ALEX Lesson Plan


Square and Cube Root Salad

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  This lesson provided by:  
Author:Morgan Boyd
  General Lesson Information  
Lesson Plan ID: 35592


Square and Cube Root Salad


This lesson will develop the knowledge of squared and cubed numbers. The students will know when to use the square root and cube root to solve an equation. The students will memorize perfect squares and some cube roots. The answers will be left in radical form. Finally, the students will be able to identify the radicals as rational or irrational.

This lesson results from the ALEX Resource Gap Project.

 Associated Standards and Objectives 
Content Standard(s):
MA2019 (2019)
Grade: 8
4. Use square root and cube root symbols to represent solutions to equations.

a. Evaluate square roots of perfect squares (less than or equal to 225) and cube roots of perfect cubes (less than or equal to 1000).

b. Explain that the square root of a non-perfect square is irrational.
Unpacked Content
Evidence Of Student Attainment:
  • Evaluate expressions involving squared and cubed numbers.
  • Solve equations with radicals with a square or cube root solution.
Teacher Vocabulary:
  • Radical
  • Square Root
  • Cube Root
Students know:
  • that the square root of a non-perfect square is an irrational number.
  • Equations can potentially have two solutions.
  • how to identify a perfect square/cube.
Students are able to:
  • define a perfect square/cube.
  • Evaluate radical expressions representing square and cube roots.
  • Solve equations with a squared or cubed variable.
Students understand that:
  • there is an inverse relationship between squares and cubes and their roots.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.4.1: Define square root, cube root, inverse, perfect square, perfect cube, and irrational number.
M.8.4.2: Recognize the inverse operation of squaring a number is square root and the inverse of cubing a number is cube root.
M.8.4.3: Restate exponential numbers as repeated multiplication.
M.8.4.4: Calculate the multiplication of single or multi-digit whole numbers.
M.8.4.5: Recognize rational and irrational numbers.

Prior Knowledge Skills:
  • Restate exponential numbers as repeated multiplication.
  • Define rational number.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.4 Calculate the square of numbers 1 through 10.

Local/National Standards:


Primary Learning Objective(s):

The student will be able to solve equations using square roots.

The student will be able to solve equations using cube roots.


Additional Learning Objective(s):

The student will be able to distinguish between rational and irrational numbers with radicals.


 Preparation Information 

Total Duration:

31 to 60 Minutes

Materials and Resources:


Notebook Paper

Rubik's Cube and website to help --

Small cube blocks -- enough to have 100 blocks for each group of 4 students

Handheld calculator if 1-to-1 technology is not available

Videos from the website “Khan Academy”

Worksheet for Acceleration Activity

Worksheet for accelerated students to be copied -

Worksheet to be copied for all the students -- Rational and Irrational (see attached document)

Worksheet to be displayed on the interactive whiteboard -- Bell Ringer Squares and Cubes (see attached document)

Worksheet to be copied for all students -- Equations with Roots (see attached document)

Worksheet to be displayed on the interactive whiteboard -- Exit Slip Radicals (see attached document)

Technology Resources Needed:

Desktop computer with interactive whiteboard and wireless internet

iPad, Chromebook or MacBook for each student 

Khan Academy video for introduction to rational and irrational numbers:

Khan Academy video for introduction to squares and cubes:




The teacher will need to preview the video and other materials that are listed in the resource section. The teacher will need to make sure that he/she has enough blocks for the entire class. The blocks do not have to be the same color, but they do need to be the same size. Having blocks of identical sizes will prevent students from becoming confused. 



The student will need prior knowledge of changing decimals to fractions. The student will need to know that a repeating decimal is a rational number. Rational numbers are those numbers that can be written in the form of a fraction. The video will explain the concept briefly. The student will need experience in solving equations using inverse operations.



Bell Ringer:

  1. Before the students enter the classroom, the teacher will open the document “Bell Ringer Squares and Cubes.” The document will be displayed on the interactive whiteboard.
  2. The teacher will show the video from the website “Khan Academy”. The link is
  3. After the video, the teacher will discuss the answers to the bell ringer. The teacher will ask the question, “Explain why you chose rational or irrational?” The answers will vary, but they should be similar to “written as a fraction”.
  4. The teacher will hand out the worksheet "Rational and Irrational Worksheet" from the attachments.
  5. The teacher will use this opportunity for an informal assessment.


  1. The teacher will introduce the topic of cubes and cube root by showing a Rubik's Cube ( to the class and discussing the way the blocks arrange a 3 by 3 by 3 cube. Therefore, the cube root would be 3.
  2. The teacher will tell the students to work in groups of four to explore the idea of cubes with the small blocks. The students will make two cubes, 2 by 2 by 2 and 4 by 4 by 4. The students will count the blocks. The total will be 8 and 64. The teacher will let the groups try 2 by 3 by 3. The students will realize that the shape is not a cube, thus, no cube root. The teacher will monitor the groups as they work.
  3. After the activity, the teacher will show the video from Khan Academy.
  4. The website has some great material about equations with squares and cubes as well as roots. The website is
  5. The teacher will navigate through the website. The teacher will stop at random places to do informal assessments.
  6. The website has many opportunities to do interactive “guided practice” exercises. The teacher can call on different students to answer the problems.
  7. At the conclusion of the video, the teacher can pass out the worksheet from the attachment section called "Equations with Roots".
  8. The students will work independently to complete the worksheet. Students who require intervention could work in pairs with a peer-tutor and the manipulatives. The teacher will be able to monitor the students and provide one-on-one instruction. The teacher will use this opportunity for another informal assessment.
  9. While students are finishing, the teacher will start the review of the answers. The teacher will answer questions from the class and listen to their comments.


The teacher will display the document, “Exit Slip Radicals” on the interactive whiteboard. The students will complete the exit slip on their own paper. The students will turn in the exit slip as they leave the classroom.

If the accelerated students finish early, then the teacher will assign work from the website "Common Core Sheets”. The website is The teacher should have created the assignment in advance.

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Assessment Strategies


The teacher can ask questions while reviewing the classwork worksheet "Rational and Irrational".

The teacher will check for student understanding with the worksheet "Equations with Roots".


The teacher will check for mastery using the Exit Slip while taking into consideration the student's comprehension of the mathematical concepts observed during the lesson.


If accelerated students finish early, then they can work on a more challenging equation worksheet with radicals "Challenging Radicals". (


The intervention students can be placed in groups with a manipulative and peer-tutor. The students can be given more time to complete the assignments and one-on-one help.

View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.