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Pete the Cat and His Four Groovy Buttons
Perfect Square
by Michael Hall
Follow the adventures of a perfect square through the course of a week. They get shredded and snipped, torn and ripped, but then use those pieces to make themselves into something beautiful!
Resources for Perfect Square:
Full Book Review (English)
Full Book Review (Spanish)
Brief Book Review (English)
Brief Book Review (Spanish)
How many things can one perfect square turn into?
Math Connections:
Geometry Shapes
Transformations
Activities To Do Together:

Introduce the idea that objects are made from geometric shapes and combinations of shapes: squares, rectangles, triangles, and circles.

Talk about polygons. They are 2dimensional,
closed geometric shapes made up of
straight lines, like squares, rectangles and triangles. 
Talk about the attributes that make each shape unique. For example discuss the similarities and differences between a rectangle and a square.

Make a square from tissue paper ,then tear or cut it into different pieces and make something new by gluing the pieces onto another sheet of paper.
Extension Questions:

Is the main character in the story a perfect square?How do you know?

Which is your favorite shape?How is this shape different than other shapes?

Which images had the most pieces?Which had the fewest?

What polygons do you see in the bridge?

Which shapes in the fountain are polygons? Which are not?
Vocabulary for Building Math Concepts:
corners, equal, four, matching, perfect square, sides, square