Overview

Lesson Procedure

60-70 minutes of class time across 5 phases.

1. Warm-Up5-10 minutes
2. Direct Instruction15-20 minutes
3. Guided Practice15 minutes
4. Independent Practice20 minutes
5. Closure5 minutes

1. Warm-Up5-10 minutes

   Project the back of a food package with these two lines and give students one minute to read them.

   Warm-Up Prompt

   "Directions: Microwave on high for 2 minutes 30 seconds. Stir, then let stand 1 minute. For microwaves of 1,100 watts or more, heat for 2 minutes only. Do not heat in the paper sleeve." Your microwave is 1,200 watts. Write exactly what you do, in order. Then underline every word in the directions that told you to do something different from the main step.

   Take answers. Students who follow only the first line heat it for 2 minutes 30 seconds; the exception in the third sentence changes the time to 2 minutes. List the signal words students underlined ("for ... or more," "do not," "only") and add the ones in the table below. Tell students that the standard asks for more than following the main steps: they must notice and use the special cases the text defines.

2. Direct Instruction15-20 minutes

   Part 1: How procedures signal special cases. Keep this table up for the whole lesson.

   Words that mark a special case or exception in a procedure

   Signal	What it does	Example from this lesson
   If ... / When ...	Starts a condition: do the next part only when it is true	"If the object floats" (T1, paragraph 6)
   Do not / Never	Forbids an action, sometimes for one kind of case	"Do not use this method for them" (T1, paragraph 8)
   More than / under / above	Sets a numerical limit that decides which rule applies	"above the top mark" (T1, paragraph 5)
   Instead / in place of	Replaces a main step with a different one	The overflow can in T1, paragraph 7, replaces paragraphs 3 and 4
   A heading for a group of cases	Collects the exceptions in one place, often after the main steps	"Objects that soak up water" (T1, paragraph 8)

   Part 2: Model the density procedure (T1). Read T1 aloud once for the main steps (paragraphs 2-5) and once for the special cases (paragraphs 5-8). Point out the structure: the main steps come first, but three of the special cases change what you do before paragraph 3, so a careful reader reads the whole procedure before touching the equipment. Diagram 1 puts the checks in the order you must make them.

   1Purpose: to find the density of a small solid object that does not dissolve in water. Materials: an electronic balance that reads to 0.1 g; a 100 mL plastic graduated cylinder marked every 1 mL; tap water; a steel nut tied to a 30 cm thread; an overflow can and a 250 mL beaker; paper towels.

   2Weigh the object. Check that the balance reads 0.0 g with the pan empty. Place the dry object on the pan and record its mass, m, to the nearest 0.1 g.

   3First reading. Pour about 50 mL of water into the graduated cylinder. With your eye level with the water surface, read the bottom of the curved surface (the meniscus) to the nearest 0.5 mL. Record this reading as V1.

   4Add the object. Tilt the cylinder and let the object slide down the inside wall; never drop it straight in, which can splash water out or crack the base. Stand the cylinder upright, tap its side to free any air bubbles clinging to the object, and read the new level, V2.

   5Calculate. The object's volume is V2 - V1, and its density is m ÷ (V2 - V1), in g/mL. If V2 is above the top mark, the reading cannot be used: empty the cylinder and start again with less water.

   6Objects that float. If the object floats, it is not fully under water, and V2 - V1 is too small. Tie it to the steel nut, which sinks. First find the volume of the nut alone, using paragraphs 3 and 4. Then lower the nut and the object together and find their combined volume. The object's volume is the combined volume minus the volume of the nut. Use the mass of the object alone, from paragraph 2.

   7Objects too wide for the cylinder. Fill the overflow can until water runs out of the spout, and wait until the dripping stops. Place the empty beaker under the spout and lower the object into the can on the thread. When the dripping stops again, pour the water from the beaker into the graduated cylinder and read it: that reading is the object's volume.

