Suggested Activities

Unit 1: Unraveling the Problem-Solving Process

How Many Triangles?How Many Triangles?An Exploration of Patterns

Schema ActivatorSchema Activator

1. How many squares can you count in the figure below?

2. Draw a 3x3 square.

◦ How many squares do you count now?

◦ Do you see a relationship between the number of embedded squares in the 2x2 square and the number of embedded squares in the 3x3 square?

The 3x3 SquareThe 3x3 Square

If you’re having trouble determining the number of squares in the 3x3, consider organizing your information this way:◦How many 1x1 squares do you see?◦How many 2x2 squares do you see?◦How many 3x3 squares do you see?◦How many in total?

The 4x4 SquareThe 4x4 Square

Organize your information:◦How many 1x1 squares do you see?◦How many 2x2 squares do you see?◦How many 3x3 squares do you see?◦How many 4x4 squares do you see?◦How many in total?

What about Triangles?What about Triangles?

How many triangles can you find in each of these figures? For the second figure, consider:◦The number of “small” triangles you see.◦The number of “medium” triangles you see.◦The number of “large” triangles you see.

Your Mission: Build It!Your Mission: Build It!

Using your marshmallows and toothpicks, construct a tetrahedron.

How many triangles can you count? Discuss your observations with your team.

Homework1. “How Many Triangles?” Worksheet

A farmer had some pigs and chickens. One day he counted 20 heads and 56 legs. How many pigs and how many chickens did he have? Be prepared to share your method of solving

the problem.