Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 39139
Simply Radical!
Students will rewrite radical expressions that can be simplified to one term and perform operations on radical expressions. They will solve problems in
a Row-by-Row activity. Pairs of students work on different problems at different complexity levels that lead to the same solution. The students will
challenge each other to prove their solutions are correct. This activity does not address rational exponents.
Subject(s): Mathematics
Grade Level(s): 8, 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Computer for Presenter, LCD
Projector
Instructional Time: 1 Hour(s)
Freely Available: Yes
Keywords: operations on radicals
Instructional Design Framework(s): Direct Instruction
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
SR Row by Row Form B (r).docx
SR Suggested Examples (r).docx
SR Row by Row Form A (r).docx
SR Row by Row Key (r).docx
SR Lesson Assessment.docx
SR Lesson Assessment Key.docx
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will rewrite expressions involving operations on radical expressions (i.e.,
,
,
,
)
Prior Knowledge: What prior knowledge should students have for this lesson?
In previous lessons, students should have acquired the prerequisite knowledge on simplifying radicals to their lowest radical form from:
MAFS.8.NS.1.1 - Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational
numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
MAFS.8.EE.1.2 ­ 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.
Student understanding need only be at a low complexity level, only requiring recall.
Guiding Questions: What are the guiding questions for this lesson?
How can you determine if a radical expression can be simplified?
How can you determine if a radical expression is completely simplified?
page 1 of 3 When can radical expressions not be combined?
Teaching Phase: How will the teacher present the concept or skill to students?
The teacher will begin the lesson by displaying the set of numbers provided in the Suggested Examples document (see attached) and have the students group the
numbers into the two categories, Rational or Irrational. This activity may also be done as a sort, where the numbers are printed/written on cards (card stock or
index cards) and the students physically move the numbers (cards) into the correct category.
The teacher will review the solutions and clarify the reason for each number's placement as needed.
After determining whether the students understand the difference between rational and irrational numbers, teacher will need to determine whether the students
understand whether terms are considered like or unlike in order to combine radical expressions.
The goal is for students to understand that only like terms can be added or subtracted, and that terms do not need to be like to be multiplied together or divided.
Once the teacher has determined the students have a firm understanding, he or she should proceed with the teaching phase.
The teacher should present the following expressions and direct students to simplify (dry erase boards are best.):
Students should respond with 4.
Students should respond with 7, however, the teacher should elicit from students why this expression is able to be simplified, despite appearing to not
have like terms. Students should be able (or lead) to explain that each term in the expression can be simplified (rewritten) before being combined.
Students should respond with 2(2) + 2(3) = 4 + 6 = 10 and should be able (or lead) to explain as above.
This problem ramps up the level of knowledge needed, as students should see that
, then
. In this case, the
2s are considered to be coefficients. Because they are alike, they can be combined, and
The following is an example where the student can simplify part of the expression:
Guided Practice: What activities or exercises will the students complete with teacher guidance?
The teacher will present the problems provided in the Suggested Examples (see attached document), projected or written on the front board, and the students will
work along with the teacher to rewrite the radical expressions. The students may work on individual dry erase boards or on paper (notes) if dry erase boards are not
available.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Students will complete a Row-by-Row Activity (see attached) for independent practice. The teacher will assign pairs of students of mixed ability, one high ability/one
medium ability or one medium ability/one low ability student. The lower ability student should be given Form A, while the more able student receives Form B. The
answers are the same for each problem on both forms, so Form A problem 1 and Form B problem 1 have the same answer.
Students work each problem one at a time, compare answers, and if they are not in agreement, they will each show the procedure used to find their answer and use
error analysis to find any mistake. If they both arrive at the same solution, they proceed individually to the next problem.
The students will provide each other with feedback as they proceed through each problem. They will use the feedback to hone their skills.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will bring the class back together as a whole and review the concepts by eliciting the following information from the class:
How can you tell if an expression can be simplified? (check to see if all like terms have been combined and pairs of factors have been moved out of the radical)
Why would radical terms not be able to be simplified into one term? (they do not have the same simplest radical that is like)
When do you know that a radical term is in its simplest form? (the number under the radical has no factors that are perfect squares)
Can radical expressions be simplified into rational numbers? (yes, if you multiply two radicals and the product is a perfect square or the cube root is a perfect cube)
Summative Assessment
Students will be given a Lesson Assessment at the end of the lesson to determine mastery of the concepts taught during the instructional period. The teacher will use
these results to adjust the direction of the curriculum in the next lesson, or to review this topic further.
Formative Assessment
The teacher will assess students' prerequisite knowledge during class discussion. The teacher will check student work while circulating among students, or have each
student use a desk top dry erase board and show their answers and work as the teacher poses questions. The teacher will adjust instruction according to class needs,
reviewing if foundational knowledge of properties of exponents are not firm or advancing directly to the lesson if it appears the students have sufficient operational
skills.
Feedback to Students
Students will receive verbal feedback from the teacher on their individual responses to questions during the teaching phase. The students will use that feedback to
correct their process of rewriting radical expressions.
Students will receive instant feedback from their peers during the row-by-row activity, in which two students of different ability levels are paired. The students will
simultaneously work on different problems that result in the same solution. If their answers are different, they will have to explain their process to each other to
determine which answer is correct or incorrect. Students will use this feedback to adjust their work in future problems.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations: Students with visual processing issues should be provided with a copy of notes in skeletal form that have certain key terms or values missing.
The students still need to take notes, but do not have to take everything down, and can focus on the content being presented while still attending to the notes being
given to the class.
The teacher should provide support for English Language Learners with translations, dictionaries, and/or examples for unfamiliar vocabulary words.
Suggested Technology: Computer for Presenter, LCD Projector
Special Materials Needed:
page 2 of 3 Teacher materials:
copies of Independent Practice for each student
copies of Row-by-Row Form A and Form B one of each for each pair of students
Student materials:
desk top dry erase boards (optional)
dry erase markers/erasers (optional)
Further Recommendations: It is not recommended that students have calculators, as the concept targeted in this lesson does not require finding the actual
irrational (approximate decimal) value. Instead, students must require expressions so that simplified radicals can be compared and, if possible, combined.
Additional Information/Instructions
By Author/Submitter
This resource is likely to support student engagement in the following the Mathematical Practices:
MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.
MAFS.K12.MP.3.1 Construct viable arguments and critique the reasoning of others.
MAFS.K12.MP.8.1 Look for and express regularity in repeated reasoning.
SOURCE AND ACCESS INFORMATION
Name of Author/Source: Anonymously Submitted
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.N-RN.1.2:
Description
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
page 3 of 3