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.

3 Quick And Easy Tips To Teach Quadratic Functions

If you are an algebra teacher who wants to teach quadratic functions, here are 3 quick tips you need to know.

Tip #1: To Connect The Math Vocabulary To Prior Learning

Okay, so you've probably heard this before, but as the teacher, we must connect new information to prior learning for every lesson. During the connecting activity, I find it useful to ask the students what vocabulary we can find in this example. I like to start a list: function, function notation, domain, range, evaluate, maximum, minimum, etc.

As an algebra teacher, here's what I mean:  as you help them recall this information, students will begin to see how all the mathematics is related and works together.

This tip will help algebra teachers because students often feel like they are learning something new every hour of every day. This strategy will allow them the time to understand that this is only building on something they already understand. This will greatly reduce the overwhelm and shut down in your classroom.

To put this into action you should Download the free lesson plan and print or post the quick 10-minute activity and allow the students time to fill in the table and answer the questions. Then brainstorm the vocabulary needed for the lesson with your students.

Tip #2: Show The Problem Done Three Different Ways

This is all about the fact that when students make connections on their own, they not only own their learning, they are able to retain it longer and recall it easier. I am a huge believer in this method and I have personally seen the effects it has on my classroom. For quadratics, I find it helpful to have them find the vertex with a formula and graphing and then I have my students tell me which is the better method. And when is it the better method?

The most important thing to get understand this tip is 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.

This is critical to your success because as the students realize the similarities they are gaining a concrete understanding of what the numbers mean in the real context, not just in an algorithm.

Now the thing for you to do is to create a few problems where students can complete them in different ways and put them on the board. Create questions ahead of time to lead them along.

Tip #3: Use Real Examples

The key idea with this tip is quadratics are everywhere. Pull out as many real-world examples as you can and help students identify which arcs are really quadratic and those that are not. If you would like a list of 101 uses of quadratics this site will help you out:

You need to understand this means students will begin connecting what they are learning to real-world solutions.

This will help anyone because as students feel more connected to their learning they will take more ownership of their learning.

My advice at this point is to find some examples near your school or town that students are familiar with and integrate them into your lessons.

Once you understand the facts about teaching you can move forward with confidence - and going through these 3 tips is a great start for any algebra teacher! But as you can see, this really is just the tip of the iceberg.

One more thing before I forget. Did you know, if you really want to teach quadratic functions, this amazing new free lesson plan "the free download Graphing Quadratics Lesson Plans and 9 others" makes it super easy for you! Check it out here

3 Teaching Methods That Teach Properties Of Bisected Line Segments

Want to teach properties of bisected line Segments? Here are three quick methods every geometry teacher needs to know.

Method #1: Allow Students To Make Conclusions And Connections

Here's a simple method that so many geometry teachers miss out on when teaching midpoint and bisectors.

Here's what I mean: 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.

The connection is important to you because it means by allowing our students to do the constructions themselves and see the bisection and make the measurements, we can get the most reluctant learners engaged.

This method is important because  when you ask questions like

Will this always be true?
Can we do this will a different line?
Are the steps always the same?
Is there another way to answer this question?

Helping the students to make the relationships and connections, will place this new information into their long term memory.

So the thing for you to do here is to plan time into your schedule where students can do the constructions. Prepare with compasses and sharpened pencils (to save precious time) and cardboard or thick paper to protect your desks.

Method #2: Creating A Proof

Here's the crucial thing you need to understand with this method: when students conclude that a bisector is a midpoint, we need to progress to the next level of ensuring that the students can prove that conclusion.

The most important thing to understand with this is that if students can successfully prove geometric conclusions, they have a deep understanding of the methods of geometry.

This method is important because as the students find the pattern, they are more engaged than traditional instruction that tells them the definition of bisector or midpoint. We need students that will own their learning and when they find patterns and make conclusions that is precisely what they are doing.

My advice at this point is to find at least three questions that will help your students find the patterns if they are unable to do it on their own. Examples include:

What do you notice about the measurements?
How are these two examples the same?
What do you notice?.

Method #3: Use An Exit Slip To Ensure Understanding

The main idea for every geometry teacher with this method is that ensure understanding by all students. While to us math teachers, this can seem like a more straightforward concept, this is where students can fly under the radar.

The most important thing with this method is that you can quickly identify the students that did not understand or for some other reason did not master the content.

This method will help geometry teachers 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.

To put this into action, you should create a simple exit slip (or download mine) and use them to browse for misunderstandings quickly.

So there you have it! The 3 methods just waiting to let you wave bye-bye to all the traditional publishers and attain the dream for every geometry teacher to teach properties of bisected line segments!

Still not convinced? Well, if you want to teach properties of bisected line segments, this fantastic free lesson plan spells it all out for you! Check it out here 

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:

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.