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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.
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.
31 to 60 Minutes
Materials and Resources:
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”
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:
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.
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.
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". ( http://www.commoncoresheets.com/SortedByGrade.php?Sorted=8ee2)
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.