   8Objects that soak up water. Chalk, unsealed wood, sponge and similar materials take in water, so the level does not rise by the object's full volume. Do not use this method for them. Write "not measured: absorbs water" in the data table and tell your teacher.

   Work the three examples aloud. For each one, name the paragraph that decides what to do, and say what would go wrong if a student followed only the main steps.

   • Main steps: an object that fits and sinks

     A glass marble has a mass of 13.8 g. The water reads 50.5 mL before it goes in and 56.0 mL after. Follow T1 to find its density.

     Result: Paragraph 5: volume = V2 - V1 = 56.0 - 50.5 = 5.5 mL, and density = m ÷ (V2 - V1) = 13.8 ÷ 5.5 = 2.51 g/mL, close to the usual 2.4-2.8 g/mL for glass. Before the calculation counts, check the steps that protect it: the marble slid down the tilted wall (paragraph 4), the side was tapped to free bubbles, and V2 was read at eye level at the bottom of the meniscus (paragraph 3).

   • Special case: an object that floats

     A cork stopper (mass 3.1 g) floats. The steel nut alone raises the water from 50.0 mL to 52.0 mL; the nut and cork together raise it from 50.0 mL to 65.0 mL. What is the density of the cork?

     Result: Paragraph 6 applies, so the plain V2 - V1 of the cork would be "too small." Nut volume = 52.0 - 50.0 = 2.0 mL; combined volume = 65.0 - 50.0 = 15.0 mL; cork volume = 15.0 - 2.0 = 13.0 mL. Use "the mass of the object alone": 3.1 ÷ 13.0 = 0.24 g/mL. A reader who skips the subtraction divides by 15.0 and gets 0.21 g/mL.

   • Special case: an object too wide for the cylinder

     A smooth granite rock about 6 cm across has a mass of 212.4 g and will not fit in the cylinder. The beaker under the overflow spout collects water that reads 79.0 mL in the cylinder.

     Result: Paragraph 7 replaces paragraphs 3 and 4: the collected water "is the object's volume," so there is no V1 or V2 to subtract. Density = 212.4 ÷ 79.0 = 2.69 g/mL, within the usual range for granite (about 2.6-2.8 g/mL). The special case changes how the volume is found, not how density is calculated.

3. Guided Practice15 minutes

   Pairs read the pendulum procedure (T2) and mark each special case with a star and the main steps with numbers. Check with the class: the special cases are in paragraphs 6 and 7, and paragraph 2 contains one too (measure to the center of the mass, "not to its hook"). Then pairs work the data log in the example below, one decision at a time, before you show the answer. Diagram 2 shows the setup.

   1Purpose: to measure the period of a pendulum 50.0 cm long. The period is the time for one complete swing, out and back. Materials: a ring stand with a clamp, clamped firmly to the table; string; a 50 g hooked mass; a meter stick; a protractor; a stopwatch that reads to 0.01 s.

   2Setup. Tie the string to the clamp and hang the mass from it. Measure the length from the point where the string leaves the clamp to the center of the mass, not to its hook. Adjust the string until the length is 50.0 cm, within 0.2 cm.

   3Release. Hold the mass so that the string is straight and makes an angle of 10° with the vertical; check the angle with the protractor. Let go without pushing.

   4Timing. Let the pendulum make one full swing before you time anything. Start the stopwatch as the mass passes its lowest point, and count that pass as zero. Stop the watch on the tenth pass through the lowest point in the same direction. Record the time for 10 swings.

   5Trials. Repeat paragraphs 3 and 4 until you have five good trials.

   6Trials that must be repeated. A trial does not count if the mass hits the stand, if it swings in an oval or a circle instead of back and forth in one plane, if the starting angle was more than 15°, or if you lose count. Cross out the time, write the reason beside it and do another trial.

   7Checking the five times. Find the median of the five good times. If any time differs from the median by more than 0.30 s, do one more trial and use its time in place of that one. Then divide the mean of the five times by 10 to get the period.

