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The purple band is one side of a quadrilateral.

• What types of quadrilaterals can you make?
• How do you know what types of quadrilaterals you have made?
• Are there any types of quadrilaterals that you can't make? How do you know?

Friendly flies like to live together. They live in groups of 3 in square apartments. They enjoy having neighbors in at least 2 apartments they share walls with, but they don't want neighbors on all 4 sides. That's just too much.

Ava made pictures using three pattern shapes. Each pattern shape is worth a different number of points.  She found the total number of points for each picture.

• How many points is each shape worth?
• Can you make a picture worth 20 points?
• Can you make a picture worth 10 points?

Find as many rectangles as you can that have a perimeter that is 4 units more than the number of square units in the area.

Kayla drew 4 two-dimensional shapes. She counted a total of 18 sides. What 4 shapes might she have? How many answers can you find?

Each of these symbols represents a number. Only one of the numbers is a whole number. What could the three numbers be?

Hint: A whole number is a number such as 0, 1, 2, 3....

Use the numbers 1–9 to make the equation equal. You may use each number only once (you won't use them all).
What numbers can you use to make the equation equal?

______  ______  +  ______  =  ______  ______  -  ______

I have 45 cents. I have an odd number of coins. What combination of coins could I have?

Hint: An odd number can be divided into 2 equal groups with 1 left over.

How can you fill the flower with pattern shapes without any of the same shapes sharing a side?

• The first 4 shapes have been placed for you.
• If you use 2 of the same shape, make sure that their sides don’t touch each other. It’s okay if their vertices (corners) touch each other.
• If you get stuck, remove some of the shapes and keep trying.

How many times a day do the hands of a clock form a 90-degree angle?

Tammy has 8 coins with a total value of $1. What coins might she have? Can you find more than one possible solution?

Jada wants to know how many hardcover books she could fit in her bookcase. The bookcase is 4 feet wide and 9 inches deep. Each of the 3 shelves is 9 inches tall.

• How many hardcover books, like the one Jada is reading, could she fit in her bookcase?
• Can you find another way to arrange the books so more will fit?
• Which arrangement do you think is better? Why?