Overview

Lesson Procedure

60-65 minutes of class time across 5 phases.

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

1. Warm-Up5 minutes

   Project or read aloud this weather note: "The temperature at 6 a.m. was 12 °C. By 9 a.m. it had risen 3 degrees, it reached its high of 21 °C at 3 p.m., and by 9 p.m. it had fallen to 16 °C."

   Warm-Up Prompt

   Turn the note into a two-column table, Time and Temperature (°C). Which reading did you have to work out instead of copy, and how?

   Take answers. The table has four rows: 6 a.m., 12; 9 a.m., 15; 3 p.m., 21; 9 p.m., 16. The 9 a.m. reading is not printed as a temperature: "risen 3 degrees" is a change, so students add it to 12. Tell students that this is today's skill. RST.9-10.7 asks them to translate quantitative or technical information in words into visual form, such as a table or chart, and to translate information shown visually or in an equation back into words. A good translation keeps every number, unit and condition, and adds nothing the text did not say.

2. Direct Instruction15-20 minutes

   Part 1: The four translations. Post this table for the whole lesson. The first two rows are the words-to-visual half of the standard; the last two are the visual-or-math-to-words half.

   Four translations named in RST.9-10.7 and what to check in each

   From	To	What to do	What to check
   Words with numbers	Table	Give each quantity a column with its unit, and each reading a row	Changes ("rose 3 degrees") are turned into readings, or get their own column
   Table	Chart	Pick the chart that fits: line for change over time, bar for separate categories	The scale is even, and points sit at their real values, not at equal spacing
   Chart	Words	State the pattern, the size of the change and any exception	The sentence describes the shape, not just a list of values
   Equation	Words	Name every symbol and its unit, then say how the result depends on each one	Numbers in the equation (such as 0.85) are explained, not skipped

   Part 2: Model with Rumford (T1). Benjamin Thompson, Count Rumford, supervised the boring of brass cannon at the arsenal in Munich. In 1798 he told the Royal Society that friction alone could make heat without limit, and he backed the claim with the experiment below. The passage is John Tyndall's summary of Rumford's paper; the words in quotation marks are Rumford's own. A "deal-box" is a box of pine or fir boards, and the temperatures are in degrees Fahrenheit. Read it aloud once, then work the two examples.

   1He next surrounded his cylinder by an oblong deal-box, in such a manner that the cylinder could turn water-tight in the centre of the box, while the borer was pressed against the bottom of the cylinder. The box was filled with water until the entire cylinder was covered, and then the apparatus was set in action. The temperature of the water on commencing was 60°.

   2“The result of this beautiful experiment,” writes Rumford, “was very striking, and the pleasure it afforded me amply repaid me for all the trouble I had had in contriving and arranging the complicated machinery used in making it. The cylinder had been in motion but a short time, when I perceived, by putting my hand into the water, and touching the outside of the cylinder, that heat was generated.

   3“At the end of one hour the fluid, which weighed 18.77 pounds, or two and one-half gallons, had its temperature raised forty-seven degrees, being now 107°.

   4“In thirty minutes more, or one hour and thirty minutes after the machinery had been set in motion, the heat of the water was 142°.

   5“At the end of two hours from the beginning, the temperature was 178°.

   6“At two hours and twenty minutes it was 200°, and at two hours and thirty minutes it actually boiled!”

   • Words into a table (T1, paragraphs 1 and 3-6)

     Put every temperature reading in T1 into a table. How should the table handle "one hour and thirty minutes," "raised forty-seven degrees" and "it actually boiled"?

     Result: The finished table follows this example. All times go into one unit, minutes, so "one hour and thirty minutes" becomes 90 and "two hours and twenty minutes" becomes 140. The text gives the first-hour reading two ways, "raised forty-seven degrees, being now 107°," and the check 60 + 47 = 107 shows they agree; the change goes in its own column. The last reading has no number. The table says "boiling" with a note: water boils at 212 °F at sea level and near 209 °F at Munich's height, so the rise, about 149-152 °F, is an estimate the text does not print.

   Example 1 result: the readings in T1 as a table (the last row is an estimate, see the note in Example 1)

   Time (min)	Water (°F)	Rise since start (°F)
   0	60	0
   60	107	47
   90	142	82
   120	178	118
   140	200	140
   150	boiling (no number in the text)	about 149-152

   • A table into a chart (T1 and Diagram 1)

     Which kind of chart fits the table, which quantity goes on each axis, and how far apart do the points go?

