How many unique squares are there in a 4 x 4 grid?

Ask the students how many squares are there in a 4x4 grid of squares. Many will answer 16. Tell them that there are more than that.

After they have had a chance to think about and have yelled out some more answers ask them how many squares there are in a 1x1 grid (1) and in a 2x2 grid (the 4 small squares and the 1 big square = 5) and a 3x3 grid (9 small squares, 4 of the 2x2, and 1 big one = 14).

So the total for a 4x4 is 16 + 9 + 4 + 1 = 30. The total for any nxn square is (n squared + n-1 squared + n-2 sqaured down to 1 when n=1.
The passage contains a mathematical question about the number of unique squares in a 4x4 grid and provides the answer, along with a method to calculate the total for any nxn grid.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
How many unique squares are there in a 4 x 4 grid?

Ask the students how many squares are there in a 4x4 grid of squares. Many will answer 16. Tell them that there are more than that.

After they have had a chance to think about and have yelled out some more answers ask them how many squares there are in a 1x1 grid (1) and in a 2x2 grid (the 4 small squares and the 1 big square = 5) and a 3x3 grid (9 small squares, 4 of the 2x2, and 1 big one = 14).

So the total for a 4x4 is 16 + 9 + 4 + 1 = 30. The total for any nxn square is (n squared + n-1 squared + n-2 sqaured down to 1 when n=1.
user
The passage contains a mathematical question about the number of unique squares in a 4x4 grid and provides the answer, along with a method to calculate the total for any nxn grid.

TYPE: SINGLE_QUESTION_WITH_ANSWER