Unlocking the Mystery of Perfect Cubes and Cube Roots (6-10)

PreAlgebra Grades High School 3:54 Video
Print Lesson Plan Watch Video

Lesson Description

Learn about perfect cubes and cube roots from 6 cubed to 10 cubed. This lesson builds upon the understanding of squares and square roots and extends it to the world of cubes and cube roots. We will explore the inverse relationship between cubing a number and finding its cube root, focusing on the numbers 6 through 10.

Video Resource

Perfect Cubes and Cube Roots (6-10) | Math with Mr. J

Math with Mr. J

Duration: 3:54
Watch on YouTube

Key Concepts

  • Cubing a number (x³ = x * x * x)
  • Cube root (∛x)
  • Inverse relationship between cubing and finding the cube root
  • Perfect Cubes between 216 and 1000

Learning Objectives

  • Students will be able to calculate the perfect cubes of numbers 6 through 10.
  • Students will be able to identify the cube roots of perfect cubes from 216 to 1000.
  • Students will be able to explain the inverse relationship between cubing and finding the cube root.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concepts of squaring and square roots, connecting them to the idea of cubing. Briefly discuss what it means to 'cube' a number and introduce the cube root symbol (∛). Mention the video by Mr. J, 'Perfect Cubes and Cube Roots (6-10) | Math with Mr. J', and explain that it will cover the perfect cubes and cube roots from 6 through 10.
  • Video Viewing and Note-Taking (10 mins)
    Play the YouTube video 'Perfect Cubes and Cube Roots (6-10) | Math with Mr. J'. Instruct students to take notes on the perfect cubes and cube roots presented in the video. Encourage them to write down the calculations (e.g., 6 x 6 x 6 = 216, therefore ∛216 = 6).
  • Guided Practice (10 mins)
    Work through examples of calculating perfect cubes and cube roots together as a class. Start with 6 cubed. Review how 6 cubed equals 6 times 6 times 6. Review that 6 times 6 is 36 and 36 times 6 is 216. Therefore, 6 cubed equals 216. Work through this with the other cubes presented in the video: 7 cubed, 8 cubed, 9 cubed, and 10 cubed.
  • Independent Practice (10 mins)
    Provide students with practice problems where they need to calculate perfect cubes and identify cube roots. The problems should include numbers from 6 to 10. For example: 'What is 7 cubed?' and 'What is the cube root of 729?'
  • Wrap-up and Assessment (5 mins)
    Review the key concepts of the lesson. Administer a short quiz to assess student understanding. Preview the connection to solving equations with cubes and cube roots.

Interactive Exercises

  • Cube Root Matching Game
    Create a matching game where students match perfect cubes (216, 343, 512, 729, 1000) with their corresponding cube roots (6, 7, 8, 9, 10). This can be done using physical cards or an online interactive tool.

Discussion Questions

  • What is the difference between squaring a number and cubing a number?
  • How are cube roots related to cubes? Can you think of other mathematical operations that are related in this manner?

Skills Developed

  • Calculation of cubes and cube roots
  • Problem-solving
  • Critical thinking
  • Pattern recognition

Multiple Choice Questions

Question 1:

What does it mean to cube a number?

Correct Answer: Multiply the number by itself three times

Question 2:

What is 6 cubed (6³)?

Correct Answer: 216

Question 3:

What is the cube root of 343 (∛343)?

Correct Answer: 7

Question 4:

What is 8 cubed (8³)?

Correct Answer: 512

Question 5:

What is the cube root of 729 (∛729)?

Correct Answer: 9

Question 6:

What is 10 cubed (10³)?

Correct Answer: 1000

Question 7:

What is the cube root of 216 (∛216)?

Correct Answer: 6

Question 8:

What is 7 cubed (7³)?

Correct Answer: 343

Question 9:

What is the cube root of 512 (∛512)?

Correct Answer: 8

Question 10:

What is the cube root of 1000 (∛1000)?

Correct Answer: 10

Fill in the Blank Questions

Question 1:

Cubing a number means to multiply the number by itself ________ times.

Correct Answer: three

Question 2:

6 cubed (6³) is equal to ________.

Correct Answer: 216

Question 3:

The cube root of 343 (∛343) is ________.

Correct Answer: 7

Question 4:

________ cubed (8³) is equal to 512.

Correct Answer: 8

Question 5:

The cube root of ________ (∛729) is 9.

Correct Answer: 729

Question 6:

10 cubed (10³) is equal to ________.

Correct Answer: 1000

Question 7:

The cube root of 216 (∛216) is ________.

Correct Answer: 6

Question 8:

7 cubed is ________.

Correct Answer: 343

Question 9:

The cube root of 512 is ________.

Correct Answer: 8

Question 10:

The cube root of 1000 is ________.

Correct Answer: 10

Educational Standards

PA.N.1:Read, write, compare, classify, and represent real numbers, and use them to solve problems in various contexts. PA.N.1.4:Compare and order real numbers; locate real numbers on a number line. Identify the square roots of perfect squares to 400 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers. PA.A.3:Generate equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions.

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans