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**Thought for the day**: When you use noticing and wondering prompts regularly, students begin to apply their new observing and questioning skills in other situations—often when you least expect it!

**Concepts**: sums of consecutive odd numbers; square numbers; patterns and formulas

**Examples of noticing and wondering**

*I notice *a square filled with L-shaped pieces.*I notice *that each L-shaped piece has an odd number of squares.*I notice *that you could build the image starting with the single red square and joining one L-shaped piece at a time.*I notice *that each time you join a new L-shaped piece, it makes the next-larger square.*I notice *the expression 1 + 3 + 5 + 7 + 9 + 11 + 13.

*I wonder *if I could use the image to find a shortcut for adding odd numbers.*I wonder *if the sum of consecutive odd numbers is always a square number.*I wonder *if I could find a formula for adding consecutive odd numbers.*I wonder *if I could use rectangles to discover a formula for adding even numbers.*I wonder *if I could use other shapes to discover other kinds of formulas.

**Notes**

This image can help students discover patterns in the sum of consecutive odd numbers beginning with 1.

1 = 1

1 + 3 =4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

1 + 3 + 5 + 7 + 11 = 25

etc.

The answers are the square numbers—and the image shows why this happens!