# Why Do We Rationalize the Denominator Notes

Before I teach my algebra students to rationalize the denominator, I try to answer the looming question: why do we rationalize the denominator?

I realize that rationalizing the denominator has gone out of fashion as a result of the Common Core State Standards, but the topic is still required by the Oklahoma math standards.

I try to give my students a taste of history and the WHY of what we’re doing.

Whenever I’ve taught rationalizing the denominator in the past, students often questioned why we weren’t allowed to have a radical in the denominator. I tried to explain how it was a sort of math “tradition,” but I’m not sure my students fully understood the reason it became a tradition.

Now that we live in the days of a smartphone in every pocket, it’s hard to imagine what life was like in the days before calculators. So, for this activity, I made my students put away their calculators and do some math by hand.

First, we discussed how people found various mathematical values using books of tables in the days before calculators. Students were confused about how to read the table, but I think they caught on after a bit.

I asked them to calculate two values by hand using the decimal approximations from the table. Students had to find five divided by root two and five multiplied by root two.

My students flew through the calculation for five times root two. They couldn’t even remember how to set up the long division problem for five divided by root two. We ended up doing that one together!

They all agreed that multiplying by a radical was MUCH easier than dividing by a radical!

## Free Download of Why Do We Rationalize the Denominator Notes

Rationalizing the Denominator Notes – Why When How (PDF) (882 downloads )

Rationalizing the Denominator Notes – Why When How (Editable Publisher File ZIP) (851 downloads )

Introduction and Rationale for Rationalizing the Denominator (PDF) (799 downloads )

## More Activities for Teaching Radicals

- Prime Numbers Chart
- Radicals Task: Which is the Smallest?
- Like Radicals Card Sort Activity
- Parts of a Radical Poster
- Prime Factorization Foldable
- Prime Factorization Graphic Organizer
- Prime Numbers Below 100 Chart
- Simplifying Radicals Puzzle
- Rationalizing the Denominator Practice Book
- Operations with Radicals Question Stack Activity
- Conjugates INB Page
- The Constant Chair Regression Activity
- Prime and Composite Numbers Chart
- Multiplying Radicals Graphic Organizer
- Vocabulary Knowledge Rating Chart
- Parts of a Radical Graphic Organizer
- Radical Clock Makeover
- Dice Activity for Reviewing Square Roots

I love the Top Ten Things to Remember on your unit divider. When do kids fill that in? I was thinking it would be a nice thing to do near the end of a unit to review important concepts. Do you fill that in as a whole class or do students do that individually?

I noticed with your team roles that there are only 4 positions. How do you handle groups with more members? Like groups of 6? Thank you so much for any insight. Your blog is incredible!

Love your website and all of your amazing materials! Have you created unit dividers for Algebra 2?

I love how your divider tabs help both you and students track concept connections. I noticed you also have dividers for your science units, would you mind sharing those for us science teachers just getting into SBG?

I love my radical functions/equations unit in Algebra II. I have started memorizing some prime factorizations from using them so much when simplifying common radicals, but I never thought to have kids just go ahead and record them to quickly refer to. This is such a great idea, and may actually help the kids memorize some. I have kids who have only had to write the radicals in decimal form and keep moving. NOT in my class! I'm not sure how they got away with that when simplified radical form is on the Alg I state test. I suppose some teachers don't think it's worth teaching.

Great notes – thank you!