   • Applying the exceptions to a data log

     A pair records seven attempts with T2 (times for 10 swings): 14.21 s; 14.26 s "angle about 12°"; 13.80 s; 14.35 s "mass hit the stand"; 14.18 s; 14.30 s "started at 20°"; 14.15 s. What must they do, and what period do they report?

     Result: Paragraph 6 removes the attempts where the mass hit the stand and the start was 20°; the 12° start still counts, because only "more than 15°" voids a trial. The five good times are 14.21, 14.26, 13.80, 14.18 and 14.15 s, with median 14.18 s. Paragraph 7: 13.80 s differs from the median by 0.38 s, more than 0.30 s, so they do one more trial (14.20 s) and use it in its place. Mean = 71.00 ÷ 5 = 14.20 s, and the period is 14.20 ÷ 10 = 1.420 s.

   Debrief with one question: Why does the procedure time 10 swings and divide by 10, instead of timing one swing? (One swing lasts about 1.4 s, so a reaction delay at the start and stop of the watch would be a large part of it; over 10 swings the same delay is spread out.) Students should see that paragraph 7 is a step, not a comment: the period is not ready to report until the median check is done.

4. Independent Practice20 minutes

   Students read the ruler-drop procedure below on their own and answer quiz questions 1-20 with the passage open. They should not do the ruler drop during the quiz; if you have time, pairs can carry it out afterward (Activity 2 variation).

   1Purpose: to measure how quickly a person reacts to something they see, by finding how far a falling ruler drops before they catch it. Materials: a 30 cm ruler marked in millimeters, a table, a partner and a data table. One partner is the dropper and the other is the catcher for all of the trials.

   2Setup. The catcher sits and rests the forearm of the writing hand flat on the table, with the hand past the edge. The thumb and index finger are held open, 2 cm apart. The dropper holds the ruler at the 30 cm end so that it hangs straight down between the catcher's thumb and finger, with the 0 cm mark level with the top of the thumb.

   3Drop. The dropper says "ready," then waits between 1 and 5 seconds, changing the wait each time, and lets go without any other signal. The catcher pinches the ruler as fast as possible without lifting the forearm from the table. Read the mark at the top of the thumb to the nearest 0.5 cm. This is the catch distance.

   4Trials. Do one practice drop and do not record it. Then do five recorded trials. Keep the same hand, the same seat and the same 2 cm gap for every trial.

   5Trials that do not count. If the catcher's fingers start to close before the ruler starts to fall, the trial is void: write "early" and repeat it. If the forearm lifts off the table during the catch, the trial is also void: write "arm" and repeat it. A void trial is not one of the five.

   6Misses. If the ruler falls through the catcher's fingers, write "miss" in place of a distance. A miss counts as one of the five trials, but it is left out of the mean. If a catcher has two misses, stop, check that the gap is 2 cm and that the 0 cm mark is level with the top of the thumb, and start the five trials again.

   7Very short catches. A catch distance under 5.0 cm is shorter than a real reaction allows. It means the catcher guessed the moment of release, even if no one saw the fingers move, so treat the trial as early.

   8Results. Find the mean of the catch distances you kept, in centimeters. Change the mean to meters, then find the reaction time with t = √(2d ÷ 9.8), where d is in meters and t is in seconds. Report the reaction time to the nearest 0.01 s.

5. Closure5 minutes

   Exit ticket: "Name one special case from any procedure you read today. Quote the words that define it, and say what a student who ignored it would have done wrong." Sort the tickets into "quotes the condition and the changed action," "quotes the condition only" and "names a main step instead" to plan the next lesson.

   Teacher note on safety and the science. None of the procedures uses heat, flames or hazardous chemicals. Use plastic graduated cylinders, wipe spills at once so no one slips, and keep the ring stand clamped so it cannot tip. The formula in T3 treats the ruler as falling freely from rest, which is close enough at these distances; it gives about 0.25 s for the whole 30 cm ruler, so a reaction slower than that shows up as a miss. The pendulum period in T2 matches the simple formula T = 2π√(L ÷ g), about 1.42 s for 50.0 cm, as long as the angle stays small, which is one reason the text caps it at 15°.

