Algebra - Why?

For each of the next 8 formulae (one on each of the following slides)

find a picture (use www.google.com images or other) that explains what real life events the

formulae is used to calculate.Use the CAMERA TOOL on your activstudio toolbar to copy & paste the pictures.

e.g. F=ma

OR

A = WL

D = ST

C = 2r

C = F - 3259

F = ma

E = mc²

A = r²

C = 15 + 0.02m

Mobile Phone Costs!

A = WLFind the areas of these rectangles:

Find the WIDTH of this rectangles:

Find the LENGTH of this rectangle:

10cm

6.1cm

2.4cm

5cm

11cm

44cm²

24cm

²

3cm

1)

2)

3)

4) Challenge:Can you rearrange the formula A = LW to find a general formula for:a) W =

b) L =

D = STGermany is the only country in Europe (isle of man (UK) (no limit on most rural roads) & Uttar Pradesh in India) not to have a speed limit on its motorways ("Autobahn"- though some insurance companies will not cover any accidents had when travelling over 130km/h=81mph).

1) How far could you travel on a New York rural Freeway (100km/h) in 4hours?

b) How far could you travel on a German autobahn in 4 hours?

c) How LONG would it take to travel 420km on a Spanish "autopista"?

d) French police check average speeds by looking at the times of vehicles between toll booths. If a car took 3hrs to travel 420km what speed must it have averaged?

Germany ave speed: 134km/h. The speed limits:France 130km/hUS 100 to 120km/h (state by state)Spain&China 120km/hUK 115 km/h

e) CHALLENGE: Find a general formula (i) for finding time (ii) finding speed

D = ST

Spain

Portugal

No question here, just for interest . . . !

C = 2r or d1) The minute hand of a clockface is1m long, what is the circumference of thisclock?

2) One of the first bicycles, the "Penny Farthing", the front wheel had a circumference of 9.42m, what was it's diameter?

3) Germany's "enercon" constructs the largest wind turbines in the world with a circumference of 395.8m! What is the radius of one of the blades?

5MW = 85 000 household

bulbs.

C = F - 3259

1) Complete this table below using the above formula and your calculator!

the lowest temperature possible in the whole universe (though it cannot actually exist, it is a limit (MIT record = -272.65°C)

F = ma1) If average 14yr old has a mass of 50kg and you drop him/her with acceleration due to gravity of 9.8 m/s², with what force will they hit the ground?

2) Mike tyson's best punch exerts a pressure equivalent to that exerted by a weight of 1980kg on a board 1m². If the mass of his arm is 16kg, what must the acceleration be to achieve a force of 1980 N(kg)?

3) Write a general formula for finding the acceleration of a car at any give time if you know its mass and the force it is exerting.

E = mc² This is the principle of the atom bomb - if you can release all the energy contained in 1gram of matter, the results are explosive!

1) If the speed of light (c) is approximately 300 000 000 m/second andmass is measured in kilograms. How much energy is there in 1 gram (0.001kg) of matter?

2) If m=500kg and E = 1million joules, what acceleration would be reqiured to produce this force?

3) a = 10ms², E = 1million, find m.

4) Challenge: What mass of matter would you need, if we could release all its energy at once, to produce the same eletrical output as the world's biggest wind turbine = 5million joules (per second)?

A = r²1) The minute hand of a clockface is1m long, what is the area of thisclock?

2) One of the first bicycles, the "Penny Farthing", the front wheel had an area of 4.5m², what was it's diameter?

3) Germany's "enercon" constructs the largest wind turbines in the world with an area of 39 408m²! What is the radius of one of the blades?

5MW = 85 000 household

bulbs.

C = 15 + 0.02m

Extension Questions:1)

a) Rearrange this formula to make 'r' the subject.

b) Rearrange the formula to make 'v' the subject.

c) Rearrange the formula to make the "efficiency factor" the subject.

How do we know what number to put into an expression or

Formula?

You can put in any number you like, that's the POWER of a

Formula/Expression

NEXT THREE SLIDES are for TEACHER ONLY!

(you could look, but it’ll ruin the game for you).

Examples of Students Reactions to this Activity

(from a low ability, easily distracted group)

2n - 1

Biggest 6n + 4

Reason6n is bigger than the other "n"s and +4 is bigger than all the other 6n additions.

Smallest2 is the smallest of all mulitples and -1 the most taken away

Even Number(multiple of 2)

4n - 2?6n + 4?

5n + 4

5 10 15 209 14 19 24

3n - 1

3 6 9 122 5 8 11

l Both numbers have to be odd to given an even?

l Both numbers have to be even?

e.g. 5n + 1: 5 10 15 20 6 11 16 21

e.g. 4n - 24 8 12 16 202 6 10 14 18

6n + 4

6 12 18 2410 16 22 28

If in doubt, take an expression and sub in some no.'s to see and look for patterns or use results to help form a theory!

Experiment, Theorise, Test, Conclude

Student: "all even numbers timestables are even because you're adding evens together". Is this true?

Always Odd? Has to be an ODD + EVEN?

odd x "n" + even? even x "n" + odd?

Student reasoning:

l even xtable is always even so when add an odd it must be odd.

l odd numbers timestables can sometimes be even so when + even can get an even.

Conculsion:Must be even multiple and even addition/subtract?Test?

Student: "If you have a multiple of 3 plus or minus a multiple of 3 you always get a multiple of 3?" Is this true?

Multiples of 3?

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