Fill out the table below. Build a simple shape with pattern blocks using only the hexagon, trapezoid, fat rhombus, and triangle. Use at least 3 blocks and draw it below.

Question

1) Draw your shape

2) How many blocks are in your shape?

3) How many small triangles would equal the area of your shape?

4) One hexagon has an area of 6 triangles. How many hexagons would have an area equal to the area of your shape? (This may be a fraction.)

5) If a shape has an area of t triangles, write an expression for its area in hexagons.

6) How did you find this expression?

8)These larger patterns could continue forever. Imagine that a pattern is pattern is made up of x copies of your small shape.

Write an expression for the number of blocks in the pattern.

Write an expression for the area of the pattern in triangles.

Write an expression for the area of the pattern in hexagons.

How did you find these expressions?

9)Take the blocks in your design and rearrange them into a new shape. Imagine that this new shape is used to make a large pattern with x copies of the small shape.

Write an expression for the number of blocks in the pattern.

Write an expression for the area of the pattern in triangles.

Write an expression for the area of the pattern in hexagons.

Which expressions changed and which didn't? Why?

10) Make a new version of one of your small shapes using different blocks. Imagine that this new shape is used to make a large pattern with x copies of the small shape.

Write an expression for the number of blocks in the pattern.

Write an expression for the area of the pattern in triangles.

Write an expression for the area of the pattern in hexagons.

Which expressions changed and which didn't? Why?