Grade 08 Mathematics - EC: M08.C-G.2.1.2

Continuum of Activities

The list below represents a continuum of activities: resources categorized by Standard/Eligible Content that teachers may use to move students toward proficiency. Using LEA curriculum and available materials and resources, teachers can customize the activity statements/questions for classroom use.

This continuum of activities offers:

Instructional activities designed to be integrated into planned lessons
Questions/activities that grow in complexity
Opportunities for differentiation for each student’s level of performance

Grade Levels

8th Grade

Course, Subject

Mathematics

Related Academic Standards / Eligible Content

M08.C-G.2.1.2 M08.C-G.2.1.2

Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (Figures provided for problems in three dimensions will be consistent with Eligible Content in grade 8 and below.)

Activities

Find the missing side length. Round to the nearest tenth if necessary.

Find the missing side length. Round to the nearest hundredths if necessary.

A pool table is 8 feet long by 4 feet wide. How far is it from one corner pocket to the diagonally opposite corner pocket? Round your answer to the nearest tenth if necessary.

An envelope is classified as a large envelope if the length exceeds 11.5 inches. Is the following envelope classified as large? Justify your answer.

Two trains left a station at the same time. Train A traveled south at 50 mph and Train B traveled east at 40 mph. How far apart, to the nearest mile, were the trains at the end of 3 hours? Show or explain your work.

Identify the length of the longest nail that could fit entirely within a cylindrical can with a radius of 6 cm and a height of 45 cm. Nails are only sold by whole centimeters. Justify your reasoning.

The floor of a room is 5 m by 8 m, and its height is 4 m. Find the distance from a corner point on the floor to the opposite corner point on the ceiling. Round your answer to the nearest tenth of a meter.

Answer Key/Rubric

16.1 m
78.24 cm
8.9 ft.
Yes, it is a large envelope.
Acceptable justifications may include, but are not limited to:

Use the Pythagorean theorem to find the missing length; a² + b² = c²
Fill in a or b with the 6 and c with the 14; 14 is the hypotenuse
Solve the equation: a² + 6² = 14²
or a = 12.6491
12.6491 inches is greater than 11.5 inches so it is a large envelope

192 miles
Acceptable answers may include, but are not limited to:

Train A: 50 mph x 3 hours = 150 miles
Train B: 40 mph x 3 hours = 120 miles
Picture similar to:
Right triangle is formed by missing distance; use Pythagorean theorem to find distance: a² + b² = c²
Substitute known values: 120² + 150² = c²
Students should show all work to solve for missing value

46 cm
Acceptable responses may include, but are not limited to:

Radius of can is 6 cm, so the diameter is 12 cm
Use Pythagorean theorem to find length of nail: 12² + 45² = c²
Solve equation: c = 46.5725
Can only buy nails in whole cm; longest nail is 46 cm because 47 cm would be too large to fit

10.2 m
Acceptable responses may include, but are not limited to:

Identify the right triangles:

Set up equations using the Pythagorean theorem:

Combine the two equations by substituting in the x²: y² = 5² + 8² + 4²
Solve for y: y = 10.2469