The measurements you make in the science laboratory, whether for time,

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1 Measuring Up Middle Grades Science Middle Grades Measuring Science Up Exploring Experimental Error through Measurement MATERIALS balance beaker, 250 ml copy of Nick and Nack template graduated cylinder, 100 ml meter stick scissors The measurements you make in the science laboratory, whether for time, distance, temperature, or mass, are more than just numbers they also include units. To make comparisons between measurements, it is necessary to have measurements in the same units. UNITS AND THE FACTOR-LABEL METHOD The factor-label method is the tool used to convert one unit of measurement to another unit of measurement. The first step is finding a unit factor that will convert back and forth between different units. Multiplying a measurement by a unit factor changes the measurement s units but does not change its numeric value. For example, suppose you measured the distance between two locations to be 2.5 km and you want to know that distance in meters. Step 1: Determine the unit factor. 1 km = 1000 m Step 2: Create the unit factor. Place the unit you want to convert in the numerator and the units you have in the denominator m 1 km Step 3: Multiply the unit factor by the measurement m 2.5 km 2500 m 1 km EXPERIMENTAL ERROR For scientific investigation to be repeated and validated, experimental error must be minimized. As you conduct investigations, you should be aware of the types of error and how they occur. 1

2 Systematic error is an error inherent in the lab setup. It causes the results to be skewed so that a measured value is consistently too large or too small. For example, if a balance reads 0.15 g when there is no mass on it, this would introduce a systematic error to each mass measurement so that all measurements would be too large by 0.15 g. This error can be corrected by zeroing the balance. Most of the experiments you do will have some systematic error. All experiments have random error. The time required for someone to start and stop a stopwatch is an example of random error. It is important to point out that human reaction time is not the same thing as human error or carelessness (forgetting to push the start/stop or reset buttons). Your finite reaction time is not carelessness on your part but a limitation of one part of the experimental process. Averaging several measurements can reduce random error. This is good lab technique. ACCURACY AND PRECISION All scientists communicate in the common language of numbers, and understand that no measurement can be totally accurate and precise. Accuracy refers to the degree with which a measurement agrees with a known quantity. For example, during a recent laboratory activity students used a triple-beam balance to find the mass of an unknown solid. After two attempts, the students recorded the mass of the unknown as g and g. The teacher informed the students that the mass of the unknown solid was g. Assuming the measurement given by the teacher is correct, the measurements of the triple-beam balance would be described as inaccurate. Precision is the degree to which individual measurements agree with each other. Three more students used the same triple-beam balance to determine the mass of their unknown solid and recorded g, g, and g. Because the measurements are close to one another, the triple-beam balance could be described as precise. The accuracy of a measurement depends on the skill of the individual taking the measurement and the capacity of the measuring instrument. Because few measurements are exact, you should always read to the smallest mark on the instrument and then estimate another digit beyond that. For example, if you are reading the length of the steel pellet pictured in Figure 1 using only the ruler shown to the left of the pellet, you can confidently say that the measurement is between 1 cm and 2 cm. However, you must also include one additional digit estimating the distance between the 1-cm and 2-cm marks. The correct measurement using this ruler should be reported as 1.4 cm or 1.5 cm. It would be incorrect to report this measurement as 1 cm or even 1.45 cm given the scale of this ruler. 2

3 Figure 1. Measurement of steel pellet What if you are using the ruler shown on the right of the pellet? What is the correct measurement of the steel pellet using this ruler? 1.4 cm? 1.5 cm? 1.40 cm? 1.45 cm? The correct answer would be 1.45 cm. Because the smallest markings on this ruler are in the tenths place, carry the measurement out to the hundredths place. If the measured value falls exactly on a scale marking, the estimated digit should be zero. The thermometer in Figure 2 should read 30.0 C. A value of 30 C would imply this measurement had been taken on a thermometer with markings that were 10 apart, not 1 apart. The value 30 C represents anything that will round to 30. This means a value could fall between 29.5 to 30.4 C, and would indicate a possible error of 1 C. Figure 2. Thermometer 3

4 Always report measurements one decimal place past the accuracy of the measuring device. However, by including an additional digit the number 30.0 C indicates a value between to C. This would indicate a possible error of only 0.1 C. When using instruments with digital readouts, you should record all the digits shown. The instrument has done the estimating for you. Most liquids form a slight dip in the middle when measured with a glass graduated cylinder. This dip is called a meniscus. Your measurement should be read from the bottom of the meniscus. Practice reading the volume contained in the three cylinders illustrated in Figure 3. Record your values to the left of the graduated cylinders. Figure 3. Reading graduated cylinders Left: Center: Right: PURPOSE In this activity, you will review the importance of units and numbers in science. You will apply these concepts and skills to your own measurements and calculations, including measuring your own reaction time. 4

