Students investigate patterns that show relationships between powers and roots. They learn to identify strategies to be used to find important patterns in data.

Before the Activity

See the attached PDF file for detailed instructions for this activity

Print the transparency sheet and pages 60 - 64 from the attached Student PDF file for the class

During the Activity

Distribute the pages to the class.

Follow the activity procedures:

Calculate the square root of numbers 100, 200, ... 1,000, and record the values in the table

Determine the greatest number less than 1,000 that is a perfect square

Calculate the cube root of numbers 1,000, 2,000, ... 10,000, and record the values in the table

Determine the greatest number less than 10,000 that is a perfect cube

Write the fourth roots of the numbers 10,000, 20,000, .... 100,000 and record the values in the table

Write the seventh roots of the numbers 10,000,000, 20,000,000, .... 100,000,000 and record the values in the table

Determine the greatest perfect square and cube that can be displayed on the calculator without using scientific notation

Understand that if a < x < b, then a^{2} < x^{2} < b^{2}, and √a < √x < √b

Solve the riddles on the Activity sheet

After the Activity

Students complete the Activity pages and answer questions.

Review student results

As a class, discuss questions that appeared to be more challenging