Radicals and Exponents Content Module
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Contents |
Radicals and Exponents: Skills covered in the module
- 6.NO.1i1 Identify what an exponent represents
- 6.NO.1i2 Solve numerical expressions involving whole number exponents
- 8.NO.1i1 Convert a number expressed in scientific notation up to 10,000
- H.NO.2c1 Simplify expressions that include exponents
- H.NO.2c2 Rewrite expressions that include rational exponents
- H.NO.1a2 Explain the influence of an exponent on the location of a decimal point in a given number
Plot the Course
The rationale
The practical applications of exponents and radicals may be difficult to recognize at first, but once one realizes that exponents are used in everyday life as efficient shorthand for longer numbers…just think scientific notation! Other daily examples where exponents and radicals are used daily include cooking when you need to double or triple a recipe to feed a large number of people.
Module Goal
The goal of this module is to provide detailed instruction on the more difficult concepts of exponents and radicals to teachers of students with disabilities at the middle and high school level. This module promotes a mathematical understanding of these concepts so that a teacher can begin to plan how to teach the concepts to students. Additionally, this module will provide instructors with potential adaptations and modifications to consider when designing materials and instruction for students with severe disabilities.
Module Objectives
After viewing the content module, teachers will:
- Perform operations including exponents and square or cube roots
- Perform operations including both positive and negative exponents
- Write large numbers using scientific notation
Time for Take Off
Understanding the vocabulary used within exponents and radicals is important for both teachers and students in planning and implementing math lessons. As a teacher, knowing and using the mathematical terms not only ensures your instruction stays true to the math content, but also will help with collaborating with other math teachers or content experts. When choosing which vocabulary to teach, it is most important that the teacher selects the most salient, important, or most frequently used vocabulary for each lesson. Below you will find a list of vocabulary included within this module. It may or may not be necessary to provide instruction for all terms as students may have learned them previously. Expressions are mostly covered in middle school so vocabulary for this content module has been combined. If you are a high school teacher and are not confident your students know some of these vocabulary terms, you may want to review and teach some unknown terms in the focus and review part of your lesson plan. While providing vocabulary instruction, you may consider including pictures or objects to make the instruction more concrete for students with disabilities (see Ideas to support vocabulary learning below).
Vocabulary
- Exponent - a small number to the right of a base; indicates how many times you multiply the base together (e.g., 23)
- Scientific notation - another way to write numbers that are very large or very small (e.g., 5300.0 = 5.3 x 103)
- Squared - the product of a number multiplied by itself (e.g., 49 = 72)
- To find the square root of a number, divide the number by itself
- Cubed - the product of a number multiplied by itself three times (e.g., 343 = 73)
- To find the cube root of a number, divide the number into itself three times
Ideas to support vocabulary learning
- Visually discriminate between the position of bases and their powers (squared or cubed)
- Color code exponents so they stand out
- Incorporate the use of a scientific calculator that will allow students to enter equations as they appear
Floating on Air
Before you can begin teaching solving problems using radicals and exponents, you need a deep understanding of these mathematical concepts. Some of these concepts may be familiar to you. Below is a list of skills that should be covered at each grade level. For concepts that you need more information about, please view the accompanying PowerPoint presentations that will walk you through an example as well as make some suggestions for instruction.
Middle and High School
In middle and high school, skills include:
- 6.NO.1i2 Solve numerical expressions involving whole number exponents
Square and Cube Roots powerpoint
- 8.NO.1i1 Convert a number expressed in scientific notation up to 10,000
- H.NO.2c1 Simplify expressions that include exponents
- H.NO.2c2 Rewrite expressions that include rational exponents
- H.NO.1a2 Explain the influence of an exponent on the location of a decimal point in a given number
Great! Now that you have viewed the PowerPoint presentations most useful to you, the next section will provide some ideas to consider when planning for Universal Design for Learning.