5 PROCEDURE PART I: REACTION TIME 1. Hold a meter stick between your lab partner s thumb and forefinger (Figure 4). Place the 50-cm mark on the meter stick even with your partner s thumb and fingers. The thumb and finger should be spread 5.0 cm apart to ensure consistency. Make sure to check this distance, and do not drop the meter stick immediately. Figure 4. Initial hand placement Remember that you started at 50 cm 2. Tell your lab partner that you will drop the meter stick in the next 5 seconds and that they are supposed to catch the meter stick as quickly as possible. Drop the meter stick and have your partner catch it on the way down only by closing their thumb and fingers (not by moving their arm downward). Do not announce when you are about to drop the meter stick. 3. Measure the distance the meter stick fell in centimeters before it was caught. Repeat this step two more times. 4. Exchange places with your partner and repeat the procedure to find your own reaction distance. 5

6 PROCEDURE (CONTINUED) Remember, units are a critical part of any measurement. PART II: OBJECT LENGTHS IN DIFFERENT UNITS 1. Cut out the two paper rulers. 2. Measure and record the length of each pencil in Figure 5 in both Nicks and Nacks. Figure 5. Pencils of varied lengths Always report measurements one decimal place past the accuracy of the measuring device. PART III: VOLUME MEASURED WITH BEAKER AND GRADUATED CYLINDER 1. Record the mass of an empty 250 ml beaker. 2. Use the beaker to measure 93 ml of water, and record the mass of the beaker and water together. 3. Empty and dry the beaker. 4. Repeat Step 1 through Step 3 for a total of three trials. 5. Record the mass of an empty 100 ml graduated cylinder. 6. Use the graduated cylinder to measure 93 ml of water, and record the mass of the graduated cylinder and water together. 7. Empty and dry the graduated cylinder. 8. Repeat Step 5 through Step 7 for a total of three trials. 6

7 DATA AND OBSERVATIONS PART I: REACTION TIME Person Table 1. Reaction Time Drop Distance (cm) Trial 1 Trial 2 Trial 3 Average Reaction Time (s) PART II: OBJECT LENGTHS IN DIFFERENT UNITS Table 2. Object Lengths in Different Units Pencil Length (Nack) Length (Nick) A B C D E 7

8 DATA AND OBSERVATIONS (CONTINUED) PART III: VOLUME MEASURED WITH BEAKER AND GRADUATED CYLINDER Trial 1 Table 3. Mass Measured with Beaker Volume of Water (ml) Mass of Beaker (g) Mass of Beaker and Water (g) Mass of Water (g) 2 3 Trial 1 Table 4. Mass Measured with Graduated Cylinder Volume of Water (ml) Mass of Graduated Cylinder (g) Mass of Graduated Cylinder and Water (g) Mass of Water (g) 2 3 ANALYSIS PART I: REACTION TIME 1. Calculate your average drop distance, and record this data in Table Use Table 5 to determine your average reaction time, and record this data in Table 1. Distance Meter Stick Falls (cm) Table 5. Average Reaction Times Reaction Time (s) Speed Rating ~0.10 Cheetah ~0.14 Pronghorn antelope ~0.18 Wildebeest ~0.20 Gazelle 28+ ~0.24 Honey badger 8

9 ANALYSIS (CONTINUED) PART II: OBJECT LENGTHS IN DIFFERENT UNITS Create a graph plotting Nicks versus Nacks, and then determine the slope of the graph. Slope = (include units) 9

10 ANALYSIS AND CONCLUSION QUESTIONS 1. Why is it important to perform repeated trials when determining reaction time/distance the meter stick drops? 2. According to Figure 6, which ruler would provide a more precise measurement of the pencil? Explain. Figure 6. Measurement of pencils Hint: Look at the slope of your graph 3. What is 1 Nack equal to in Nicks? 10

11 ANALYSIS AND CONCLUSION QUESTIONS (CONTINUED) 4. How many Nicks are there in 25 Nacks? 5. If 93 ml of water has a mass of 93 g, which object was more accurate in determining volume, the graduated cylinder or the beaker? Why? 6. Which was more precise, the graduated cylinder or the beaker? Why? 7. Using the same triple balance, three students measure the mass of 93 ml of water. They record the mass to be 95.5 g, 95.0 g, and 96.0 g. Discuss the accuracy and precision of their measurements and any possible sources of error. 11

12 GOING FURTHER Convert the units in Table 6 using the factor-label method. Table 6. Converting Units Conversion Unit Factor Answer cm =? m 12.2 kg =? g ml =? L 12

13 ITEM 1 NICK AND NACK RULERS The Answer Key for this activity is based on a 1:1 scale of the Nick and Nack rulers Please do not shrink or enlarge this image NACK Cut out this center rectangle to make a window in the ruler NACK NICK Cut out this center rectangle to make a window in the ruler NICK L E S S O N C O N S U M A B L E 13

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