Creative Art Project Introduced!

Yes, some students were ho-hum ... but others ...

... explored all the trig functions to see what shapes they would make
... imported a picture into Demos to see if he could outline it with equations
... discussed the virtues of a single drawing versus a scene
... asked if abstract drawings were acceptable
... tried a few basic functions and how to limit the domain and range

I wish now I hadn't given students 3 whole weeks to complete the project ... I can't wait to see their art!

So what is expected and why?

Our algebra 2 curriculum is structured around a series of parent functions.  We introduce the concept of functions at the beginning of the year.  And then we start marching through seven of them!  With linear functions we explore systems of equations.  Then we look at absolute value functions and how they are related to linear functions.  We end our first semester with an intensive study of quadratic functions ... first examining the graph, transformations, and using graphs to solve problems.  And then we solve quadratics and problem solve some more.

In our second semester we jump into radical equations first since they are inverses of quadratics ... and then we take a detour to study rational exponents.  Next up are exponential functions and logarithms.  And last we learn about rational functions.  That's where we are now.  We are finishing our first unit on rationals which is the graphing unit.  Then we will simplify, solve, and apply rational functions to word problems.

So this creative art project is planned with the purpose of reviewing these seven functions, their transformations, domain, and range.  Students must use at least five of the seven studied to create art.  Their artwork must have at least 12 equations total but as we discussed today, most will have many, many  more.

In the past I would have students create this work on paper.  BUT oh my, DESMOS to the rescue!  How much nicer to have the art online, equations clearly identified, easy to see what students did! Now the focus is on transformations, limiting domain and range ... not on their ability to graph the functions by hand.  The thinking process is different ... better from my perspective!

Here is a link to the handout I gave students.  I can't wait to share their work with you all!  Check back after April 28!

Working on Instructions for Project in Desmos

I'm working on instructions and a rubric for students' project in Desmos.  The purpose of the project is to review the seven parent functions we have studied and to give students an opportunity to demonstrate creativity with those functions.  A key skill will be limiting domain and range.

I don't have the rubric yet ... it needs to be simple.
Here are the instructions for the project.  I would love your feedback!

Thinking out loud - in planning mode

So building off yesterday's post about how to frame the work next week ...

I don’t want to start with direct instruction … my students are able and need more time grappling with math.

What if I start with the data collection lab?  Students have enough background knowledge to do it justice without explanation.  And if they get stuck I can give them some help.

After the lab and after working through the attached problems, I’d like students to create the notes they need for analyzing a square root function.  Maybe if I create a list, better yet, a graphic organizer for the information they must know … but leave it to them to fill it out.  Then they can compare information among their classmates.  After they have done that work, then I could fill in gaps if needed or structure a conversation for them to fill in the gaps.

I like this plan better than my typical daily plan of setting up the work for them. 

Now I just need to create that graphic organizer and determine what specific practice students might need.

Where are you in planning for the first days back?  How do you engage students in critical thinking?

How to frame the work?

Second semester is looming.  Fortunately, we get one work day on Monday before students arrive on Tuesday.  I want to plan and I don't want to plan ... it's a strange conundrum!  I am enjoying this time away from the constant thinking/planning/creating!  But second semester is looming.

Our Algebra 2 curriculum is based around functions.  We started with linear functions and systems, next absolute value functions, and then quadratics.  With each function we explore the key characteristics, transformations, how to solve, and applied problems.

In second semester we will start with square root functions.  But before we jump into those completely, we will review the concept of inverse functions.  We discussed inverses in the very first unit in which we explored a variety of parent functions.  At that time we mostly looked at using a table to determine the inverse.  We didn't discuss composition of functions.

So our unit plan looks like this:
Day 1:  Inverse Functions
Day 2:  Data Collection and Key Characteristics of Square Root Functions
Day 3:  Transformations of Square Root Functions
Day 4:  Solving Square Root Equations
Day 5:  Applied Problems

Since we have studied 3 functions already with this same pattern, students should be able to generalize from previous functions to the square root functions the basic concepts - especially key characteristics and transformations.

So ... that brings me to this thought ... how can I frame our work for the coming week to maximize student independence and critical thinking?

Any ideas?

Made4Math - Parent Function Review

Our first week was very satisfying and tiring!  It's Labor Day Weekend ... glad for the respite ... and I don't have much to share.

Last week students and I created a parent function flipbook which I wrote about in a previous post.  To support students absent from class and to provide details that one class might have missed over another class, I created a set of function cards for the seven functions we studied. I'm sharing them here ... maybe they could be helpful to you or your students.  (If you want the editable version in PowerPoint, let me know).

I'm also putting together photos that could be used to represent our functions.  I'm using a website called Morgue File ... it's where photographers dump the pictures they aren't going to use.  The photos are free, completely.  Here is a link to the photos I've collected so far.

Enjoy!
Beth

PS ... Visit my 180 blog!

Families of Functions Day 1

I'm working on Day 1 plans ... they keep evolving as I talk with new team members.  Here is the outline of my Day 1 this morning :)

August 26/27 ... Lesson Plan 

• Enroll:  As students enter, invite them to complete the Fixed vs Growth Mindset survey.  
• As students complete the survey, ask them to put a sticky note on the board (number line) to get an overview of our class.  
• Briefly explain our class emphasis on growth!
• Experience:  In pairs, students will sort a set of cards into two groups – function, not a function – with no teacher direction – only questions.  (I am borrowing from Math Tales from the Spring and adding a few sorting cards from VA DOE.)
• Label:  Use Frayer model to define a function. 
• Ask students to use the definition and discussion to assess their card sorts.    
• Assign 8 Error Analysis problems.  Topic:  is it a function or not.  Answers are provided but some are incorrect.  Which ones are incorrect and why.
• Demonstrate:  Introduce 7 functions to students.  
• Students will take notes on family, equation, graph, domain, range, and characteristics.  
• Students will enter parent functions in calculator to assist in exploration.  
• Use guiding questions.
• Review:  Introduce notebook expectations … use unit overview to review briefly today’s goals.  Assign setting up notebook as homework.
• Celebrate!  (Think about how best to do this on first day )

(By the way, this is my favorite Lesson Plan outline ... for students to experience math before we label it!  The outline is called EELDRC out of Quantum Learning Training).

Here are pictures of our flip chart for families of functions ... it's a quick put-together ... individual cards taped in succession so that they flip up.



If you want the full pdf, click here.

Looking forward to seeing everyone's Day 1 plans!