Quandaries
and Queries 

Name: Liz Who is asking: parent Level: 7th grade math assignment (I'm not sure why....) I have the same question as Chris: the next four numbers to the sequence 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,___,___,___,___. My daughter recognized the pattern if commas were removed, although I'm not sure if that means the next four numbers would be 1,0,0,1 (for 100 and the first digit of 121). Or would it be 10,0,12,1? Or 10,0,1,21? Two students in her class came up with 5,4,9, 11, but neither can remember how they arrived with their answer. If you were to use these, could you then predict the next four numbers? If so, how are you calculating the numbers? Thank you. 

Hi Liz, I know why this assignment was given. The motivation is to help students see patterns in numbers, just exactly as your daughter did. Pattern recognition is very important in mathematics as is is in other areas of our lives, from hearing the chord progression in a song to knowing a dance pattern so well you can tell immediately when someone does something different. Your daughter saw that these are the squares of integers, written in a long string and then a comma put between successive digits. My answer would therefore be
In any of these "find the next few terms in the sequence" problems there is more than one correct answer. It is important that you be able to explain your answer in a logical way. There might be explanation for 5,4,9,11 but I don't see it. Penny 

