits SCIENTIFIC NOTATION & SIGNIFICANT DIGITS Often used to clarify the number of significant digits in a number. Example: 4,300 = 4.3 x 1,000 = 4.3 x 10 3 0.070 = 7.0 x 0.01 = 7.0 x 10 -2

39. Significant Digits SIGNIFICANT DIGITS IN CALCULATION OF RESULTS I.Rules for Addition and Subtraction The answer in a calculation cannot have greater significance than any of the quantities that produced the answer. example: 54.4 cm + 2.02 cm 54.4 cm 2.02 cm 56.42 cm correct answer 56.4 cm

40. Significant Digits II. Rules for Multiplication and Division The answer can be no more precise than the least precise number from which the answer is derived. The least precise number is the one with the fewest significant digits Which number has the fewest sig figs? The answer is therefore, 3.0 x 10 -8

41. For example, if you measured the length, width, and height of a block you could calculate the volume of a block: For example, if you measured the length, width, and height of a block you could calculate the volume of a block: Length: 0.11 cm Width: 3.47 cm Height: 22.70 cm Volume = 0.11cm x 3.47cm x 22.70cm = 8.66459 cm 3 Where do you round off? = 8.66?= 8.7?8.66459? Volume = lwh

42. Significant Digits Rules for Rounding Off Numbers When the number to be dropped is less than 5 the preceding number is not changed. When the number to be dropped is 5 or larger, the preceding number is increased by one unit. Round the following number to 3 sig figs: 3.34966 x 10 4 =3.35 x 10 4

43. Objective The learner will solve problems using indirect measurement & similar triangles (Lesson 4-2) The learner will solve problems using indirect measurement & similar triangles (Lesson 4-2)

44. Think – Pair - Share How thick is a sheet of paper? How thick is a sheet of paper? How much does a grain of rice weigh? How much does a grain of rice weigh?

45. Using Proportions Rates (miles/gallon, words/minute) Rates (miles/gallon, words/minute) Indirect Measurement (shadow, similar triangles) Indirect Measurement (shadow, similar triangles) Scale Drawings (maps, scales, floor plans) Scale Drawings (maps, scales, floor plans)

47. A ratio is the comparison of two numbers by division. A ratio can be written as a fraction. For example: Your school’s volleyball team has won 7 games and lost 3 games. What is the ratio of wins to losses? Because we are comparing wins to losses the first number in our ratio should be the number of wins and the second number is the number of losses. The ratio is games won 7 games 7 games lost 3 games 3 ==

48. In a ratio, if the numerator and denominator are measured in different units then the ratio is called a rate. A unit rate is a rate per one given unit, like 60 miles per 1 hour. Example: You can travel 120 miles on 60 gallons of gas. What is your fuel efficiency in miles per gallon? Rate = 120 miles________ 60 gallons = ________20 miles 1 gallon Your fuel efficiency is 20 miles per gallon.

49. Example The table at right gives several prices for different sizes of the same brand of apple juice. Find the unit rate (cost per ounce) for the 16-oz size.

50. A proportion is an equation that states that two ratios are equal. In a proportion, the cross products are equal.

52. Examples

58. The scale of the map at the left is 1 inch : 10 miles. Approximately how far is it from Valkaria to Wabasso?