1. Copyright © Ed2Net Learning, Inc.1 Description and Measurement Grade 6 Unit 1 : Lesson #5

2. Copyright © Ed2Net Learning, Inc.2 What you’ll learn  Vocabulary:  Measurement  Estimation  Precision  Accuracy  Using estimation to determine how reasonable a measurement is.  Identify the rules and use them for rounding a number.  Distinguish between accuracy and precision in measurements.  Why it is important?  Ideas and information can be communicated with the help of measurement.

3. Copyright © Ed2Net Learning, Inc.3 Measurement 3  Measurement is a way to describe the world with numbers. Questions such as how long, how much, or how far can be answered using measurements.  For example: Measurement can be used to determine the amount of milk in a carton, the cost of a book, distance between two places, weight of a person, or how fast a train is moving.

4. Copyright © Ed2Net Learning, Inc.4 Measurement 4  Engineers measure the performance of an automobile in a crash test to design safer vehicles.  It is very important that scientists rely on measurements instead of individual opinions for scientific endeavors. If a report says that, “Vehicle did fairly well in head- on collision when traveling at a moderate speed”, we would not know what does “fairly well” or a “moderate speed” mean. The report would not help us determine if the automobile is safe.

5. Copyright © Ed2Net Learning, Inc.5 Describing events 5  Measurement can also describe events.  For example: Alex, John and Chris took part in a 100 meter swimming competition this year, and John, the winner completed the race in 1 minute and 10 seconds. In this example, measurements convey information about the year of the swimming competition, the length, and the time taken by the winner. Information about who all competed in the event are not measurements but help describe the event completely. Alex John Chris

6. Copyright © Ed2Net Learning, Inc.6 Try this! 6  ___________ is a way to describe the world with numbers. Answer: Measurement

7. Copyright © Ed2Net Learning, Inc.7 Try this! 7  Why would not a clock that measures in minutes be precise for calculating the time in any race? Answer: Because in any race, winners may win by fractions of a second.

8. Copyright © Ed2Net Learning, Inc.8 Qualitative and Quantitative descriptions 8  A qualitative description is one that describes matter without involving measurements.  For example: Water is composed of hydrogen and oxygen.  A quantitative description uses numbers to describe everything.  For example: One water molecule is composed of two hydrogen atoms and one oxygen atom.

9. Copyright © Ed2Net Learning, Inc.9 Estimation 9  Estimation can help make a rough measurement of an object. When we estimate, we can use your knowledge of size of something familiar to estimate the size of the new object.  Estimation is a valuable skill based on previous experience and is useful when we are in a hurry and exact numbers are not required. Estimation skills improve with experience, practice, and understanding.  For example: A chef in a restaurant prepares for each night’s crowd based on estimation. Firefighters use estimation skills to determine the how much hose to pull off the truck when they arrive at fire disaster.

10. Copyright © Ed2Net Learning, Inc.10 Using estimation 10  Comparisons can be used to estimate measurements. While estimating, we often use the word about.  For example: Annie wants to measure the height of the ladder but finds it very tall to measure easily. But since she knows her height, she uses that to estimate the height of the ladder. I am 3 feet, so the ladder must be about 5 feet.

11. Copyright © Ed2Net Learning, Inc.11 Using estimation 11  Estimation can be used to check if an answer is reasonable.  For example: Claris tells Emma that she can run at a speed of 50 meters per second. Emma, being familiar with how long a second is and how long a meter is thinks about it. Using estimation, Emma realizes that 50 meters per second is unrealistically fast and Claris must be trying to fool her. 50 meters is too long a distance to cover in a second. Claris must be fooling me. Emma, I can run at the speed of 50 meters per second

12. Copyright © Ed2Net Learning, Inc.12 Try this! 12  When should we not estimate a value? Answer: We should not estimate a value when we need to know the exact measurement.