     Result: A line graph fits, because the temperature is one quantity changing over time. Time goes on the horizontal axis and temperature on the vertical axis, each with an even scale: 0-160 minutes in steps of 20 and 0-240 °F in steps of 40. The points are placed at their real times, 0, 60, 90, 120, 140 and 150 minutes, so the gaps between them are 60, 30, 30, 20 and 10 minutes. A common error is to space the six rows evenly across the page, which makes the first hour look as short as the last ten minutes. The boiling point is drawn as an open circle, because the text gives no number for it. Diagram 1 is the finished chart.

   Close the model by naming what changed and what stayed the same. The table and the chart hold exactly the information in T1, with nothing added except the labeled estimate for "boiled." The table is better for reading off exact values; the chart is better for seeing how the warming went. Students will put Diagram 1 back into words in the quiz.

3. Guided Practice15 minutes

   Pairs read the kettle guide (T2), a modern technical text written for this page, and circle each symbol in the formula with the words that explain it. Then work the two examples as a class, using Diagram 2, which draws the guide's formula for three kettles.

   1How long will it take? The time your kettle needs to bring water to a boil depends on three things: how much water you put in, how many degrees the water must warm, and the power of the kettle in watts. This section gives a formula so you can estimate the time before you switch the kettle on. The kettle is invented for teaching; the physics is standard.

   2The formula. t = (m × 4.19 × ΔT) ÷ (0.85 × P). Here t is the time in seconds, m is the mass of the water in grams, ΔT is the temperature rise in °C and P is the power of the kettle in watts. The number 4.19 is the energy in joules needed to warm 1 gram of water by 1 °C. The number 0.85 is the share of the electrical energy that ends up in the water; the rest warms the kettle itself and the air around it.

   3Using the formula. One liter of water has a mass of about 1,000 grams. Tap water usually comes out at 15-20 °C, and water boils at 100 °C at sea level. Always fill the kettle between the MIN line (0.5 L) and the MAX line (1.7 L).

   4What the formula leaves out. The formula treats the share 0.85 as fixed, and it assumes the kettle body starts at room temperature. A kettle that was just used is already warm, so it boils a little sooner than the formula says. Hard-water scale on the heating plate slows heating, so descale the kettle every few months.

   • An equation into words (T2, paragraph 2)

     Write the formula t = (m × 4.19 × ΔT) ÷ (0.85 × P) as sentences a customer could follow without the symbols. Then test your sentences on 1.0 L of tap water at 20 °C in a 1,500 W kettle.

     Result: In words: multiply the grams of water by 4.19 and by the number of degrees the water must warm; that is the energy the water needs, in joules. Divide it by 85 percent of the kettle's power, because only that share of the power reaches the water. The answer is the time in seconds. Test: 1.0 L is about 1,000 g, and the rise is 100 - 20 = 80 °C, so the water needs 1,000 × 4.19 × 80 = 335,200 J. The kettle delivers 0.85 × 1,500 = 1,275 J each second, so the time is 335,200 ÷ 1,275 ≈ 263 s, about 4 minutes 23 seconds. A translation that leaves out the 0.85 gives about 223 s and is wrong by 40 seconds.

   • A chart into words (Diagram 2)

     Describe Diagram 2 in two sentences for someone who cannot see it. Say what pattern each line shows and how the three lines compare.

     Result: Each line is straight and, if extended, would pass through zero, so the time to boil is proportional to the amount of water: twice the water takes twice as long in the same kettle. At any amount, the 2,000 W kettle takes half as long as the 1,000 W kettle, and the 1,500 W kettle two-thirds as long, because the time is divided by the power. A weaker description lists values ("the top line goes up to about 670") without saying what they show.

   Debrief: Which translation lost information: the formula into words, or the formula into the chart? Students usually notice that the chart fixes the starting temperature at 20 °C, so it cannot show what the formula says about warmer or colder tap water, while the sentences keep every quantity. Each form makes some things easy to see and hides others.

