Radical Unit Planning

Maybe because I have an early case of spring fever ... after all it's 70+ degrees in February ...
or
Maybe because I have the winter doldrums ... don't the days between January and March seem very long ...
or
Maybe because it just isn't my favorite skill to practice ...
I'm struggling to pull together plans for our unit on Radicals ... but plans are coming together thanks to math bloggers!

In our unit we have to address inverse functions, transformations, writing radical expressions in various forms, solving equations, and applying the function to word problems ... pretty standard for each of the functions we examine.  Our district sets a timeline ... it's 6 class days, each class is 90 minutes!

Here's my plan so far ...

Day 1 Inverses
We did inverses early in September ... so this will be a review day emphasizing domain and range.
I plan to use a Desmos teacher created activity to facilitate conversations about inverses.  I'm using J Orr's What's the Point with minor modifications and S Carranza's Practice with Inverses - again with minor modifications.  Students will practice pencil/paper style to follow up with the online work ... filling in a table of functions, their inverses, and their respective domains/ranges.

Day 2 Attributes & Transformations
We will explore square root and cube root functions on this day - noting their attributes - comparing them to the functions we have already studied.  We'll also work on transformations using Desmos - again, borrowing from S Carranza's work, Transformations of Square Root and Cube Root Graphs.  I'm planning stations for class practice.

Day 3  Rational Exponents and Radicals
I don't have this day totally mapped out but I am excited to use K Belmonte's radical catchers in class!  I think the students will enjoy creating the foldables and make the practice a bit more interesting.  Speed dating is in the works as well!

Day 4 Solving
I'm planning for this day to be mostly practice.  I will provide a few examples, but I know students learn best when they do the work.  I'm looking at a scavenger hunt, a tic tac toe game, or a row game ... decisions!  All of the activities I'm considering we can do in pairs to promote math talk and peer coaching.

Day 5 Applications
I have a few good problems, well-constructed ones.  I'm thinking students will create posters to solve and explain their thinking.  I need more structure for this day for sure!

Day 6 Review
I'll use daily data to determine how best to organize this day.  We typically use games for about half the class period and paper/pencil review for the other half.

Tomorrow I'll create the outlines for each day ... goals, activities, and practice!  I'm almost there ... with a little help from my friends.

They created their own Quizizz!

We are wrapping up our unit on Rational Functions.

First we studied their graphs!
We learned about asymptotes (ditches) and removable discontinuities (holes).
Students able to analyze the key attributes of rational functions.

Then we jumped into the simplifying and solving.
We learned how to find common denominators.
We learned how to apply rational functions to a variety of word problems involving rate ... travel rate, distance rate, cost per person, mixture rate.

Instead of my creating a game for students to review, I asked students to create their own Quizizz game.  They created accounts, developed 10 problems, determined thoughtful multiple choice answers, and uploaded those.

They came to class armed with their Quizizz links!  I grouped desks together, and invite them to share their games.  They played for 40 - 50 minutes.  They swapped codes, advertised their codes on the board.  The conversations were lively.  They checked each other's work; complained when they found errors; got excited when they scored well on games.

After playing I asked students about their confidence level on the math skills.  I also asked them if they enjoyed creating their own games.

Their test is Tuesday.  I'm concerned about their confidence levels.  I've provided review documents, videos, and will provide a study prep session before school.  I realize that the data showing is just a few students - but the average is only about 3 out of 5.

Students reported not enjoying putting the Quizizz test together.  They said it was a lot of work.  It's the last week of the marking period and students were feeling the pressure from many courses.  Timing wasn't great.  If I ask students to create a game again, we will definitely work in teams on the assignment.  We might also develop a problem or two after each lesson so students aren't having to create a game from scratch at the end of a unit.

As I work Tuesday's test this weekend, I know we have prepared well.  In my mind this is the more difficult of the units we study; the more abstract; the more challenging.  

Somehow I want to help students with their confidence levels.  How do you do that in your classroom?

#ExploreMTBoS2016 An Ordinary Lesson

The "Explore MTBoS" challenge is to blog a lesson.  I chose to report on today's lesson.  It's a skill lesson - adding/subtracting rational expressions.  We've analyzed graphs, discussed asymptotes and holes, and we are going to work on application problems in a few days... work, travel, cost, mixture, and inverse variation.

But in the middle of graph analysis and problem solving ... we have to learn the skill of adding/subtracting/multiplying/dividing expressions and solving equations.  We'll only spend 2 class periods on these basic skills.

This is one of those less glamorous lessons.

Today I have leftover popcorn from a fundraiser at Saturday's academic competitions.  I invite students to scoop out a cup and munch while we work.  I tell them I hope that every time they smell/taste popcorn in the near future they remember how to find the LCD of a rational expression.

My students are 9th and 10th graders - not too far removed from the middle school - so I ask them about their feelings towards fractions, and how they learned to add fractions.

I give them the problem, 1/6 + 4/15, and ask them to tell their neighbor how they found the sum.

I factor the denominators ... and then I launch into a story about my neighbor.  The story is borrowed directly from George Woodbury.  By the third class, I guess I get good at it ... they are hanging on every word ... and clap when I make the connection to the fractions on the board.  Later I hear them talking about the upgraded model of the grill (x + 4) vs (x + 4) squared as they are finding sums.

Then we jump into ClassKick, my favorite iPad app.  I've prepared slides for taking notes.  On those slides I demonstrate step by step how to add/subtract rational expressions.  The students follow along, working the problems with me.

Then I provide 2 slides with problems worked out with errors.  I ask students to find the errors, and then check in with their neighbors to see if they agree.  If they don't agree I encourage them to talk it out.









In these error problems we discuss the excluded values.  We've already studied asymptotes and holes so students are familiar with the concept of excluded values.  I ask students, "Why are values are excluded from the addends?"  I ask again - would those values be excluded even if the simplified sum was not affected by the values?









Next we stop for a couple of minutes of reflection.  What is the muddiest point for you?  Or on what step are you have the most difficulty?  And on a scale of 1 - 10, what is your confidence level at this time?

It's at this point that students' actions diverge depending on their confidence levels.  On the next slide I give them 3 videos I found online that explain adding/subtracting rationals.  None of the videos are long ... just one problem each.  I tell students that if their confidence level is less than a five, I want them to watch at least one video, and all three if they prefer.  Then move on into the class practice.  For others who rated themselves high on confidence they begin working on the class examples. Differentiation is based on students' perception of their understanding.




As students work on the class examples, I give simple "sticker" feedback electronically or help them at their desks as requested. Students who chose to watch a video get started on the problems a few minutes later.  Some students finish early and are asked to either help others or work on their BrainGenie goal which reinforces the skill.  I monitor student progress visually from the ClassKick projection showing everyone's work, and also specifically as I tour the room.




Overall the lesson went well.  Students will need more practice ... and that's difficult with our schedule.  I'm hoping they choose to do the 10 problems I assigned for homework.  I won't grade them ... I gave them worked out solutions.  They know they'll complete a learning check in the next class on this skill.

I wish I had had one more reflective time at the end ... has your confidence level improved with this practice today?

Exciting times in Algebra 2.