13. Copyright © Ed2Net Learning, Inc.13 Precision 13  Precision is a description that tells how close measurements are to each other. Measurements can be evaluated by determining whether they are precise.  For example: Elise and Jonah are measuring the height of a plant twice a day using a measure tape. Each time, Elise determines the height of the plant to be 30 centimeters. Jonah determines the height as 29 centimeters the first time he measures and 30 centimeters the second time. Since, Elise’s measurements were close to each other than Jonah’s, Elise’ were more precise.  The term precision is also used when referring to the number of decimal places a measuring device can measure.  For example: A clock with a second hand is considered more precise than one with only a minute or an hour hand.

14. Copyright © Ed2Net Learning, Inc.14 Degrees of precision 14  Over the years, the timings for Olympic events has become more precise. Events that were measured in tenths of a second 100 years ago are measured to the hundredth of a second today.  Today’s measuring devices are more precise.  For example: Before the invention of clocks, a sundial was used to determine the time of a day. As the sun passes through the day, a shadow moves around the dial. After the invention of clocks, an analog clock was used as the standard to determine the time. Nowadays, digital clocks are being used, which are quite common as the analog ones.

15. Copyright © Ed2Net Learning, Inc.15 Accuracy 15  Accuracy is described when a measurement is compared with the real, actual, or accepted value.  For example: A watch with a second hand is more precise than one with only an hour hand, but if the time is not properly set, the reading could be off by an hour or more. Therefore, the watch is not accurate. On the other hand, measurements of 1.02m, 1.04m, and 1.05m when compared to an actual value of 1.03m is accurate, but not precise.

16. Copyright © Ed2Net Learning, Inc.16 Try this! 16  What is the difference between precision and accuracy? PrecisionAccuracy Precision describes the exactness of a measure. Accuracy compares a measurement to the actual or accepted value.

17. Copyright © Ed2Net Learning, Inc.17 Visualizing Precision and Accuracy 17  Many sports require precision and accuracy. Archery is a sport that involves shooting arrows into a target. An archer must be accurate enough to hit the bull’s-eye and precise enough to do it repeatedly. This archer’s attempts demonstrates precision but not accuracy as the arrows were shot consistently to the left of the target. The archer who shot these arrows is neither accurate not precise as the arrows are scattered all around the target. This archer is a winner as all the arrows have hit bull’s eye – A result which is both precise and accurate.

18. Copyright © Ed2Net Learning, Inc.18 Precision and Accuracy 18  Precision and accuracy are very important in many medical procedures. One of these procedures is the radiation delivery in the treatment of cancerous tumors, Since, radiation damages cells, it is very important to limit the radiation to only the cancerous cells that are to be destroyed.  A technique called Stereo tactic Radiotherapy (SRT) allows doctors to be accurate and precise in delivering radiation to the areas of brain.  The patient makes an impression of his or her teeth on a bite plate, which is then attached to the radiation machine. This bite plate is each treatment to position the patient precisely the same way each time. A CAT scan locates the tumor in relation to the bite plate, which helps the doctor pinpoint with precision and accuracy where the radiation should go.

19. Copyright © Ed2Net Learning, Inc.19 Try this! 19  Which parts of the Stereo tactic Radiotherapy procedure make the measurement precise and accurate? Answer: The instruments and the techniques used such as the bite plate positions of the patient make the measurements precise. The CAT scan locates the tumor accurately.

20. Copyright © Ed2Net Learning, Inc.20 Rounding a measurement 20  Not all measurements need to be measured with great precision.  For example: We may want to measure the length of the sidewalk outside our home. We could measure it to the nearest millimeter. However, we need to know the length only to the nearest meter or tenth of a meter. So if we found the length was 140.452 m, we can round off that number to the nearest tenth of a meter and still be considered accurate.  To round a given value, follow these steps: 1. Look at the digit to the right of the place being rounded to.  If the digit to the right is 0,1,2,3,or 4, the digit being rounded to remains the same.  If the digit to the right is 5,6,7,8, or 9, the digit being rounded to increases by one. 2. The digits to the right of the digit being rounded to are deleted if they are also to the right of a decimal. If they are to the left of the decimal, they are changed to zeroes.

