The Political Economy of Anglo-French Trade, 1689-1899 ...

Mm Brennan

Description

• cours - matière potentielle : from the lower level of the duty

AMERICAN ASSOCIATION OF WINE ECONOMISTS AAWE WORKING PAPER No. 38 Economics POLITICAL ECONOMY OF ANGLO- FRENCH TRADE, 1689-1899: AGRICULTURAL TRADE POLICIES, ALCOHOL TAXES, AND WAR John V.C. Nye July 2009

• alcohol taxes
• distortionary import tariff
• domestic excises
• beer
• tariffs
• britain
• duties
• trade
• wine

Sujets

• London
• Royaume-Uni
• England
• Tariff
• Britain
• Domestic

Informations

• Publié par: viol0
• Nombre de lectures: 27
• Langue: English

Extrait

Hot Air Balloon Integer Arithmetic Chris Eldredge Waynesboro City Public Schools

Topic: addition and subtraction of positive and negative integers Overview Students struggling to understand addition and especially, subtraction, of integers may need another concrete way of “seeing” it.This lesson depends upon some prior knowledge of integer arithmetic and helps the learner think about integer operations vertically in addition to horizontally (as on a number line).

Grades: 6 – 9

Time Allotment Two 45-minute periods

Learning Objectives On completion of this lesson students will be able to: €Determine the most likely affect of adding a negative number €Determine the most likely affect of subtracting a negative number This lesson addresses Va. SOL Math 7.5

Media Components €PC and Video projector €PowerPoint €Copy of PowerPoint presentation (a presentation in which images of a hot air balloon move up, then down after clicks of the mouse) th €Recording of “My Beautiful Balloon” by The 5Dimension (CD preferably)

Materials and Student Handouts €Small helium filled balloon (1 per three students) attached by a one foot long string (or ribbon) to a small Dixie cup (the gondola) €One gram weights (5 per three students) €Worksheets with simple integer arithmetic problems which the student must solve (one per student, teacher developed) €Pictures of hot air balloons

Teacher Preparations €Setup PC and Video projector and PowerPoint presentation €Prepare CD to play background music ”My Beautiful Balloon” €Place in back of the room but visible.Make balloons with gondolas attached.

NTTI Fall 2004

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Hot Air Balloon Integer Arithmetic Chris Eldredge Waynesboro City Public Schools

Introductory Activity Focus:[make certain that the helium balloons are visible in the back of the room] Think about adding and subtracting positive and negative numbers.Think about the things which cause balloons to go up and down. Activity: PLAY(about five minutes) Music “My Beautiful Balloon” Follow-up:Show pictures of hot air balloons.SAYLook at these pictures.Has anyone ever been up in a hot air balloon?The music is about balloons.Think about hot air balloons. Whatcauses hot air balloons to go up and down?[discuss the affects of hot air and weight]

Learning Activities ADDING A POSITIVE 1. Focus:SAY I want you to think about two things:Think about adding hot air to the balloons, and think about adding positive numbers...Which way do hot air balloons go when you add hot air?That’s right, UP!Which way do we go to add a positive number? That’s right, UP!Let’s watch it another way. Activity:PLAYPowerPoint (ordinal numbers indicate clicks of the mouse)SAYThese are actually images of a hot air balloon.(ordinal numbers indicate clicks of the mouse) st : 1 bunnyballoons spin (attention grabber only) nd 2 :header appears, read as it finishes appearing rd 3 :picture #1 footer appears, bunny goes UP (read to reinforce and discuss) Follow-up:WRITEon chalkboard: 10 + 6 =?SAY:Raise your hand if you know the answer to this ... That’s right: 16.[write answer on board]Why? Canyou describe that using our hot air balloon model? [the description should say something like ... the balloon goes up as hot air is add to the balloon, the 10 goes up as the 6 is added to it.]

