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

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

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)

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

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 mm B. 250 cm C. 28 m D. 2 km

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

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 , divide by , multiply by 8 3.5, divide by , multiply by , multiply by 12

Worksheet Choosing best measurement Choosing best measurement

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

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

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

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

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.

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.

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

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

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.

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?

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.

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.

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

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)

Objective The learner will calculate relative error based on absolute error. The learner will calculate relative error based on absolute error.

Absolute Error Depends on the precision of the measuring instrument Depends on the precision of the measuring instrument Absolute error is ½ of the precision of the instrument Absolute error is ½ of the precision of the instrument  For example, if the ruler measures to ¼ of an inch, the absolute error is 1/8.  If the ruler measures to 1/16 of an inch, the absolute error is 1/32

Error in Measurement Accurate measurement is one which uncertainty is small as compared to the measurement Accurate measurement is one which uncertainty is small as compared to the measurement Example: An uncertainty of +4mg out of 342 mg indicates more accuracy than +4mg out of 12 mg. Example: An uncertainty of +4mg out of 342 mg indicates more accuracy than +4mg out of 12 mg. Uncertainty in measurement is represented as a percent of uncertainty called relative error. Uncertainty in measurement is represented as a percent of uncertainty called relative error.

Relative Error The smaller the relative error, the more accurate the measurement. The smaller the relative error, the more accurate the measurement.

Previous Examples Example: An uncertainty of +4mg out of 342 mg indicates more accuracy than +4mg out of 12 mg. Example: An uncertainty of +4mg out of 342 mg indicates more accuracy than +4mg out of 12 mg. Calculating the relative error shows a big difference in accuracy in the second, although their absolute errors where the same!

Example The students measure the length of a chalkboard. One students uses 1 inch units, while the other student uses 1 centimeter units. The first student measured the chalkboard to be 100 in, while the other student found the length to be 254 cm. Which student has the more accurate measurement?

Solution MeasurementUnit Absolute Error Relative Error 100 inches 1 inch ½ inch.5/100 x 100 =.5% 254 cm 1 cm ½ cm.5/254 x 100 =.2% Answer: 254 cm is more accurate because the relative error is smaller

You Try! Use your ruler to measure a the diameter of a penny. Use your ruler to measure a the diameter of a penny. Measure twice: Measure twice:  Customary to the nearest 1/16 of an inch  Metric to the nearest millimeter Find the precision of the instrument, the absolute error, and the relative error of each. Find the precision of the instrument, the absolute error, and the relative error of each.

Measurement Lab Pencil Pencil Paper Clip Paper Clip Height Height Weight Weight

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

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

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

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: cm Volume = 0.11cm x 3.47cm x 22.70cm = cm 3 Where do you round off? = 8.66?= 8.7? ? Volume = lwh

Significant Digits RECOGNITION OF SIGNIFICANT DIGITS All nonzero digits are significant has 3 significant digits Zeros located between nonzero digits are significant 4055 has 4 significant digits

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

Significant Digits How many significant figures are in the following?

Significant Digits

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 = 7.0 x 0.01 = 7.0 x 10 -2

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 cm 54.4 cm 2.02 cm cm correct answer 56.4 cm

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

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: cm Volume = 0.11cm x 3.47cm x 22.70cm = cm 3 Where do you round off? = 8.66?= 8.7? ? Volume = lwh

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: x 10 4 =3.35 x 10 4

Worksheets Math Review Worksheet Math Review Worksheet Calculating Perimeter and Area Calculating Perimeter and Area GEE pg 258 (Surface Area & Volume) with GEE formulas GEE pg 258 (Surface Area & Volume) with GEE formulas

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)

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?

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)

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