One of you should pick a clear pattern on the calendar. For instance, I may choose to pick $4$4 days that form a box, or I can choose $4$4 days that create a diagonal on the calendar. Don’t show your partner which days you pick, just mark them on your calendar. Choose at least $2$2 days.
Sum up all of the numbers of the days you have chosen and tell this number to your partner along with the count of numbers you summed together to reach it. Also, give them the dimension of any shapes you made in your pattern or tell them how long any lines you created are.
Your partner will create a one- variable expression and use it to guess the days you chose.
Keep taking turns, creating new patterns, and guessing the days that your partner chose.
Answer all of the following questions every time you are trying to guess the days your partner chose.
What equation did you use to represent the sum of the days in terms of one variable?
Is there another way to write this equation? If so, what is it?
Why does the second representation work as well?
What were the days that your partner was thinking of?
If your partner were to just give you the sum and the number of days that they added up would you be able to guess which days they are thinking of? Why or why not?