How To Teach Trigonometric Ratios for Retention

If you want to teach trigonometric ratios, here are 3 quick methods every geometry teacher needs to know.

 

Method #1: Connect Trig Ratios To What The Students Already Understand

Here's the big thing geometry teachers must understand about this method: as the teacher, we must connect new information to prior learning for every lesson. Research shows that this will help our students retain the new knowledge that they are learning.

Image result for knowledge

 Geometry teachers need to understand this method means that for trig ratios to make sense and be remembered, we need our students not to see only a fraction, but for that fraction to tell them something about the angles. We need to ask questions that get students to connect the size of the angle in a right triangle with the fraction created.

This is important because when you ask questions like
*What happens to the sin ANGLE as that ANGLE gets larger? Smaller?
Helping the students to make the relationships and connections, will place this new information into their long term memory.

You should plan out at least ten questions you will ask your students so that they can connect this new learning with something they already understand and feel confident about from previous learning. Add these to your lesson plans.

Method #2: Show The Problem Done Three Different Ways

The key to this method is when students make connections on their own; they not only own their learning, they can retain it longer and recall it easier.

So, here's what this means: when you put the problems on the board. I like to use a minimum of three. You can, as the teacher and guide, start asking questions to lead them in the right direction of understanding.

For example, I would draw one large right triangle and label all the sides lengths and angle measurements. Next, I would begin writing true statements about the triangle while encouraging the students to find a pattern.

Image result for image of right triangle with measurements

 Geometry teachers need to know this method because as the students find the pattern, they are more engaged than traditional instruction that tells them the definitions of trig functions. And we all understand that engaged students are going to learn more and understand more.

To put this into action, you should find three more examples of right triangles where students can look at patterns and relationships.

Method #3: Start With Success

The bottom line for you with this is that this is the first lesson in a unit of lessons. Give them success today. Help them to feel confident. This is the most important lesson of the whole unit. Make sure every student walks out today feeling confident.

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 The most important thing to get with this is students will be more engaged, more willing to complete work, and are much less likely to feel overwhelmed during the rest of the unit.

This method is important because by planning a lesson and daily work where each student feels successful on the first day, your students will have much more success with the whole unit.

So the thing for you to do here is to take a look at your students and make a realist plan for the first day working with trig functions.

It will amaze you how much faster you can get things done as a geometry teacher just by understanding these three teaching methods and how to use them to your advantage.

Hey, one more thing before I forget, if you're a geometry teacher serious about teaching success, this free lesson plan I just released "the free Introduction to Trigonometric Ratios Lesson Plan and Resources along with nine other lessons" helps you teach trigonometric ratios and more! Check it out: https://highschoolmathteachers.com/optin-geometry-lessons/ 

How to Teach Transformations with These Ready To Use Free Resources

I love teaching transformations. It's so fun to get visual with the students and allow them to see the world around them with new vocabulary and new appreciation.

Take a look around for examples

Transformations are everywhere. I like to ask the students to brainstorm as many reflections and then translation and finally, rotations that they can think of in 5 minutes or less.

Once they do this, we can share on the board all their different answers. As the other students start to answer they can add to their lists. After a bit, as their brains are still processing the new information they just learned from their classmates, I like to add have them add to their list again.

With the challenge of not listing something on somebody else's paper, their answers can get very creative. Usually, too creative, and someone will oversimplify the definition. This is a great time to emphasize common misconceptions and mistakes around transformations.

And if they need more ideas, this video shows so many. While I don't enjoy the music during this video, I really like that it is simply a slideshow of images we can use during class as discussion pieces.

Use technology to encourage curiosity

http://www.shodor.org/interactivate/lessons/TranslationsReflectionsRotations/

Let them play

I like to put a shape on the board that has undergone a translation to see if the students can recreate it within the program. We always start with easy ones, making sure students are understanding the formulas and patterns they are seeing.

If the class is doing well we can then start combining transformations to challenge their understanding.

And don't forget to ask...

"How do you make it look like this?"

"Is there another way to do that?"

Check for understanding

And in all my lessons, I like to have practice pages where the students can show me independent mastery of the skills we've learned in class. This along with exit slips can give me a clear picture who understands the materials.

If you'd like my complete lesson plan for free and transformation,

please enter your name and email below and will be sure you get it right away.

Just for fun!

Common Core Standards:

CCSS.MATH.CONTENT.HSG.CO.A.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

Mathematical Practices

CCSS.MATH.PRACTICE.MP7

Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Algebra Connections:

Translating Graphs Lesson Plan

The Statistics Resources Roundup

So after the last blog post all about functions (if you missed it, you can find it here), I received a few asking about statistics. So I thought I would do another round-up for you. Every resource mentioned is free below. Enjoy!

Before I begin, feel free to email me and let me know what you are teaching and I will do my best to prepare something for you too!

Gapminder

Gapminder is an amazing tool! It worked so well with my students. I just know you will want to use this amazing, free, online tool as well.

https://highschoolmathteachers.com/how-to-use-gapminder-to-teach-statistics-s-id-in-algebra-1/

Causation vs Correlation

The first time I taught this lesson was eight years ago during an election year when political commercials were all over the place. After this lesson, the history teacher (yes, this is also a history standard in most states) pulled up some of those commercials and we had great discussions about the difference between causation and correlation and how advertisers assume we don't know the difference.

https://highschoolmathteachers.com/causation-vs-correlation-activity-free/

Two-Way Tables

 Overall my students enjoy learning about two-way tables, and it makes sense to them. It's something they feel very confident with understanding the way that we have structured this lesson so that it builds makes it very easy for students to get this knowledge down in a relatively quick amount of time.

https://highschoolmathteachers.com/two-way-tables-s-id-5/

Standard Deviation Lesson Plan

The standard deviation lesson plan is based on the understanding of what standard deviation is calculating. This is done before they ever learn how to calculate it using technology. Understanding that standard deviation is measuring the deviation of the change off of the mean is very important in Algebra 1, and this activity is visual and straightforward for students to understand.

https://highschoolmathteachers.com/standard-deviation-lesson-plan/ 

Line of Best Fit Lesson Plans

Teaching the concept of the line of best fit can put together a lot of strategies and skills. Today I would love to share with you a couple of my favorite worksheets and activities that engage students.

https://highschoolmathteachers.com/line-of-best-fit-lesson-plans/

4 resources to help you teach functions

I have been getting a lot of emails regarding functions. How to teach them in a way that helps students to understand and remember what they are and why they are so important in mathematics (and science and computers and...)

So, I thought I would share some previous blog posts to help you feel encouraged and empowered when teaching functions. 

The first resource I would like to pass along will give you ideas for helping students to master all the content in your linear equations/functions in the time you have planned

https://highschoolmathteachers.com/unit2/

Do your students hate radical functions? If they do, follow these three tips to not only make learning them easier for your students but teaching them easier for you. Let’s jump right in! 

https://highschoolmathteachers.com/radicalfunctions/ 

I like teaching inverse functions. This inverse functions lesson plan will help you find connections with your students. With the real world context, students understand this concept well by the end of class. 

https://highschoolmathteachers.com/inverse-functions-worksheet/

If you need a bigger understand of F.IF.1 within Algebra 1, you will want to look at this example. Feel free to add to the discussion while you are there.

https://highschoolmathteachers.com/f-if-1-understanding-functions/ 

Rewards of a Job Well Done

While it may take more time up front to ensure that students understand the concept of functions, in the long run, it will save you time. The ability to see patterns and complete the calculations without help will be priceless. When you give students an in-depth understanding and allow time for processing the concepts, they go into long-term memory and students gain quite an advantage as they continue their math education.