Fresh Ideas to Help You Teaching Transformations

Fresh Ideas to Help You Teach Transformations

Learning geometry is like making a snowball

You want a firm foundation to build on, so it doesn't crumble later. One of the foundations of geometry is teaching transformations. It’s also a great topic for allowing group interactions. Teaching transformations allows for plenty of opportunities for examples, activities, and discussions.

What are transformations?

Transformation in geometry is when an object is turned, flipped, stretched or otherwise changed from its original form. The most common transformations are translation, rotation, reflection, and dilation.

Once students develop a firm foundation for what these terms mean, it is easier for them to translate it into a mathematical function.

There are many ways to teach transformations

Teachers can explain each of the terms and show examples using graphs and objects around the classroom.

Teaching transformations is a great time to let the students do a group activity and work together to understand the concept. Repetition is key in geometry. If students can break down the lesson in different ways to teach each other accurately, then that proves that they have a firm understanding of transformations.

Let the students practice writing transformations as functions.

Below is a free transformation lesson plan to get you going

It provides a chance for students to see, hear, and get hands-on in the learning process. While working in teams, encourage students to engage in conversations to help each other understand the lesson.

Working with transformations will provide an opportunity for a big group discussion on what worked and what didn’t. It’s also an opportunity for teachers to engage one- on- one with students who may not always feel comfortable asking questions or speaking out in large groups.

How to Have More Engaged Students (Video)

One of the fastest ways to have more engaged students is to get them curious.  Now, if you'd like students that try while we are teaching math, this video has sure-fire tips for doing just that!

So there you have it! This video will help any and every math teacher to have more engaged students.

By the way, we just released FREE live webinar invite on how to have more engaged students! It's called "How to Teach All Your Standards In One Year" We build on these strategies and apply them to algebra and geometry in an actionable way. 

You can register here: https://highschoolmathteachers.com/training-invite/

10 Questions every Math Teachers should ask to build retention

We all need our students to remember what we teach and be able to recall it when necessary. The best way I have found to do this is to help our students connect their learning to previous experience inside and outside of our classrooms.

Here are 10 questions that will help you do just that!

1. Where have you seen something like this before?

2. Can you do this problem another way?

3. How are these problems the same/different?

4. Can you draw a picture or a model to show that is true?

5. Does that always work?

6. Can you find the pattern?

7. How can you check your answer?

8. Have we ever solved a problem like this before?

9. Where else would this strategy be useful?

10. Can you create a similar problem to this one? harder? easier?

Using these questions everyday will not only build retention, but also connections and interest. And we all know engaged and interested students do best. 

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.

Image result for success

 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/ 

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. 

Do you really need to cut sarcasm out of your classroom?

Humor is good, right?

Sarcasm is so easy. It is fun to get a laugh. It certainly had a place in our home growing up and within my extended family too.

I brought it with me as a teacher in my classroom. Humor is good, right?

My embarrassment

What I didn't realize is that I was tearing apart the most important relationships that I had with my students.  I often thought that the better our relationship the more I could use sarcasm as a humor mechanism and it would be okay. But that meant I was hurting the students that were relying on me the most.

What I came to understand is that sarcasm comes at someone's expense. And even more, with the ever-growing emotional needs of our students, many students don't hear or understand sarcasm and are left in the dark. So what I thought of as bringing humor and connection into my classroom was actually doing the opposite.

So, unfortunately, what I learned, is that the better relationship I had in the fall with my students would often deteriorate by the spring. This was a tough lesson and it's hard to share with you. But that's why I must do it.

In no way would I ever want to hurt my students or allow them to feel left out of a common joke. And no way would I want to deteriorate the relationships that I work so hard to build up.

Learning a new way

The first time this came to my attention, was at a conference. and when they said this I realized all the harm I've been doing. And I have to admit the cutting it out of my classroom was one of the hardest things I've ever done. I had grown up with sarcasm it was valued as wit and smarts and if I was being completely honest I respected kids that could hand it right back.

But what I learned and how my classroom changed spoke for itself. My students begin to trust me more, my struggling students started to open up more, my room became a safe place for all students, not just ones with a quick wit.

So I have a challenge for you, do your best this week to cut sarcasm from your classroom and take note of the difference it makes and your students. I think you will be as pleasantly surprised as I was many years ago.

Want to learn more?

If you'd like more ways to connect with your struggling students, right now we are enrolling in our 10-day challenge: how to teach Common Core math to at-risk students. For only $17, you can enroll in our 10-day challenge that will give you actionable steps in only a few minutes a day. click here to learn more

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