Playing with Energy

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Purpose

This is a level (3+ to 4+) mathematics in science contexts activity from the Figure It Out series.
A PDF of the student activity is included.

Achievement Objectives
NA4-1: Use a range of multiplicative strategies when operating on whole numbers.
S4-2: Evaluate statements made by others about the findings of statistical investigations and probability activities.
Student Activity

  

Click on the image to enlarge it. Click again to close. Download PDF (1110 KB)

Specific Learning Outcomes

Students will:

  • solve problems using rates and unit conversions.
Required Resource Materials
counters for energy game tokens

classmates

FIO, Energy, Levels 3+-4+, Playing With Energy, pages 2 - 3

a different-coloured counter for each player

the types of energy table; energy game cards (see copymasters)

Activity

Preparation and points to note

This activity familiarises students with the terms kinetic energy* and potential energy in a fun way. To progress in the game, the students are required to solve simple problems based on kinetic energy contexts (for example, a radio broadcast, a rolling skateboard, or a boiling kettle). When any student encounters a kinetic card, all players should work out the problem and confirm the answer. (The answers are provided as a copymaster. You will need to decide who has the answer sheet for students to check against.)

Students need to be able to distinguish between potential and kinetic energy to play the game.  Before introducing it to your students, review the answers so that you can provide guidance if called upon.

Preferably, the students will play the game with a minimum of introduction but, if they are confused about what to do, walk them through a few turns.

All players start with their counters on the banana. They should discuss whether a banana is potential or kinetic energy. When each student starts, they collect 2 potential energy tokens (thanks to the banana being a potential energy square). They can then either trade in 2 tokens and end their turn on the petrol tank, trade in 1 token and end their turn on the wind (retaining 1 token), or stay on the banana and keep both tokens. In the next round, students on the petrol tank or the banana will collect 2 more tokens. Students on the wind (kinetic energy, because it is air in motion) don’t collect any tokens; they must pick up an energy card and try to solve the problem on it. If another student disputes their answer and it differs from that on the answer sheet (see copymaster), they lose their turn and stay on the wind square. On their next turn, they pick up another kinetic card and try to answer the question on it.

The game provides natural opportunity to mix up groups so that the students work with a diversity of
classmates. By being actively involved in a group with a common interest and focus, they are using and further developing the key competency participating and contributing.

Points of entry: Mathematics

There are two types of kinetic problem cards: rate conversions and number patterns.

The rate conversion problems require the students to convert from one unit to another closely related unit as in the Energy Stations problems on page 1. For example,

“Sefo burns 1 kilojoule per second playing soccer. Move forward 1 square for each minute he needs to burn 300 kilojoules.”

To solve this problem, students need to convert kilojoules per second (kJ/s) into kilojoules per minute (kJ/min) and calculate the number of minutes it will take to burn 300 kJ. If students are not sure how to approach a problem like this, prompt them to think about equivalent quantities: 60 seconds is the same as 1 minute, so 1 kJ/s is the same as 60 kJ/min. Similarly,

“A skier is travelling downhill at 30 kilometres per hour. Move forward 1 square for each kilometre he travels in 8 minutes.”

In this case, the conversion is from kilometres per hour to kilometres per minute: 30 km/h = 30 km/60 min = 1 km/2 min = 4 km/8 min. Once the hour has been converted to 60 minutes, doubling and halving type strategies are all that is needed.

The Richter scale problem, the ball rolling downhill, and other similar problems involve number patterns. Students may fi nd that it helps to put the given information into a table. For example, knowing that an earthquake that measures 2.0 on the Richter scale is 10 times as powerful as one that measures 1.0 or that an earthquake that measures 6.0 is 100 times as powerful as one that measures 4.0 is sufficient to identify the pattern in this table:

Scale1.02.03.04.05.06.07.08.0
Multiple1101001 00010 000100 0001 000 00010 000 000

Similarly, the ball rolling downhill problem can be represented by and solved using this table:

Elapsed time1 s2 s3 s4 s5 s
Speed2 m4 m6 m8 m10 m
Total distance2 m6 m12 m20 m30 m

Total distance is the distance travelled in the previous seconds plus the distance travelled in the current second.

Points of entry: Science

As the students work through the examples of energy listed on the copymaster, the aim should be for them to come up with their own everyday language definitions for potential and kinetic energy. The different examples should enable them to test and refine their definitions as they go.

As the students play the game, they may not always readily agree on whether a particular space represents potential or kinetic energy. Encourage them to debate the subject and justify their decisions. For example, the spinning wheel of a bike translates energy into forward momentum (kinetic), but a spinning flywheel mounted on a stationary block is also a source of stored (potential) energy.

Prompt students to think about how, in each situation, the energy could be changed from potential to kinetic or vice versa. For example, the coiled spring is potential energy, but when it expands, it converts its potential energy into motion (kinetic).