4. Independent Practice20 minutes

   Students read the second Rumford excerpt below on their own and answer quiz questions 1-20. Questions 1-5, 12-16, 19 and 20 use this excerpt (T3), questions 6, 7, 17 and 20 use Diagram 1, and questions 8-11 and 18 use the kettle guide (T2) and Diagram 2. This excerpt comes from earlier in the same paper as T1: Rumford first bored a cylinder with no water around it, and then worked out how much heat the whole experiment produced. Tell students before they read: a "grain troy" is a small unit of weight (7,000 grains make a pound), "celerity" means speed, and "victuals" means food.

   1He then designed a cylinder for the express purpose of generating heat by friction, by having a blunt borer forced against its solid bottom, while the cylinder was turned around its axis by the force of horses. To measure the heat developed, a small round hole was bored in the cylinder for the purpose of introducing a small mercurial thermometer. The weight of the cylinder was 113.13 pounds avoirdupois.

   2The borer was a flat piece of hardened steel, 0.63 of an inch thick, four inches long, and nearly as wide as the cavity of the bore of the cylinder, namely, three and one-half inches. The area of the surface by which its end was in contact with the bottom of the bore was nearly two and one-half inches. At the beginning of the experiment the temperature of the air in the shade, and also that of the cylinder, was 60° Fahr. At the end of thirty minutes, and after the cylinder had made 960 revolutions round its axis, the temperature was found to be 130°.

   3Having taken away the borer, he now removed the metallic dust, or rather scaly matter, which had been detached from the bottom of the cylinder by the blunt steel borer, and found its weight to be 837 grains troy. “Is it possible,” he exclaims, “that the very considerable quantity of heat produced in this experiment—a quantity which actually raised the temperature of above 113 pounds of gun-metal at least 70° of Fahrenheit's thermometer—could have been furnished by so inconsiderable a quantity of metallic dust and this merely in consequence of a change in its capacity of heat?”

   [...]

   4He then carefully estimates the quantity of heat possessed by each portion of his apparatus at the conclusion of the experiment, and, adding all together, finds a total sufficient to raise 26.58 pounds of ice-cold water to its boiling point, or through 180° Fahrenheit. By careful calculation, he finds this heat equal to that given out by the combustion of 2,303.8 grains (equal to four and eight-tenths ounces troy) of wax.

   5He then determines the “celerity” with which the heat was generated, summing up thus: “From the results of these computations, it appears that the quantity of heat produced equably, or in a continuous stream, if I may use the expression, by the friction of the blunt steel borer against the bottom of the hollow metallic cylinder, was greater than that produced in the combustion of nine wax-candles, each three-quarters of an inch in diameter, all burning together with clear bright flames.

   6“One horse would have been equal to the work performed, though two were actually employed. Heat may thus be produced merely by the strength of a horse, and, in a case of necessity, this heat might be used in cooking victuals. But no circumstances could be imagined in which this method of procuring heat would be advantageous, for more heat might be obtained by using the fodder necessary for the support of a horse as fuel.”

5. Closure5 minutes

   Exit ticket: "Pick one sentence with numbers from T1 or T3. Put it into a table row or a sketch of a chart, and write one sentence saying what your visual shows that the words do not make easy to see." Sort the tickets into "complete and accurate," "a unit or condition lost" and "something added that the text does not say" to plan the next lesson.

   Teacher note on the historical text. T1 and T3 mix John Tyndall's summary with Rumford's own words, which are the parts in quotation marks; students should cite them as Rumford's. Rumford wrote when many scientists thought heat was a fluid called caloric. His result, that the horses' work could keep producing heat with no sign of running out, was an early step toward the idea that heat is a form of energy. The figures are his own estimates from 1798. Munich lies about 520 m above sea level, where water boils near 209 °F, not 212 °F, so any number written for "actually boiled" is an interpretation; accept either with a note. The text has no dated or offensive language.

   Homework passage. The homework uses the technical bulletin below, a modern text written for this page. Its test and data are invented.

   1Why this bulletin. Rim brakes slow a bicycle by pressing rubber pads against the metal rim of each wheel. The motion the brakes take away does not disappear: it becomes heat in the pads and the rims. On a long, steep descent that heat can build up, and a very hot rim can overheat the inner tube or soften the glue that holds some racing tires. This bulletin reports one test of how hot a rim gets. The rider, the road and all data are invented for teaching; the physics is standard.

