Supports students to find patterns in tables, also improves number and operation sense and keeps the classroom quiet for a few minutes.
- Think of a rule: e.g. y = x-4. As students get more proficient, choose more difficult rules.
- Put a table on the board with mostly just x values and blanks for y values, but have some y values without x values. (Use your rule so that you choose good values). Save the x variable for last, until the table has been filled out.
- Don’t put x values in order. You want students to see the x- y pattern, not the x-x or y-y pattern. As students gain experience, get wilder in your number choices (decimals, fractions, maybe even irrationals). I don’t usually put in the y-intercept.
- Explain to the rules: I will add values to table that are part of a pattern, when you think you might have the pattern figured out, offer to enter a value. If you are incorrect, I will erase it. No talking at all!
The initial table might look like this (but with more x values):
After all of the entries have been filled, add the “x”. Students may have more than one way to show their “y”, a great opportunity to discuss equivalent expressions.
Make sure to debrief how students tried to make sense, how they knew an attempt was wrong. Step through how to see the pattern with almost every entry.