Sharing the Sky
UNIVERSAL DESIGN FOR LEARNING
| Some examples of options for teaching radicals and exponents to students who may present instructional challenges due to: | ||||
| Visual Impairment or Deaf/Blind | Physical impairment:
Little/ no hand use |
Lacks basic numeracy concepts | Motivational/ attention issues | |
| Representation | Add corresponding textures (e.g., Velcro) to equations and calculators; add texture to exponents (e.g., raised numbers) and to radicals | Student scans an array of possible options and uses a switch to select the appropriate terms | Use a talking graphing calculator so students can just plug in the equation | Create personally relevant word problems or stories |
| Expression | Student states answer or scans raised numbers to select correct answer; use voice output devices for student to select the correct answer | Use a switch to indicate correct answers; use an eye gaze board to select answer; "yes/no" response, these can easily be answered using an eye gaze, head turn, two switches, etc. | Student selects numbers or terms versus writing them; selection of correct answer is done after a model | Student solves problems with radicals or exponents using computer software or other technology |
| Engagement | Use a talking calculator possibly a talking graphing calculator so students can enter radicals and exponents as they appear in the equation. | Use a computer with AT where the student can click to answer; use manipulatives that are large and easily manipulated; pair student with another student without a physical impairment and have them work together | Use objects to represent numbers in the problem; color code problem and calculator buttons to assist in solving radicals and exponent problems | Include personally relevant contexts for radicals and exponents (e.g., their growth as they get older) |
Prepare for Landing
Below you will find ideas for linking radicals and exponents to real-world applications, the college and career readiness skills addressed by teaching these concepts, module assessments for teachers, sample general education lesson plans incorporating Universal Design for Learning framework, blog for teachers to share their ideas, and a place to upload and share lesson plans from teachers who completed this module.
One way to help assist in a special educator's development within this curricular area is through collaboration with other teachers in your building. Some activities with real world connection include:
- Graphing the growth of a living object (e.g., the student's own height, a plant in science)
- Doubling or tripling a recipe to have enough food to serve 10 people
In addition to the real-world applications of these concepts, skills taught within this content module also promote the following college and career readiness skills.
Communicative competence:
Students will increase their vocabulary to include concepts related to "squaring" or "doubling" In addition, they will be learning concepts such as: "radical" and "exponent".
Fluency in reading, writing, and math:
Students will have an opportunity to increase their numeracy and sight word fluency while participating in problem solving related to "radicals and exponents" such as number recognition, counting, and grouping similar things.
Age appropriate social skills:
Students will engage in peer groups to solve problems related to "radicals and exponents" that will provide practice on increasing reciprocal communication and age appropriate social interactions.
Independent work behaviors:
By working with real life problems related to "radicals and exponents" students will improve work behaviors that could lead to employment such as marketing or any job that has to analyze sales rates, stock clerks, order fillers, and other construction based professions. When providing opportunities for real life problems leave some materials out and prompt/teach the students to determine who they should ask and what they should ask for to be able to solve the problem.
Skills in accessing support systems:
At times, students will need to ask for assistance to complete activities related to "radicals and exponents" which will give them practice in accessing supports. Students will gain practice asking for tools such as graphing calculators, or other manipulatives. They can ask a peer to complete the physical movements of the tasks they are not able to do themselves. Be sure to teach students to ask versus having items or supports automatically given to them. In addition to collaborating with other educational professionals in your building, the following list of resources may also help provide special educators with ideas for activities or support a more thorough understanding of the mathematical concepts presented in this content module.
Additional Resources
- http://www.learningfront.com/jfk/pages/david_1.html - This website includes fully developed general education lesson plans for solving radicals and exponents
- http://www.ncpublicschools.org/acre/standards/common-core-tools - This website provides an "unpacking document" for the Mathematics Common Core Standards that helps teachers identify what is most important and the essential skills for each standard
- http://www.uis.edu/ctl/mathematics/documents/Radicals.pdf - This pdf provides step by step instructions solving various problems including radicals and exponents
- http://www.mathforum.com - This website specifically for teachers that provides a variety of ideas and activities to use in your classroom
- http://www.teachertube.com - Youtube for teachers! Simply search for your content area and this websites provides a variety of videos including videos of math experts working through math problems step by step (free registration required)
- The Use of Manipulatives as an Instructional Strategy to Help Students Who are Blind or Visually Impaired Understand and Learn Math Concepts powerpoint - This website provides a webinar about how to adapt materials for students who have visual impairments
Module Assessments
Below are links to assessments for the purpose of self-checking your understanding of the content in this module. After answering the assessment questions, you may want to review the key to check your work.
Radicals and Exponents Assessment pdf
Radicals and Exponents Assessment Key pdf
Sample General Education lesson plans
Writing and Comparing Numbers in Scientific Notation lesson plan pdf
Adapt the following general education lesson plan; adapt, and upload. These lesson plans may be shared with higher education professionals developing strategies to provide meaningful academic instruction in mathematics to students with severe disabilities.
