Algebra 1 Unit 5 Interactive Notebooks: Exponents and Radicals

This year I’ve committed to posting each unit of both my Algebra 1 and Algebra 2 INBs.

My district is moving to a standards based curriculum, and has identified priority standards for every course. These are the standards we are required to address and assess our students over, so they pretty much form our units.

You can find my Algebra 1 (year long class) INB posts here:

Unit 1 | Unit 2 | Unit 3 | Unit 4

And my Algebra 2 INB posts here:

Unit 1 | Unit 2 | Unit 3 | Unit 4

And finally, my posts from a 2nd go around I’m teaching of Algebra 1 here:

Unit 1 | Unit 2

Our 5th Algebra 1 Unit focuses on the N.RN.2 standard:

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

This standard assumes that students are already proficient in the exponent properties using whole numbers, but that is certainly not the case for my students. Most of them act like they have never seen the exponent properties before, and some of them don’t even know the definition of an exponent. So we start at the beginning – here is the skill breakdown I used.


Skill 1: I can combine exponents with like bases


In retrospect, I should have really focused this skill in on a single property at a time, very simple problems only. My students were starting with so little understanding of this that they became overwhelmed as soon as we got to the inside of the example booklet where they had to use more than one property in the same problem. When I teach this next, I plan to do a lot more examples here with one isolated property in them, and then move into combining problems with a few examples and in the scaffolded practice activity I created.

However, I do like teaching the properties as one generalization involving the order of operations instead of teaching them as several separate properties. We start this unit off with an exponent exploration that helps the students discover these patterns and properties, so formalizing them in one cohesive swoop is nice and gives them less to remember, plus they always have the expanded form strategy to fall back on if they forget.

Skill 2: I can rewrite negative and zero exponents

I am really happy with the front page of this and all the pattern finding we did while we filled it out. Once my students found the dividing by 5 pattern, they immediately found decimals for the negative exponents, and I asked “how else can you write decimals?” “Fractions…” they replied with a groan in every class, but then all of them persevered in coming up with fraction equivalents for 0.2, 0.04, and 0.008 – either from things they knew or by using place value and reducing the fractions. We wrote the “rules” for negative exponents and zero exponents only after we figured out what was happening, and I really think this developed a strong understanding.

Many of my students struggled with not knowing how we moved from step to step in the examples when they were looking back on their notes, so I think next time we will bust out the highlighters and highlight the portion of the problem we are addressing in each step so that it’s more clear when they look back on their notes.

Skill 3: I can rewrite exponential expressions in equivalent forms

I love this “goals when ‘simplifying’ exponent expressions” checklist. When are you done simplifying? How do I know that this is the “simplest”, since that word is subjective? This tells my students what I am looking for when I am grading and makes the process of “simplifying” much more objective.

Then we took the opportunity to practice some of the “really long” problems, as my students say.

Skill 4: I can convert between exponential and radical forms


I like these notes, but I need to include more that involve variables in the examples and less of the “convert and evaluate” examples. Perhaps reverse the ratio of these types. Fun part: my students are now all horrified that imaginary numbers exist and that they’re eventually going to have to do something with them. That was a really awesome portion of the lesson, actually, to just watch their faces as their minds exploded a little. One of them, when he put the expression into his calculator, informed me that he got an error message. I responded “YES! What does it say?” and he just went “Nooooo. I already don’t like this.”

Skill 5: I can rewrite radicals in equivalent forms

I need better instructions for the Sieve of Erasthothenes. Somehow. I looked at Shaun Carter’s activity and perhaps that is a better way to go for next time. Half of my students have an incorrect list of primes in their notebooks because they did not follow my instructions. For many of them, the problem was as simple as counting by threes incorrectly though, and I am not really sure how to fix that. I do think it’s beneficial to do this and not just GIVE them a list of primes, but it’s not helpful if they end up with the wrong information. I’ll keep thinking about this one.

I love teaching the two methods of prime factorization and letting the students choose which one they prefer. It varies drastically student by student and they are all incredibly defensive about their preferred method, which I find hilarious.

I got the prime number coloring chart and the simplifying radicals instructions from Sarah Carter, although I changed the examples on the inside. We played a really cool game to practice this that the students really found useful – inspired by this post from Mrs. Awadalla, resulting in this activity by me.


Files from this post that I created can be found here, in PDF and editable forms. If I got the resource from another teacher, the place you can find it is linked within the post 🙂

Author: missmastalio

Math teacher at an alternative high school. Living the best life.

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