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Linear Relations & Equations Performance Task
Take Up Juan’s Party An Amazing Number Trick
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Juan’s Party Looking for multiple representations:
Equations Tables of values Graph Looking for valid conclusion: Less than 14 guests – restaurant is better (cheaper) More than 14 guests – community center is better (cheaper) Exactly 14 guests – both places are the same – he can pick where he likes.
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Equations (with explanations)
Let n represent the number of people Let C represent the cost Restaurant C = 10n + 60 $10 per person $60 fixed cost Community Center (need two equations) C = (if n <= 16) C = 6(n – 16) (if n > 16) $6 per person (when over 16 people) $200 flat fee
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Table of Values (for both)
Restaurant (C = 10n + 60) Community Center n C 60 200 6 120 8 140 10 160 12 180 14 **cost the 16 220 Same ** 17 230 206 18 240 212 20 260 224
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Graph Cost ($) Juan’s Party Cost for Number of Guests Number of Guests
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Number Trick Looking for explanation of why it works.
Looking for good communication LS and RS (split up ... ) Or writing in a method where did not need it
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Example of Good Solution
Let x represent the number they chose Double your number 2x Add 2x + 12 Add your original number again 2x x Simplify 3x + 12 Divide your answer by 3 (3x + 12)÷3 Simplify x + 4 Subtract your number again x + 4 – x Simplify 4
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Explanation Then of Why It Works
As you can see the number they chose does not make a difference. This is because ... once you have performed the necessary algebra the variable representing the number chosen cancels out (it no longer exists). You are only left with a 4. Making it obvious that the number trick will always equal four.
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Another Method If you take the full equation and solve it out for x ... You get 0x = 0 as the final statement. Plugging in any value of x will make this equation true. Therefore, this shows that this equation works no matter what number is chosen by the player.
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