Trig Ratios – #made4math

Through the years, I’ve seen students struggling trying to remember which Trig Ratio is which.  I have a colleague who draws a big bucket with a toe dipped into the water.  She says she tells the students “Soak-a-Toe” to help them recall SOH-CAH-TOA.  Another has described the “Native American”  SOH-CAH-TOA tribe as the one who constructs their teepees using Right Triangles.  The most entertaining though is the rap from WCHS Math Department “Gettin’ Triggy Wit It” on youtube.

I wanted to use an inquiry activity to help them develop the definitions of the Trig Ratios.  Basically, they constructed 4 similar triangles, found the side measures, then recorded ratios of specific side lengths.  Next, I had them measure the acute angles, then we used the calculator to evaluate the sin, cos and tan for each angle measure.  Students were asked to compare each value to the ratios they had recorded in the table and determine which ratio was closest to their value.  Here’s the file https://www.dropbox.com/s/gfvhnictujfj2ik/similar%20triangles%20intro%20trig.docx?dl=0 Similar Triangles Trig Ratios.  Anyway, its not a perfect lesson, but a starting point.  If you use it, please comment to let me know how you modified it to make it a better learning experience for students.

In the past, students sometimes struggle trying to decide which ratio they need to use when solving a problem. I put together an activity adapted from a strategy called  Mix-Pair-Freeze I’ve used from my Kagan – Cooperative Learning and Geometry book.  This book offers numerous, quality activities for engaging your students.

You can make copies of this file, Trig Ratio Cards File, then cut cards apart to use.

Each student gets a card.  They figure out which Trig Ratio is illustrated on their card (& why).  They mix around the room (with some fun music would make it better), then pair up with someone.  Each person tells which Trig Ratio and why (can be peer assessment, if one is mistaken).  They swap cards, mix and pair with another classmate.  This continues for several minutes, allowing students to pair with several different people.

When I call “Freeze!” Students are to go to a corner of the room which is designated Sin, Cos or Tan.  Within the group in each corner, students double check one-another’s card to determine if they are at the right location.  Again, peer assessment, if someone is wrong, they coach to explain why, then help them determine where they belong.

Students swap cards, mix-pair-freeze again.

I like this activity for several reasons:

• 1. Students are out of their seats and active.
• 2.  Students are talking about math.
• 3.  It allows them to both self-peer assess in a low-stress situation.
• 4.  I can listen to their descriptions and address any misconceptions as a whole-class as a follow-up.

 

To clarify, the intent of this activity is for students to determine what information they are given in relation to a given angle, then decide which ratio it illustrates. It is meant to help students who struggle deciphering what information is given.

Developing Definitions

I’m back!  Nearly 2 months? Yikes. Some fellow teachers on Twitter were committing to blogging once each week.  I think  that’s reasonable – besides, usually my best reflection comes during the moments I blog.  Reflection – seems to be the first thing I push aside when I just don’t have the time.  Yet, its the most valuable use of my time.

I’m sharing some successes from Kagan Geometry (one of my favorites by the way).

I was going to be out for a number of days due to being seated on the jury for a trial (give me 100+ teenagers over the courtroom anyday!).  I wanted to leave something productive.  I did short videos (<10 minutes) filling out certain pages in the INBs in addition to other activities.

The first Kagan activity was for vocabulary.  Each strip of paper included examples and counter-examples for each term.  I modified from the round-table recording it suggested.  Students were asked to pair up (a new partner for each new term) and develop their own definitions.  I loved it simply because most were terms students had previously been exposed to in middle school.

When I returned to the classroom, I ran through all I had left during my absences to address any concerns/questions.  Several students commneted how they liked (appreciated) doing the definitions this way.  Their comments ranged from – ‘You actually had to think about the terms; Talking with someone about it really helped you process what it was before writing it down;  The pictures of examples / nonexamples really helped understand the word better.’

Yesterday, we developed more definitions about angles.  When I told them what we were doing – they were excited about the activity.  Listening to the conversations – I was very happy with their discussion / questions / specifics they included in their definitions.

I remember several times in the past doing examples / non-examples, especially when using Frayer Models.  I believe taking it out of my hands/mouth and giving them the opportunity to work in pairs really enhanced their understanding of the terms.  Even when discussing HW  today – they used appropriately terminology.  Yeah!