   2The test. A rider and bicycle with a total mass of 85 kg coasted down a mountain road 6.0 km long that drops 540 m from top to bottom. The rider used both brakes to hold a steady 25 km/h the whole way. A small sensor taped to the inside of the front rim sent its reading to a handlebar computer at the top and at the end of every kilometer.

   3Results. The air temperature was 17 °C, and at the top the front rim read the same. After the first kilometer the rim read 38 °C. It read 52 °C after the second kilometer, 61 °C after the third and 67 °C after the fourth. After the fifth kilometer it read 70 °C, and at the bottom, after the sixth, 72 °C.

   4An upper limit. The most energy the brakes could have turned into heat is the energy the rider and bicycle lost by coming down the hill: E = m × g × h, where E is in joules, m is the total mass in kilograms, g is 9.8 m/s² and h is the height lost in meters. Some of this energy never reaches the brakes, because the air pushes back on the rider all the way down.

   5How hot could the rims get? If every joule of E stayed in the two rims, their temperature would rise by ΔT = E ÷ (M × c). Here M = 1.1 kg is the mass of the two aluminum rims together, and c = 900 J/(kg·°C) is the specific heat of aluminum: the energy needed to warm 1 kg of it by 1 °C. Compare that figure with the rise the sensor measured.

Differentiation Strategies

Assessment Guidance

1. Question 1 of 20 · Multiple Choice

   T3, paragraph 2, reports the first cylinder test. A student starts a table with the columns Time (min), Revolutions and Temperature (°F). Which two rows are correct?

   A0, 0, 60 and 30, 960, 130 B0, 0, 60 and 960, 30, 130 C0, 0, 70 and 30, 960, 130 D0, 0, 60 and 30, 960, 190

2. Question 2 of 20 · Multiple Choice

   The student adds a column for the turning rate in revolutions per minute during the test in T3, paragraph 2. What value belongs in it?

   A16 B0.031 C28,800 D32

3. Question 3 of 20 · Multiple Choice

   A column for the rate of warming in the same test (T3, paragraph 2) should show about how many degrees Fahrenheit per minute?

   A4.33 B2.33 C0.43 D2.00

4. Question 4 of 20 · Multiple Choice

   A student wants one bar chart, in one unit, comparing the weight of the metal dust in T3, paragraph 3, with the weight of wax whose burning gives the same heat, in paragraph 4. Which pair of bar heights, in grains, is correct?

   A837 and 4.8 B113.13 and 26.58 C837 and 2,303.8 D837 and 480

5. Question 5 of 20 · Multiple Choice

   Paragraph 5 of T3 compares the heat from friction with the heat of "nine wax-candles." Which visual translates that comparison faithfully?

   AA bar for the friction heat and a bar for the nine candles, drawn the same height BA bar for the friction heat that is taller than a bar for the nine candles CA pie chart that splits the friction heat into nine equal slices, one per candle DA line graph of each candle's temperature over time as it burns down to the end

6. Question 6 of 20 · Multiple Choice

   In Diagram 1, the line from 60 to 90 minutes is steeper than the line from 0 to 60 minutes. Which sentence puts that difference into words correctly?

   AThe water gained more degrees in that half hour than in the whole first hour BThe water was at its hottest at 90 minutes, so it was warming fastest then CThe water began to cool after 60 minutes, so the line changed direction DThe water warmed faster per minute then than during the first hour

7. Question 7 of 20 · Multiple Choice

   Which sentence best describes Diagram 1 from 60 to 140 minutes?

   AThe line is nearly straight: the water gained 1.1 to 1.2 °F a minute BThe line curves upward: the water warmed faster and faster until it boiled CThe line rises in equal steps: the water gained the same 35 °F in each interval DThe line keeps its first-hour slope: about 0.8 °F each minute the whole way

8. Question 8 of 20 · Multiple Choice

   An appliance label gives the formula cost = (P × t ÷ 1,000) × r, where P is the power in watts, t is the time of use in hours and r is the price of electricity in dollars per kilowatt-hour. Which sentence says in words what the formula says?

   AThe cost is the power in watts times the hours of use, divided by the price per kilowatt-hour BThe cost is the power times the hours of use, and the 1,000 is a fixed fee added to the bill CThe cost is the power in kilowatts times the hours of use times the price per kilowatt-hour DThe cost is the price per kilowatt-hour divided by the number of hours the appliance runs

9. Question 9 of 20 · Multiple Choice

   Use the formula in T2 for 0.6 L of water that starts at 15 °C in a 2,000 W kettle. About how long will it take to boil at sea level?