21. Copyright © Ed2Net Learning, Inc.21 Rounding a measurement 21  The sidewalk length was found to be 140.452 m. To round off this length to the tenths place, look at the digit to the right of 4. Because that digit is a 5, we increment the 4 by one and round it off to 140.5 m.  To round off 140.452 m to the ones place, look at the digit to the right of 0. In this case we have a 4, so we keep the 0 and round it off to 140 m.

22. Copyright © Ed2Net Learning, Inc.22 Try this! 22  The length of one object is 2.923 m. The length of the second object is 5.487 m. What are their rounded values. What we know: Mass of first object = 2.923 m, Mass of second object = 5.487 m What you need to know: The number to the right of one’s place for both the objects First object: 9, Second object = 4 We need to use: If the digit to the right is 0,1,2,3,or 4, the digit being rounded to remains the same. If the digit to the right is 5,6,7,8, or 9, the digit being rounded to increases by one. Solution: For the first object, since the digit to the right is 9, the number 2 rounds up to 3. For the second object, since the digit to the right is 4, the number 5 remains the same. The round value of 2.923 m is 3 m and the round value of 5.487 m is 5 m

23. Copyright © Ed2Net Learning, Inc.23 Precision and Number of Digits 23  Imagine you have to divide a 2 kg cake equally among 7 people. When you divide 2 by 7, the calculator display reads 0.285714285. Can you measure exactly 0.285714285 kg for each person? You cannot. All you need to know is each person gets about 0.3 kg of cake.

24. Copyright © Ed2Net Learning, Inc.24 Using Precision and Significant digits 24  Significant digits are the number of digits that truly reflect the precision of a number.  Significant digits can be figured as follows:  Digits other than zero are always significant.  Final zeroes after a decimal point (5.869000 g) are significant.  Zeroes between any other digits (708.0567 g) are significant.  Zeroes before any other digits (0.000007890 g) are NOT significant.  Zeroes in a whole number (7560) may or may not be significant.  An exact number such as the number of people in a family or the number of grams in a kilogram has infinite significant digits.

25. Copyright © Ed2Net Learning, Inc.25 Following the rules 25  There are rules to follow when deciding the number of significant digits in the answer to a calculation. They depend on what kind of calculation we are doing.  For multiplication and division, we first determine the number of significant digits in each number in the problem. Then, the significant digits of the answer are determined by the number with fewer digits.  For example: Consider the multiplication of 7.34 and 2.5 7.34 X 2.5= 3 digits2 digits 18. 35 2 digits

26. Copyright © Ed2Net Learning, Inc.26 Following the rules 26  For addition and subtraction, we first determine the place value of each number in the problem. Then, the significant digits of the answer are determined by the number that is least precise.  For example: Consider the addition of 7.34 and 2.5 7.34 + 2.5= To the hundredthsTo the tenths 9.8 4 To the tenths In the cake example, you are performing a division. The limiting number of digits is determined by the amount of cake, 2 kg. There is one significant digit there; therefore, the answer you got also has only one significant digit.

27. Copyright © Ed2Net Learning, Inc.27 Try this! 27  The mass of a substance is determined to be 0.0054 kilograms. How many significant digits are there in this measurement? Answer: There are two significant digits. The zeroes in 0.0054 are used to show only the place value of the decimal and are not counted as significant digits.

28. Copyright © Ed2Net Learning, Inc.28 Summary 28  Measurements are used to describe objects and events.  Common measurements made in daily life are length, mass, volume, temperature, weight, and time.  Estimation is used to make an educated guess about a measurement.

29. Copyright © Ed2Net Learning, Inc.29 Summary 29  Precision is a description that tells how close measurements are to each other.  Accuracy compares a measurement to the actual or accepted value.  A technique called Stereo tactic Radiotherapy (SRT) allows doctors to be accurate and precise in delivering radiation to the areas of brain.

