options: Draw, construct, and describe geometrical figures and describe the relationships between them.

Find arc lengths and areas of sectors of circles.

Apply trigonometry to general triangles.

Solve real-world and mathematical problems involving area, surface area, and volume.

Make geometric constructions.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Use coordinates to prove simple geometric theorems algebraically.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Translate between the geometric description and the equation for a conic section.

Apply geometric concepts in modeling situations.

Experiment with transformations in the plane.

Classify two-dimensional figures into categories based on their properties.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Prove geometric theorems.

Define trigonometric ratios and solve problems involving right triangles.

Understand congruence in terms of rigid motions.

Visualize relationships between two-dimensional and three-dimensional objects.

Explain volume formulas and use them to solve problems.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Understand and apply theorems about circles.

Analyze, compare, create, and compose shapes.

Understand and apply the Pythagorean Theorem.

Reason with shapes and their attributes.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Understand similarity in terms of similarity transformations.

Prove theorems involving similarity.
problem_activity: Task
Amy and Greg look for a method to estimate the number of leaves on a $35$ foot tree in their yard. Greg notices that the tree blocks almost all of the sunlight beneath its leaves so he thinks of the following way to estimate how many leaves are on the tree:
We can first measure the area of the ground covered by the tree.
Then we measure the area of an average leaf.
We will need to estimate how much of its area an average leaf shades and how many leaves lie over an average point under the tree.
With all of this information we should be able to get a good estimate for the number of leaves on the tree.
Amy and Greg find that the tree covers a region which is roughly a circle $30$ feet in diameter. What is the approximate area covered by the tree?
How can Amy and Greg effectively measure an irregular shape such as a tree leaf?
How can Amy and Greg effectively decide what number to multiply by to account for multiple leaves lying over the same area and leaves shading less than their full surface area?
Suppose $a$ is the approximate area underneath the tree, $b$ the average leaf area, $c$ the proportion of its area an average leaf shades, and $d$ the average number of leaves found over a spot underneath the tree. In terms of the numbers $a$, $b$, $c$, and $d$ what formula will Amy and Greg find for the number of leaves on the tree?


correct_option_index: 10