SUBTRACTING A NEGATIVE 2. Focus:SAY:Now, think about these two things: Think about the removing weight from the balloons, and think about subtracting negative numbers...Which way do hot air balloons go when you remove weight from them?That’s right, UP!Which way do we go to subtract a negative number? [answers will vary, someone will get it right as you respond]That’s right, UP! Let’s watch it in our bunny model. th Activity:PLAY: picturePowerPoint (ordinal numbers indicate clicks of the mouse) 4 #4 footer appears, bunny goes UP (read to reinforce and discuss) Follow-up: WRITEon chalkboard: 10 – (-6) =?SAY:Now before you respond, think about our model...What did it say would happen when we removed weight? That’s right: it should go up.So, by how much will 10 go up in the problem on the board? That’sright: 6. What will it go up to?That’s right: 16.[write answer on board] Why? Canyou describe that using our hot air balloon model?[the description should say something like ...the balloon goes up as weight is removed from the balloon, the 10 goes up as the (-6) is subtracted from it.]WRITEon chalkboard: (-17) – (-4) =?SAY: Here’s a more difficult one, however, the rule is the same.Now before you respond, think about our model.What did it say would happen when we removed weight?That’s NTTI Fall 2004Page 2 of 5

Hot Air Balloon Integer Arithmetic Chris Eldredge Waynesboro City Public Schools

right: it should go up.That’s right: 4. And what will itSo, by how much will it go up? go up to?That’s right: (-13).[write answer on board]Remember, what makes this problem more difficult than the previous one is the fact that we’re taking away from a negative number instead of a positive number[point out the difference in the two problems, if necessary] SAY:In summary, what we’ve seen so far supports the rule, “SUBTRACTING A NEGATIVE IS LIKE ADDING A POSITIVE”Let’s continue. ADDING A NEGATIVE 3. Focus:SAY Now, think about these two things:Think about adding weight to the balloons, and think about adding negative numbers.Which way do hot air balloons go when you add weight to them?That’s right, DOWN!Which way do we go to add a negative number?[answers will vary, someone will get it right as you respond]That’s right, DOWN!Let’s watch it in our bunny model. th Activity:PLAY: footerPowerPoint (ordinal numbers indicate clicks of the mouse) 5 th appears, read as it finishes appearing6 :picture #3 footer appears, bunny goes DOWN (read to reinforce and discuss) Follow-up:WRITEon chalkboard: 10 + (-6) =?SAY:Now before you respond, think about our model.What did it say would happen when we added weight?That’s right: it should go down.That’s right: 6. And what will it goSo, by how much will it go up? down to?That’s right: 4. [write answer on board]Whyyou describe that using our? Can hot air balloon model?[The description should say something like ...the balloon goes down as weight is added to the balloon, the 10 goes down as the (-6) is added to it.] WRITEon chalkboard: (-14) + (- 8) =?SAY:Now before you respond, think about our model.What did it say would happen when we added weight?That’s right: it should go DOWN .That’sSo, by how much will (-14) go down in the problem on the board? right: 8. And what will it go down to?That’s right: (-22).[write answer on board] Why? Canyou describe that using our hot air balloon model?[The description should say something like ... the balloon goes down as weight is added to the balloon, the (-14) goes down (becomes more negative) as the (-8) is added to it.] SUBTRACTING A POSITIVE 4. Focus:SAY:Think about two things: Think about removing hot air from the balloons, and think about subtracting positive numbers. Which way do hot air balloons go when you REMOVE hot air?That’s right, DOWN!Which way do we go to subtract a positive number?That’s right, DOWN!Let’s watch it another way. th Activity:PLAYPowerPoint (ordinal numbers indicate clicks of the mouse) 7: picture #2 footer appears, bunny goes DOWN (read to reinforce and discuss) Follow-up: WRITEon chalkboard: 10 - 6 =?SAY:Now before you respond, think about our model.What did it say would happen when we removed hot air?That’s right: it should go DOWN .So, by how much will 10 go down in the problem on the board? That’s right: 6. And what will it go down to?That’s right: 4. [write answer on board] Why? Canyou describe that using our hot air balloon model?[The description should say something like ... the balloon goes down as hot air is removed from the balloon,the 10 goes down as the 4 is subtracted from it.]WRITEon chalkboard: (-14) - 8 =? SAY:Now before you respond, think about our model.What did it say would happen NTTI Fall 2004Page 3 of 5

Hot Air Balloon Integer Arithmetic Chris Eldredge Waynesboro City Public Schools

when we removed hot air?That’s right: it should go DOWN.So, by how much will (- 14) go down in the problem on the board?That’s right: 8. And what will it go down to? That’s right: (-22).[write answer on board]you describe that using our hotWhy? Can air balloon model?[The description should say something like ...the balloon goes down as hot air is removed from the balloon,the (-14) goes down (becomes more negative) as the 8 is subtracted from it.]SAY:In summary, what we’ve seen so far supports the rule “SUBTRACTING A POSITIVE NUMBER IS LIKE ADDING A NEGATIVE” Let’s wrap it up.

