1. Linear Relations & Equations Performance Task
Take Up
Juan’s Party
An Amazing Number Trick

2. 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.

3. 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

4. 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

5. Graph
Cost ($)
Juan’s Party Cost for Number of Guests
Number of Guests

6. 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

7. 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

8. 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.

9. 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.