Radical Functions and Rational Exponents
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Do your students hate radical functions? If they do, follow these three tips to not only make learning them easier for your students, but teaching them easier for you. Let’s jump right in!
Tip #1 - Radicals Are Simply Variables
I once had a student working very hard to understand Algebra though it wasn’t her strong suit. When we got to radicals, she admitted to me that she hadn’t paid much attention the year before and had no idea what radicals were.
I went through the process of teaching her how we use symbols for real numbers the way we use the pi symbol for 3.14. Once I explained it that way, she was able to grasp the fact that radicals stand for real numbers that are irrational and, therefore, difficult to write out.
Make sure your students have a firm grasp on the fact that these symbols stand for irrational numbers. If they miss this basic step, it will be difficult for them to move on to the next thing, something we must remember as teachers.
Tip #2 - Connecting to Previous Learning
I have said it before and I will say it again: make sure you always remind your students of something they already know when you are teaching them something new.
Your students should already understand variables, so remind them of variables as you begin to teach radical functions. When I do this, I stop for a moment and ask my students easy questions like, “What do you get if you multiply x by x?” They can tell me that it equals x squared. I ask, “What happens if you add x to x?” That’s an easy one; it’s 2x.
Now they can see that if they know how to work with variables, they can work with radicals.
Tip #3 - Review, Review, Review
Begin or end each math class by reviewing basic facts. Give a speed drill of the square root facts, progressing to the ones they inevitably forget.
My kids always forget the square root of 1 because we spend so much time reviewing the larger numbers. The truth is that you can’t expect your students to have success with more complicated topics if they can’t rattle off their square and cube roots without thought.
I use charts of exponent equations with my students at the beginning of class, and for my struggling learners or my ESL/ELL students, I have them keep the charts on their desk as I teach. Just reviewing these basic facts goes a long way toward the students retaining the information and being ready to tackle more difficult concepts.
I also do this is to get students off of the calculator, which can be very frustrating for a teacher. Beyond that, once we get to more complicated lessons, the calculators won't help anyway. This is why I recommend doing these types of drill charts in every class session.
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Common Core State Standards
- Change expressions using the rules of exponents (N.RN.2)
- Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values (N.RN.1)
- Use the properties of exponents to interpret expressions for exponential functions. (F.IF.8.b)
- Write a function that describes a relationship between two quantities. (F.BF.1.a)
Day 101 - Simplifying Radicals
This should be a review from 8th grade, but I do not want to set them up for failure if the class did not transition this far into the common core.
Day 102 - Performing operations with Radicals
(i.e. adding, subtracting, multiplying and dividing, including rationalizing the denominator)
Day 104 - Write the equation for an exponential function, given a table, or graph, situation, or two points.
Day 105 - Common Core Assessment Examples
- Sample MAP Questions for radicals
- Sample assessment item from Smarter Balanced.
- Checking a calculation of a decimal power - Illustrative Mathematics
- Rational or Irrational - Illustrative Mathematics
- Smarter Balanced Sample Question #42906