30. Copyright © Ed2Net Learning, Inc.30 Summary 30  Significant digits are the number of digits that truly reflect the precision of a number.  For multiplication and division, we first determine the number of significant digits in each number in the problem. Then, the significant digits of the answer are determined by the number with fewer digits.  For addition and subtraction, we first determine the place value of each number in the problem. Then, the significant digits of the answer are determined by the number that is least precise.

31. Copyright © Ed2Net Learning, Inc.31 Critical thinking activity 31  Would you use half centimeters or millimeters to measure the following: Thickness of a thin wire Length of a book Length of a fork Length of a stapler

32. Copyright © Ed2Net Learning, Inc.32 Assessment 32  Students test how different surfaces affect run off. They use pans of soil set at a slant. Water is poured over each different type of surface and collected. Which tool does the student need to complete the investigation? A. Graduated cylinder B. Meter stick C. Spring scale D. Timing device Answer: A

33. Copyright © Ed2Net Learning, Inc.33 Assessment 33  The table below lists the density of common liquids. Which statement is best supported by the data? A. Most liquids are not very dense. B. Low-fat milk is less dense than water. C. Solids have a greater density than liquids. D. Alcohol floats on water. Answer: D Densities of liquids LiquidDensity (g/mL) Alcohol0.80 Water1.0 Milk1.03 Corn syrup1.36

34. Copyright © Ed2Net Learning, Inc.34 Assessment 34  To round a given value, we must look at the digit to the _______ of the place being rounded to. A. Right B. Left Answer: A

35. Copyright © Ed2Net Learning, Inc.35 Assessment 35  What determines the number of significant digits in the answer to an addition or a subtraction problem? Answer: The number that is least precise.

36. Copyright © Ed2Net Learning, Inc.36 Assessment 36  What determines the number of significant digits in the answer to an multiplication or a division problem? Answer: The number with fewer digits.

37. Copyright © Ed2Net Learning, Inc.37 Assessment 37  What would you use to measure length? A. Spring scale B. Graduated cylinder C. Meter stick D. Balance Answer: C

38. Copyright © Ed2Net Learning, Inc.38 Assessment 38  What would happen to the digit being rounded if the digit to the right is 0,1,2,3, or 4? Answer: If the digit to the right is 0,1,2,3,or 4, the digit being rounded to remains the same.

39. Copyright © Ed2Net Learning, Inc.39 Assessment 39  What would happen to the digit being rounded if the digit to the right is 5,6,7,8, or 9 Answer: If the digit to the right is 5,6,7,8, or 9, the digit being rounded to increases by one.

40. Copyright © Ed2Net Learning, Inc.40 Assessment 40  A technique called _________ allows doctors to be accurate and precise in delivering radiation to the areas of brain. Answer: Stereo tactic Radiotherapy (SRT)

41. Copyright © Ed2Net Learning, Inc.41 Assessment 41  Match the following terms with their definitions. Measurement Compares a measurement to the actual or accepted value. AccuracyA method of making a rough measurement. PrecisionA description with numbers. EstimationA description of how close measurements are to each other.

42. Copyright © Ed2Net Learning, Inc.42 Assessment 42  The dog kennel in Victoria’s home is 5.94 m long. Round to the nearest tenth of a meter. Answer: 5.9 m

43. Copyright © Ed2Net Learning, Inc.43 Assessment 43  Elise’ cat has chewed on her ruler. Will the measurements done using the ruler be accurate or precise? Answer: The measurements will not be precise in the area in which the measuring lines have been destroyed by the cat. They may still be accurate, depending on what she is measuring and what the cat destroyed.

44. Practice 44  Practice measurement skills with computer temperature probes and thermometers. Procedure: 1. Fill a 500 ml beaker with crushed ice. Add enough cold water to fill the beaker. 2. Make 3 measurements of the temperature of the ice water using a computer temperature probe. Before each measurement, remove the computer probe and allow it to warm to room temperature. Record the measurements in a science journal. 3. Repeat step 2 using an alcohol thermometer. Question 1: What is the average of each set of measurements? Question 2: Which measuring device is more precise and which one is more accurate? Explain.

45. Copyright © Ed2Net Learning, Inc.45 Thank You! 45