Answers

Example of energyType of energy (potential or kinetic)
PetrolPotential
A stretched rubber bandPotential
A batteryPotential
2 billiard balls collidingKinetic
An apple about to fall from a treePotential
An apple falling from a treeKinetic
A flying rubber bandKinetic
A child riding a bicycleKinetic
A vibrating bass drumKinetic
Air blowing out of a hairdryerKinetic
Hot springsPotential

Game
The type of energy for each space

SpaceType of energy
BananaPotential
WindKinetic
Petrol tankPotential
Lump of sugarPotential
Hydroelectric damAnswers can vary. A dam stores water, which is potential. The power station uses the fl ow of water to generate electricity, which is kinetic.
Rolling skateboardKinetic
RainKinetic
Coiled springPotential
JoggingKinetic
Wound-up yo-yoPotential
EarthquakeKinetic
CharcoalPotential
Boiling kettleAnswers can vary. The steam coming from the kettle is kinetic. The heat stored in the water is potential.
Shaken-up soft drink canPotential
Spinning wheelKinetic
TornadoKinetic
Ball at the top of the stairsPotential
Speeding carKinetic
Diver on a high diving boardPotential. (It only becomes kinetic when the diver actually jumps.)
Ball rolling downhillKinetic
Kicking a soccer ballKinetic
AA batteryPotential
Stretched rubber bandKinetic
A shoutKinetic
Dried fruit and nutsPotential
Compressed airPotential (as long as it remains in the tank)
Person skiing downhillKinetic

 Answers for energy game cards

 

CardAnswersSpaces to move if your answer is correctMethod
1. Wind5 metres per second5300 m per minute is 300 m in 60 seconds. 300 ÷ 60 = 5
2. Tornado1 year11 year There are 365 days in a year (excluding leap years). 28 kilowatt-hours per day x 365 = 10 220 kilowatthours per year, so a small tornado is roughly equivalent to 1 household’s energy use for 1 year.
3. Rain3 millimetres per minute3180 mm per hour is 180 mm in 60 minutes. 180 ÷ 60 = 3
4. Running2 kilometres25 km in 30 minutes is 10 km/h. 12 minutes is 1/5 of an hour. 10 ÷ 5 = 2
5. Earthquake4.043.0 is 10 times more powerful than 2.0. 4.0 is 10 times more powerful than 3.0, so it’s 100 times more powerful than 2.0.
6. Cycling4 kilometres410 minutes is 1/6 of an hour. 24 ÷ 6 = 4
7. Car travel6 hours6It takes a car 6 hours to travel 420 km at 70 km/h because 420 ÷ 70 = 6.
8. Kicks3 kicks31 kick is 33 m. 2 kicks is 66. 3 kicks is 99, which is about the length of a soccer field.
9. Sound3 kilometres3If sound travels at 0.340 km in 1 second, multiply by 9 to get the distance in 9 seconds. 0.340 x 9 = 3.06 km
10. Ski-lift2 people27 200 people per hour is 7 200 in 3 600 seconds (60 seconds in a minute x 60 minutes in an hour = 3 600). 7 200 ÷ 3600 = 2
11. Penalty: cellphonen/an/an/a
12. Penalty: lunchn/an/an/a
13. Bonus: surfingn/a5n/a
14. Wind speed5 knots59.5 is half of 19. If 19 km/h is about 10 knots, 9.5 km/h is about 5 knots (half of 10).
15. Tornado4 minutes4The tornado travels at 30 km/h, or 30 km in 60 minutes. In 1 minute, it travels 0.5 km (30 ÷ 60 = 0.5), so it will take 4 minutes (4 x 0.5 = 2) to travel 2 km.
16. Skateboarding6 minutes6500 kJ in 10 minutes is the same as 50 kJ per minute (500 ÷ 10 = 50). 300 kJ ÷ 50 kJ per minute = 6 minutes.
17. Rain4 millimetres4There are 4 hours between 8 a.m. and noon (12 p.m.) 16 mm ÷ 4 hrs = 4 mm /h on average.
18. Jogging3 minutes3250 kJ in 5 minutes is 50 kJ per minute (250 ÷ 5 = 50). 150 kJ ÷ 50 kJ per minute = 3 minutes
19. Earthquake4.042.0 is 10 times more powerful than 1.0. 3.0 is 10 times more powerful than 2.0, or 100 times more powerful than 1.0. Since 4.0 is 10 times more powerful than that, it is 1 000 times more powerful than a 1.0 earthquake.
20. Boiling water1 minute1If a half-full kettle boils in 90 seconds, a full kettle should boil in 180 seconds (twice as much water, twice as much time.) of 180 seconds is 60 seconds or 1 minute.
21. Cycling2 minutes2500 kJ in 10 minutes is the same as 50 kJ per minute (500 ÷ 10 = 50). 100 kJ ÷ 50 kJ per minute = 2 minutes.
22. Car travel3 hours3A car moving at 60 km/h will travel 180 km in 3 hours because 180 ÷ 60 = 3.
23. Ball speed5 seconds5In the first second, the ball travels 2 m. In the next second, it travels 4 m, for a total of 6 m. In the next second, it goes 6 m more, for a total of 12. Then another 8 m, for a total of 20 m, then another 10 m, for a total of 30 m after 5 seconds.
24. Soccer5 minutes51 kJ per second is the same as 60 kJ per minute (60 seconds in a minute). 300 kJ ÷ 60 kJ per minute = 5
25. Skiing4 kilometres430 km/h is 0.5 km per minute (60 minutes in an hour, and 30 ÷ 60 = 0.5). After 8 minutes, the skier would travel 8 x 0.5 = 4 km.
26. Penalty: frictionn/an/an/a
27. Bonus: skateboardn/a4n/a
28. Bonus: windn/a3n/a
29. Penalty: rubber bandn/an/an/a
30. Bonus: cellphonen/an/an/a
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Level Four