ALEX Lesson Plan

     

Square and Cube Root Salad

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

Title:

Square and Cube Root Salad

Overview/Annotation:

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):
Mathematics
MA2015 (2016)
Grade: 8
4 ) Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.


NAEP Framework
NAEP Statement::
8A3c: Perform basic operations, using appropriate tools, on linear algebraic expressions (including grouping and order of multiple operations involving basic operations, exponents, roots, simplifying, and expanding).

NAEP Statement::
8NPO2a: Establish or apply benchmarks for rational numbers and common irrational numbers (e.g., ?) in contexts.

NAEP Statement::
8NPO2d: Estimate square or cube roots of numbers less than 1,000 between two whole numbers.



Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.4- Find the square root of the perfect squares up to 100.


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:

Pencils

Notebook Paper

Rubik's Cube and website to help --https://www.rubiks.com/

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”

https://www.khanacademy.org/math/algebra/rational-and-irrational-numbers/alg-1-irrational-numbers/v/introduction-to-rational-and-irrational-numbers

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-roots/v/introduction-to-square-roots

Worksheet for Acceleration Activity

Worksheet for accelerated students to be copied - http://www.commoncoresheets.com/SortedByGrade.php?Sorted=8ee2

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: https://www.khanacademy.org/math/algebra/rational-and-irrational-numbers/alg-1-irrational-numbers/v/introduction-to-rational-and-irrational-numbers

Khan Academy video for introduction to squares and cubes: 

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-roots/v/introduction-to-square-roots

Calculator

Background/Preparation:

Teacher:

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. 

 

Student:

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.

  Procedures/Activities: 

Before:

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 https://www.khanacademy.org/math/algebra/rational-and-irrational-numbers/alg-1-irrational-numbers/v/introduction-to-rational-and-irrational-numbers.
  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.

During:

  1. The teacher will introduce the topic of cubes and cube root by showing a Rubik's Cube (https://www.rubiks.com/) 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 https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-roots/v/introduction-to-square-roots.
  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.

After:

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 http://www.commoncoresheets.com/SortedByGrade.php?Sorted=8ee2. The teacher should have created the assignment in advance.



Attachments:
**Some files will display in a new window. Others will prompt you to download.
  Assessment  

Assessment Strategies

Informal:

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".

Formal:

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.

Acceleration:

If accelerated students finish early, then they can work on a more challenging equation worksheet with radicals "Challenging Radicals". ( http://www.commoncoresheets.com/SortedByGrade.php?Sorted=8ee2)

Intervention:

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.