   A107 s B148 s C91 s D126 s

10. Question 10 of 20 · Multiple Choice

    Read Diagram 2. About how long does the 1,000 W kettle take to boil 1.5 L of tap water?

    AAbout 395 s, a little over 6.5 minutes BAbout 590 s, a little under 10 minutes CAbout 295 s, just under 5 minutes DAbout 670 s, just over 11 minutes

11. Question 11 of 20 · Multiple Choice

    The lines in Diagram 2 start at 0.5 L and stop at 1.7 L. Which sentence best puts that feature of the chart into words?

    AThe chart gives estimates only for the fill range the kettle allows BThe kettles were tested at 0.5 L and 1.7 L, and the lines join those tests CWater below 0.5 L would boil at once, so the chart has no time to show there DThe formula gives times below zero for amounts smaller than 0.5 L

12. Question 12 of 20 · Multiple Choice

    Which labeled sketch matches the borer described in T3, paragraph 2?

    AA steel plate 0.63 in long, 4 in wide and 3.5 in thick, touching the bore over 2.5 square inches BA steel plate 4 in long, 2.5 in wide and 0.63 in thick, touching the bore over 3.5 square inches CA steel plate 4 in long, nearly 3.5 in wide, 0.63 in thick, touching the bore over 2.5 square inches DA steel plate 4 in long, nearly 3.5 in wide and 0.63 in thick, touching the bore over 14 square inches

13. Question 13 of 20 · Multiple Choice

    Rumford's total in T3, paragraph 4, can be written as the equation 26.58 × 180 = 4,784.4. Which sentence puts that equation into words, keeping the text's units?

    AWarming 26.58 lb of water by 180 °F takes the heat that warms 4,784.4 lb by 1 °F BThe water in the box reached a temperature of 4,784.4 °F by the end of the experiment CBurning 26.58 grains of wax for 180 minutes gave 4,784.4 units of heat in all DEach of the 26.58 lb of water needed 4,784.4 °F of heat to reach the boiling point

14. Question 14 of 20 · Multiple Choice

    T3, paragraphs 1 and 3, give the weight of the cylinder and the weight of the dust, and a pound is 7,000 grains. Why is a bar chart of the two weights a poor way to show paragraph 3's comparison?

    AGrains and pounds cannot be converted into each other, so no chart can use them BA line graph from 837 to 113.13 would show the change in weight more clearly CA pie chart is always better than a bar chart for showing two weights side by side DThe dust bar would be about a thousandth of the cylinder bar, too short to see

15. Question 15 of 20 · Short Answer

    Make a table of the quantities in T3, paragraphs 4 and 5, with three columns: What was measured or estimated, Value and Unit. Then say which row needs a note, and why.

    Show model answer

16. Question 16 of 20 · Short Answer

    A classmate graphs the cylinder test in T3, paragraph 2, as a straight line joining its first and last readings. What does the straight line claim that the text does not say? Describe a more honest graph.

    Show model answer

17. Question 17 of 20 · Short Answer

    Use Diagram 1 to estimate the water temperature at 30 minutes and at 75 minutes by reading along the line. Explain in words which estimate is more trustworthy, and why.

    Show model answer

18. Question 18 of 20 · Short Answer

    At a mountain town, water boils at 95 °C. Using the formula in T2, explain in words what changes in the calculation, and find the time for 1.0 L of water starting at 20 °C in a 1,500 W kettle there.

    Show model answer

19. Question 19 of 20 · Short Answer

    Rumford's heat in T3, paragraph 4, was produced over the whole water-box experiment, which lasted two and a half hours (T1). Write an equation for the average rate of heat production in pound-degrees Fahrenheit per hour, solve it, and put the result into words. One horsepower is about 2,545 of these units per hour. Does your result agree with paragraph 6?

    Show model answer

20. Question 20 of 20 · Short Answer

    Compare the table in Example 1 with Diagram 1. In words, name one thing the line graph makes easier to see and one thing the table gives more exactly. Then say which form you would choose to show Rumford's claim in T3, paragraph 5, that heat came "in a continuous stream," and why.

    Show model answer

These standards connect to RST.9-10.7: 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.