CLOSING COMMENTS 5. Focus:SAY: What are the two rules of subtraction we’ve discussed today? 1.SUBTRACTING A POSITIVE IS LIKE ADDING A NEGATIVE 2.SUBTRACTING A NEGATIVE IS LIKE ADDING A POSITIVE Let’s take one last look at our floating bunnies. th Activity:PLAY:PowerPoint (ordinal numbers indicate clicks of the mouse) 8 th Underline appears under text of topmost header. [read to reinforce]9 :Footers for pictures #1 and #4 go up [and bunnies spin] Follow-up:SAY:So, we’ve learned that SUBTRACTING A NEGATIVE IS LIKE what...? That’sright, ADDING A POSITIVE.Both operations make numbers get larger, that is, go up. th Activity:PLAYPowerPoint (ordinal numbers indicate clicks of the mouse)10 : th Underline appears under text of bottom-most footer. [read to reinforce]11 :Footers for pictures #2 and #3 go up [and bunnies spin] Follow-up:SAY:And, finally, we’ve learned that SUBTRACTING A POSITIVE IS LIKE what...?That’s right, ADDING A NEGATIVE.Both operations make numbers get smaller, that is, go down.

Culminating Activities DISTRIBUTEthe helium filled balloons with gondolas, and the five 1-gram weights to each trio of students.SAY:Before we begin, let’s discuss the similarities and differences between hot air balloons and helium filled balloons.How is hot air like the helium?Both gasses make theThat’s right, hot air for one and helium for the other. balloon go up.What else makes a balloon go up?That’s right, removing weight.By the way, since helium is not readily available, we won’t be able to demonstrate adding helium to the balloons.What makes the balloon go DOWN?That’s right, removing hot air or helium, and adding weight. 1. Focus:(ADDING A NEGATIVE)SAY:We’re going to start this activity out by making the balloons go DOWN.What can we do to make them go down besides removing helium from them? That’s right.Add weight. Activity:SAY:Add weights that I’ve given you until the balloon sinks down to the table. [assist/guideas necessary and prudent]It may take more than 5 grams to make some of the balloons go down. Follow-up:SAY:Who can write an arithmetic statement on the board that represents our helium balloon models?

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Hot Air Balloon Integer Arithmetic Chris Eldredge Waynesboro City Public Schools

2. Focus:(SUBTRACTING A NEGATIVE)SAY:Now we’re going to make the balloons go UP.What can we do to make them go up besides adding helium to them? That’s right.Remove weight. Activity: SAY:Remove weights that I’ve given you until the balloon FLOATS UP TO EYE LEVEL BUT NO HIGHER.[even more assistance/guidance is necessary and prudent]If too much weight is removed, you must adjust what you’re subtracting. Follow-up:SAY:Who can write an arithmetic statement on the board that represents our helium balloon models?

Assessment €PLAYMusic “My Beautiful Balloon”;(replay once or twice during assessment) Display pictures of hot air balloons.Have the students complete a worksheet containing problems with addition and subtraction of positive and negative integers.

Community Connections €Investigate how blood pressure is regulated in the body at the hospital €Investigate how a person with Diabetes regulates their blood sugar or insulin level

Cross-Curricular Extensions Language Arts €Write a story about a balloon ride.You should include exact numbers in your adventure making certain you start at ground level, ascend and descend at least twice, and finish the trip on the ground again.Tell about the things you see during your flight. Science €Discuss temperature changes and relate to adding and subtracting integers

Adaptations (optional) Culminating activity could use hot air hair dryers and brown paper bags instead of helium filled balloons.There are quite a few websites which provide details of this type of experiment.

About the Author Chris Eldredge is a seventh/eighth grade mathematics teacher at Kate Collins Middle School in Waynesboro, Virginia.

This lesson was written as part of the Fall 2004 WVPT NTTI for the Virginia Enhancing Education Through Technology Ed Tech Grant awarded to the Shenandoah Valley Technology Consortium (SVTC).

NTTI Fall 2004

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