Another Kagan activity I used as a LHP activity

from Kagan Geometry

– very similar to Everybody Is a Genius’  Blind Draw.  Students were placed into small groups and given 12 cards with written directions.  Person 1 chose a card, read the directions, gave others time to think and draw a diagram with labels.  The reader confirms/coaches/praises others’ work.  A new person chose a new card and the rounds continued until all cards had been used.  One thing I appreciated about this – another card asked students to draw a ray from E through M.  This allowed students to realize differences in very similar diagrams.

Again, when I returned to the classroom, students shared how this activity was different from anything they’d done before, saying it was both challenging but helpful in that it helped to clarify certain misconceptions they had; especially with labeling the diagrams.

I have learned the Kagan strategies help students develop and process concepts.  There are “game like” activities where students must find their match and discuss.  Visual, Auditory, Kinesthetic – something for everyone.  Its not an end all – be all resource.  But the amount of HW / practice is minimal when I’ve used these strategies correctly.  I am a firm believer that they help start a strong foundation to build upon.  Hey – if students are smiling and laughing while “doing definitions” – its gotta be good.

#MyFavFriday – Kagan Geometry

Last week I stood glancing at a shelf of books left behind by my colleague.  I’m not sure why I didn’t notice it before – but there on the middle shelf was a Kagan Geometry book.

Two days this week I’ve smiled at the end of the day and it felt great.  Becky Bride has compiled simple to implement, engaging activities.  I’ve read snippets about the Kagan books – but never really sat down to read/do any of the activities.

Boss-Secretary

One of the activities this week was using a strategy called Boss – Secretary.  Students work in pairs.  The boss tells the secretary what to write, explaining their reasoning for the steps/work.  IF the secretary sees the a mistake, he/she respectfully points out the mistake to the boss and praises her/him when they corrects their work.  If they work through it correctly, the secretary is asked to praise the boss, vice-versa.  After completing a problem, they switch roles.

The students have been funny with this simple, yet VERY effective activity.  Speaking of resumes, tough bosses, etc.  One asked today – do I really have to praise them when they do it correctly?  I’m really not a praise-y kind of person…  I said a high 5 would suffice.

Here is what I love about this – Students are talking/explaining their work so the secretary can do it.  Secretaries are listening, following directions, hopefully picking up on any mistakes.  I’ve heard multiple times – student exclaim – oh, now I get it.  They’ve all said they like this activity – its helped them really figure out “their thinking” – having to say what they’re doing – is difficult, and sometimes what they say/tell the secretary to write it not exactly what they meant.

This is a great formative assessment activity to observe / listen to students.  I’ve learned a lot about their thinking this week and I believe they have as well.  When students, notice plural, ask to do an activity again because it really helped them, well – isn’t that what we’re here to do?

INB LHP assignment

As a left-hand page assignment in the INBs, I asked them to pick one problem they completed as a secretary – and they had to write out the boss’s diaglogue to solve the problem.  (midsegments or isosceles triangles this week).

Another activity in the Kagan book was something I have completely taken for granted… Processing altitudes.  Students draw one of each type triangle, and are asked to draw an altitude. Pass their paper to the next person, who then draws another altitude, etc.   Even after a couple of examples / illustrated definition for reference…they still struggled with “drawing” it.  What?  If they cannot draw an altitude, how can they actually know what one is in order to use it to solve problems?

Applying Some Brain Research

Its been many, many years since I taught geometry – but I always remember students confusing medians, altitudes, perpendiuclar bisectors and angle bisectors of triangles.  I remember attending a David Sousa How the Brain Learns training several years back.  An example was shared how students often confuse concepts that are closely related because they are often times taught on the same day.  Concepts are stored by similarities, but are retreived by differences.  When we teach similar things on the same day, they are stored together, at the same time – when students are asked to retrieve that information, there’s not enough distinction between the two – therefore, they are often mixed-up, confused.  Hmmm.

So do I choose to teach each of these similar concepts (special lines/segments in triangles) on separate days – but is that even enough space between?  Should I skip a day between them?  Anyone with experience pacing it out this way – please share successes / need to make adjustments!  I really think this is an opportunity, by using Bride’s processing lessons – to make a difference, giving students the chance to build concrete understanding of these other-wise intertwined concepts.

If you’re not familar with the Kagan series – I think its definitely worth checking out.  There is very little prep time – other than working through the lessons yourself.  All blackline masters needed are included in the book!

I am soooooo excited about using more of these strategies in the weeks to come!  🙂