   Homework passage. The homework uses the bicycle tire procedure below, a technical task rather than an experiment. It has special cases of three kinds: numerical limits (the range, 20 psi, 3 psi), conditions that change a step (a warm tire, a Presta valve) and conditions that stop the task altogether (a leak, a cut or bulge).

   1Purpose: to set a bicycle tire to the right pressure before a ride. Materials: the bicycle and a floor pump with a gauge that reads in psi (pounds per square inch). A tire at the wrong pressure wears faster, grips the road less well and goes flat more easily.

   2Find the range. Read the pressure range printed on the side of the tire (the sidewall), for example "50-80 PSI." Never go below the first number or above the second, whatever the steps below say.

   3Set the target. Start at the middle of the range and round down to a multiple of 5 psi. For a 50-80 PSI tire the middle is 65 psi, so the target is 65 psi. Add 5 psi if the rider has a mass over 80 kg. Subtract 5 psi if the ride will be on gravel or wet roads. If both apply, they cancel.

   4Wait for a cold tire. Check the pressure only when the bicycle has not been ridden for at least 15 minutes. A tire warmed by riding reads higher than it will once it cools.

   5Connect the pump. Remove the valve cap. A Schrader valve, the same kind as on a car tire, is ready as it is. A Presta valve is thinner and has a small nut at its tip: unscrew that nut until it stops, then press the tip once to free it. Push the pump head straight onto the valve and lift its lever to lock it.

   6Pump. Pump five strokes at a time and read the gauge after each set. Stop when the gauge shows the target. If you go over, lower the lever, press the valve tip briefly to let out some air, lock the head again and read the gauge.

   7Flat or leaking tires. If the first reading is below 20 psi, do not pump straight to the target. Pump to 20 psi, wait 10 minutes and read the gauge again. If the tire has lost more than 3 psi, it has a leak: tag the bicycle "repair" and do not ride it. If not, pump to the target.

   8Finish. Lower the lever and pull the head straight off. On a Presta valve, tighten the small nut. Replace the cap. Check the sidewall for cuts or bulges; a tire with either must not be ridden, whatever its pressure.

Differentiation Strategies

Assessment Guidance

1. Question 1 of 20 · Multiple Choice

   According to paragraph 2, where is the 0 cm mark of the ruler at the start of a trial?

   ALevel with the bottom of the catcher's thumb BLevel with the top of the catcher's thumb CLevel with the edge of the table D2 cm above the catcher's index finger

2. Question 2 of 20 · Multiple Choice

   What does the dropper do between saying "ready" and letting go?

   ALets go at once, so the catcher cannot prepare BCounts to three aloud, then lets go CWaits between 1 and 5 seconds, a different wait each time DWaits until the catcher nods, then lets go

3. Question 3 of 20 · Multiple Choice

   What happens to the practice drop described in paragraph 4?

   AIt is recorded as trial 1 BIt is recorded but left out of the mean CIt is done only if the first trial is a miss DIt is done but not recorded

4. Question 4 of 20 · Multiple Choice

   On one trial the catcher's fingers start to close before the dropper lets go, and the ruler is caught at 3.5 cm. What should be recorded?

   A"early," and the trial is repeated; it is not one of the five B3.5 cm, because the ruler was caught C"miss," because the catch was not a real reaction D3.5 cm, but only if the dropper agrees

5. Question 5 of 20 · Multiple Choice

   On trial 3 the ruler falls through the catcher's fingers. How is this trial handled?

   AIt is void and repeated, like an early trial BIt is recorded as 30 cm, the full length of the ruler CIt is recorded as "miss," counts as one of the five and is left out of the mean DIt is recorded as "miss" and replaced by a sixth trial, so that five distances go into the mean

6. Question 6 of 20 · Multiple Choice

   A catcher's five recorded trials are 15.5 cm, 18.0 cm, miss, 17.0 cm and 20.5 cm. What mean catch distance does the procedure call for?

