In the game activity, Guess My Rule, you give your students the x value of a linear function and have them find the y-value.
They need to determine the rule that you have in mind to get the correct y-value.
No one is allowed to share their rule until the end.
For the rule to be established, the teacher must provide two initial x and y pairs.

Here are some suggestions for implementing this warm-up activity:
Present one pair of x,y values and let students guess the y for the second x.
Do not present the x-values in numerical order.
Have a goal in mind for your rules.   Perhaps present the rule in the form y = mx + b.
When half the class seems to know the rule, make the x-value a fraction or a negative number to challenge them.

Steps:

  1. Present the initial pair of values.
  2. Enter the next x-value and have students suggest the y-value.
  3. Enter the correct y-value and caution the students not to give up the rule.
  4. Continue in this manner until at least half of the class appears to know the rule.
  5. To make it possible for more students to access the rule, make a new table and this time order the values of x.   Now more students will be able to determine the y-value because there will be a pattern.
  6. Have the students share their rules.   Record them as word or symbol rules.

What's My Rule (With Circles)

When studying circles, I give several coordinate pairs and have my students guess the equation of the circle that I have in mind.

Example #1:
  X     Y  
  2     0  
  -2     0  
  0     2  
  0     -2  

                      What's My Rule?    

Example #2:
  X     Y  
  5     3  
  4     4  
  -3     -3  
  1     -5  
  5     -3  
  -4     0  
  1     5  
  6     0  

                      What's My Rule?