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Cube Roots & Perfect Cubes Guided Notes & Doodle | 8th Grade Sketch Notes Lesson
$4.25
Overview
- Standard: CCSS 8.EE.A.2
- Unit: 8th Grade → Unit 1: Real Numbers
- Grade: 8th Grade
Get the Lesson Materials
Cube Roots & Perfect Cubes Guided Notes & Doodle | 8th Grade Sketch Notes Lesson
$4.25
Learning Objectives
After this lesson, students will be able to:
- Define perfect cubes and cube roots.
- Identify perfect cubes and solve simple equations in the form x³ = p.
- Apply the concept of perfect cubes and cube roots to solve real-world problems.
Prerequisites
Before this lesson, students should be familiar with:
- Basic multiplication and division skills
- Understanding of the concept of exponents and their rules
- Familiarity with the concept of square roots and finding square roots of numbers
- Knowledge of rational numbers and their operations
Materials
- Pencils
- Colored pencils or markers
- Cube Roots and Perfect Cubes Guided Notes
Key Vocabulary
- Perfect cubes
- Cube roots
- Equations
- Rational numbers
Procedure
Introduction
As a hook, ask students why understanding cube roots and perfect cubes is important in real life. Refer to the real-life application on the last page of the guided notes as well as the FAQs below for ideas.
Use the first page of the guided notes to introduce perfect cubes. Walk through the concept of perfect cubes and explain that a perfect cube is the result of multiplying a number by itself three times. Emphasize key points such as how to recognize perfect cubes and how to express perfect cubes using exponents. Refer to the FAQ below for ideas on how to respond to common student questions.
Use the second page of the guided notes to introduce cube roots. Explain that a cube root is the opposite operation of finding a perfect cube and is the number that, when multiplied by itself three times, equals a given value. Walk through the process of finding cube roots using the ∛ symbol and how to express cube roots using exponents. Refer to the FAQ below for ideas on how to respond to common student questions.
If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.
Practice
Have students practice perfect cubes and cube roots using the practice maze activity provided in the resource. Walk around the classroom to answer any student questions and provide support as needed.
Fast finishers can dive into the color by code activity for extra practice. You can also assign these activities as homework for the remainder of the class.
Real-Life Application
Bring the class back together, and introduce the concept of designing cube-shaped water tanks as a real-world application of perfect cubes and cube roots. In this application, students will learn how to calculate the dimensions of a water tank based on its capacity.
Explain to the students that water tanks are commonly used to store and supply water in various settings, such as residential areas, farms, and industrial sites. The capacity of a water tank is measured in cubic units, which is where the concept of perfect cubes and cube roots becomes relevant.
Using the example of a cubic water tank, discuss with the students the formula for calculating the volume of a cube: V = x^3. Explain that in this formula, the side length (x) is the only dimension needed to determine its capacity.
Then guide a discussion on other places in everyday life that use perfect cubes in everyday life. Students can use the space in the guided notes to brainstorm their response first before sharing with the class.
Refer to the FAQ section for more ideas on how to further explore the real-life application of perfect cubes and cube roots, such as exploring different shapes of water tanks or discussing the importance of precise calculations in engineering and construction projects.
Extensions
Additional Self-Checking Digital Practice
If you’re looking for digital practice for cube roots and perfect cubes, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.
Here’s 1 activity to explore:
FAQs
Perfect cubes are numbers that can be expressed as the result of multiplying an integer by itself three times (e.g., 1, 8, 27, 64). Cube roots, on the other hand, are the inverse operation of finding perfect cubes – they tell us the original number that, when multiplied by itself three times, gives us a perfect cube.
Finding the cube root of a number is like asking, "What number, when multiplied by itself twice (three times in total), gives me the original number?" There are several ways to find the cube root, and here are a few methods that are easy to understand:
- Prime Factorization: For smaller numbers, you can use prime factorization. Break down the number into its prime factors and group them into sets of three identical factors. The product of the unique factors in each set is the cube root. For example, the prime factors of 64 are 2, 2, 2, 2, 2, 2. Group them into two sets of three 2s each. The cube root of 64 is 2 x 2 = 4.
- Guess and Check: Make an educated guess of what the cube root might be, then cube it to see how close you are to the original number. Adjust your guess based on the result and try again until you're as close as you want to be.
- Long Division: Break down a given number into groups of three digits, starting from the right. By repeatedly subtracting multiples of the cube of smaller numbers from these groups and progressively deducing the digits of the cube root, you gradually uncover the cube root approximation. This process allows you to approximate the cube root of a number with increasing accuracy through successive divisions.
For students that need a more visual explanation, I find the Khan Academy video helpful:
Perfect cubes and cube roots have a variety of applications in real life that your students can relate to. Here are a few ways you might encounter cube roots:
- Packing and Storage: Imagine you have a big box and you want to fit smaller boxes inside it perfectly, without any wasted space. Knowing how to calculate the cube root can help you figure out how many smaller boxes can fit in the larger one. This is a bit like playing a 3D version of Tetris!
- Gardening and Agriculture: If you're growing plants in a cubic planter, you might want to know how much soil you'll need. You can use cube roots to reverse-engineer the volume of the planter and figure out how much soil to buy.
- Sports: In games like Minecraft, the world is made up of cubes. Understanding cube roots can help you calculate distances and volumes in the game, making your gameplay more efficient.
- Cooking: Let's say you're following a recipe that requires you to melt a cube of butter, but you only have a larger block. You can use cube roots to figure out what portion of the larger block equals the smaller cube needed for the recipe.
- Science Experiments: If you're doing a science experiment that involves changing the volume of a liquid or a solid, cube roots can help you understand how the dimensions of the object will change. For example, if you're studying how water expands when it freezes, you could use cube roots to predict the size of the ice cube you'll end up with.
So, cube roots aren't just something you learn in math class; they can help you solve real-world problems too!
To determine if a number is a perfect cube, you need to find the cube root of the number and check if the resulting number is an integer. If the cube root is an integer, then the number is a perfect cube.
Some properties of perfect cubes include:
- The cube of an even number is even.
- The cube of an odd number is odd.
- The sum of two perfect cubes is not always a perfect cube.
Cube roots are important in mathematics because they allow us to solve equations involving perfect cubes, estimate values, and solve real-world problems related to dimensions and volumes of objects.
An example of an equation involving cube roots is x³ = 125. To solve this equation, we need to find the cube root of 125, which is 5. Therefore, the solution to the equation is x = 5.
Guided notes and doodles can be an engaging way to teach cube roots and perfect cubes. Students can actively participate by filling in the guided notes with the main concepts and examples. Doodles and sketches can help visualize the concepts, making them more memorable.