   A14.2 cm B17.75 cm C17.5 cm D20.2 cm

7. Question 7 of 20 · Multiple Choice

   During a catch the catcher's forearm lifts off the table. What does the procedure say to do?

   AWrite "miss" and keep it as one of the five BKeep the distance and note that the arm moved CWrite "early" and repeat the trial DWrite "arm" and repeat the trial

8. Question 8 of 20 · Multiple Choice

   A catcher has two misses. What does paragraph 6 say to do next?

   AStop, check the 2 cm gap and the 0 cm mark, and start the five trials again BFinish the five trials, then average the three distances that were caught CDo two extra trials to replace the misses DSwitch hands and continue

9. Question 9 of 20 · Multiple Choice

   A catch reads 4.5 cm. The dropper is sure the catcher's fingers did not move before the release. What should be recorded?

   A4.5 cm, because no one saw the fingers move B"early," and the trial is repeated C"miss," and the trial counts as one of the five D4.5 cm, left out of the mean

10. Question 10 of 20 · Multiple Choice

    A catcher's mean catch distance is 19.6 cm. Using paragraph 8, what is the reaction time?

    A2.00 s B0.04 s C0.20 s D1.96 s

11. Question 11 of 20 · Multiple Choice

    Which of these must stay the same for every recorded trial?

    AThe catcher's hand, seat and finger gap BThe length of the wait after "ready" CThe catch distance DThe mark on the ruler that the catcher aims for

12. Question 12 of 20 · Multiple Choice

    Paragraph 3 tells the dropper to change the wait each time. Which later paragraph shows why that matters?

    AParagraph 4, because it keeps the same seat for every trial BParagraph 6, because a miss is left out of the mean CParagraph 8, because the time is found from the distance DParagraph 7, because a catcher who can guess the release catches too soon

13. Question 13 of 20 · Multiple Choice

    A pair's log reads, in order: practice 21.0 cm; 18.0 cm; 2.5 cm; 16.5 cm; "arm"; 19.0 cm; miss; 18.5 cm. What mean catch distance should they report?

    A14.4 cm B18.6 cm C18.0 cm D14.9 cm

14. Question 14 of 20 · Short Answer

    Use the mean you found in Question 13 to find that pair's reaction time. Show each step of paragraph 8.

    Show model answer

15. Question 15 of 20 · Short Answer

    The procedure has two kinds of problem trials: void trials (paragraph 5) and misses (paragraph 6). Explain two differences between them. Quote each paragraph.

    Show model answer

16. Question 16 of 20 · Short Answer

    A catcher's log reads 17.5 cm, 16.0 cm, 4.0 cm, 18.5 cm and 17.0 cm, and the catcher reports the mean of all five, 14.6 cm. Explain what went wrong and what the catcher must do before calculating again.

    Show model answer

17. Question 17 of 20 · Short Answer

    A catcher's five trials are 14.5 cm, 16.0 cm, miss, 15.0 cm and 17.5 cm. Find the mean catch distance and the reaction time, and name the paragraph behind each step.

    Show model answer

18. Question 18 of 20 · Short Answer

    A dropper says "ready," counts silently to three and lets go, the same way on every trial. Which instruction is broken, and how could it change the results? Use paragraphs 3 and 7.

    Show model answer

19. Question 19 of 20 · Short Answer

    Halfway through, the partners swap roles, so trials 4 and 5 are caught by the other partner. Can the pair report one reaction time from the five trials? Cite paragraphs 1 and 4.

    Show model answer

20. Question 20 of 20 · Short Answer

    Write the checks a recorder makes for one drop, in the order they must be made, from the moment the dropper lets go to the number written in the table. Cite the paragraph for each check.

    Show model answer

These standards connect to RST.9-10.3: prerequisites to review first, parallel standards at the same level, and next steps that build on it.

Standard text: Common Core State Standards for English Language Arts & Literacy. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.