Grade 08 Mathematics - EC: M08.B-E.1.1.2

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.B-E.1.1.2 M08.B-E.1.1.2

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of perfect squares (up to and including 12^2) and cube roots of perfect cubes (up to and including 5^3) without a calculator. Example: If x^2 = 25 then x = ±√25.

Activities

Identify the square root of 121.
Identify the cube root of 27.
List all the perfect squares between 0 and 150.
A shipping box in the shape of a cube has a volume of 800 cubic inches. To find the length of one side of the box, s, in inches, you need to solve the equation s³ = 800. Which answer correctly represents one side of the box?
1. 100 inches
2. inches
3. inches
4. inches
A farmer’s field has an area of 2000 square feet. To find the length of one side of the field, x, in feet, the farmer needs to solve the equation x² = 2000. What is the length of one side of the farmer’s field in feet?
3. 1000
4. 500

Solve the following equation and explain how you got your answer:

Solve the following equation and explain how you got your answer:

Andre has a square field that he knows has an area of 144 square miles. He wants to put a fence around the field and needs to know how long a side is. Explain to Andre how he can do this, and be sure to include what the length of the side is.

Answer Key/Rubric

3
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
D
B
Acceptable explanations may include, but are not limited to:

The opposite of multiplying by 4 is dividing by 4
Divide both sides by 4; end up with
The opposite of squaring is taking the square root
Take the square root of both sides
The square root of 81 is

p = 4
Acceptable explanations may include, but are not limited to:

The opposite of multiplying by -2 is dividing by -2
Divide both sides by -2; end up with
The opposite of cubing is taking the cube root
Take the cube root of both sides
The cube root of 64 is 4

Side length is 12 miles
Acceptable explanations may include, but are not limited to:

Formula for area is:
Set up the equation:
The opposite of squaring is taking the square root
The square root of 144 is
Distance cannot be negative, so the length of the side must b