Definition of Angles

Defining Angles in the Real-World

Math Vocabulary

Vocabulary building has always been essential to success in math, and teaching angles is no exception. Lessons plans should include learning vocabulary and how the terms and concepts relate to each other.

Angles are the measurement of space between two rays that diverge from a common point or cross a common endpoint.

Teaching angles is a great opportunity for vocabulary building. Students must first understand the concepts of points, rays, lines, vertices, and how they relate to each other. Once they comprehend these concepts, it makes for an easier transition into angles.

Real-World Applications

Teaching angles also allows for an opportunity to learn about real-world applications.

One of the cool things about geometry is that students can physically see what is going on. You can begin your lesson by introducing the concept in a presentation.

For practice, students can work on example problems and vocabulary activities. It also helps to point out real-world examples in your classroom.

Real-world examples can lead to discussion on where they can find examples of points, rays, lines and angles or a quick assessment of do they understand this skill by asking is A is an example of a Term B or Term C. When there is a split decision, let them discuss why they believe in there answer.

Definition of Angles Lesson Plan

Here you can find a Free “Definition of Angles” lesson plan that follows this progression. It teaches the basics of points, rays, and lines to transition students into understanding angles, how they occur, and how to name them.

This geometry lesson plan includes clear instructions, practice sheets, a bell ringer and more that align with the common core standards. It breaks down the vocabulary with definitions and examples, while also teaching real-world application.

Click to get your free copy today. The angles lesson plan is easy to understand and implement. It’s relatable and a great resource to add to your classroom.


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Inscribed Triangles

Equilateral Triangle Inscribed in a Circle

Integrating Compasses

Compasses remain reliable and helpful tools to work with when teaching lessons that revolve around circles. Many figures can be drawn inside a circle with all their vertices touching the circle’s edge. Today, we are going to focus on inscribing the equilateral triangle.

An inscribed triangle is one that is drawn inside a circle. Some of the geometry terms that students will review in this lesson include circle, radius, arcs, and equilateral triangles.

This lesson is a chance to teach and reinforce the skill of using a compass. You can demonstrate for students how to measure the radius of a circle and draw arcs based on that measurement.

Connecting Activity

During this connecting activity you will find another good opportunity to let students interact in groups. It allows them to reinforce the lesson when they recall their thought process to get to the answer.

As they work through their practice problems, monitor and check on the different groups to see which students may need more guidance, maybe heading in the wrong direction, or are completely off topic as our student occasionally like to be.

Group Disussions

This activity allows for great discussions, especially if some groups show that they have a firmer grasp on the concept. As those groups wrap up, they can help another group who is struggling so that everyone remains engaged in the lesson.

After everyone is wrapping up their work,  review the main points of the lesson to clear up any misconceptions, and assess how well the students did.

Inscribing Equilateral Triangles within a Circle Lesson Plan

There is a free lesson plan for inscribing equilateral triangles into circles here. The activity for this lesson plan includes step by step instructions for leading students through a group activity with compasses.

Pick up this great resource which includes a lesson presentation, bellringer, activity with a worksheet, exit slip and more all aligned to the common core standards.

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Circle Similarity

Circle Similarity Made Easy

Ways to Prepare to Teach Similarity in Circles

When teaching transformations, most teachers don’t begin with circles because students find it easier with shapes like triangles, quadrilaterals, and pentagons. However, using circles to show similarity may be easier than you think.

Prerequisites for Working with Circles

Before beginning, it's a good idea to do a quick review of the terms circle, radius, circumference, and scale factor.

A lessons’ opening is not busywork. It should always incorporate a review of previously taught skills or an introduction to the current lesson. The bellringer mentally prepares students for the lesson.

Making Connections

Circles are figures on a plane where all points are equal distance from a center point — proving that two circles are similar mean understanding the type of transformation used on the original or primary circle. In teaching this, you can use drawings, discuss verbal examples, or compare objects found around the room.

Usually, to find out the transformation of the original circle, students need to search for the scale factor due to the difference in size between two circles. Be sure to connect the visual of different sized circles with the math involved in finding the scale factor.

Similarity in Circles Lesson Plan

In the “Similarity in Circles” lesson plan, you will find an activity that utilizes balloons and wires to demonstrate how two same shaped objects can similar by blowing the balloons up different sizes. It is also a visual example of how to measure the scale factor between objects.

Included in this free lesson plan are activity instructions, a bellringer, an exit pass assessment, and a presentation to go over with your students to make sure they understand the vocabulary and concepts.

Take advantage of using exit passes as a quick assessment of how effective the lesson was.

Click now for your chance to download this free “Similarity in Circle” lesson plan. It already has the common core standards marked is waiting for you to try it out.

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Complementary and Supplementary Angles

Ways to use Complementary and Supplementary Angles to Develop Independent Learners.

It’s always a challenge to motivate students to use their problem solving skills to and not wait for the teacher to explain the problem and give the answer.

This lesson plan on Complementary and Supplementary Angles allows you to encourage them to be independent learners.

Complementary angles occur when the sum of two angles add up to 90 degrees whereas Supplementary angles are when the sum of two angles add up to 180 degrees.

Building Connections

Knowing this information allows students to solve for unknowns when working with right angles and straight lines. It also helps make connections with lessons students learn about algebraic equations within the geometry they are studying.

When starting your lessons, it’s always helpful to review first.

A few concepts to review are what are angles, how to name them, and practicing examples that solving for 90 and 180 angles. Most mistakes in math are made from students rushing and not taking their time to double-check their work.

Tips to Develop Independent Learners

Enforce students writing down every step so that you can help them to help themselves. This way we can analyze where the disconnect is in learning. We want to develop independent learners.

This “Complementary and Supplementary Angles” lesson plan encourages students to work through the process themselves to understand the concept before introducing the terms.

Students work in groups to work through the activity and review their answers. Allow them to struggle and work it out together for a few minutes before leading them to a discussion about the patterns they are seeing.

When you finally reveal the definitions of complementary and supplementary angles and how to use it as a short-cut or clue to how to solve these types of problems, the light bulbs should start going off for students.

This geometry lesson plan on “Complementary and Supplementary Angles” encourages students to become independent learners. It’s complete with applicable standards, openings, practice problems, lesson presentation, and more. Get yours today.

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Trig Ratios

Tips for Introducing Trig Ratios

Introduction to Trigonometric Ratios

Today we are focusing on setting the tone and building a foundation for trigonometry. Once students master the basic terms and formulas, then it’s easier for them to understand how to apply them.

Trigonometry is everywhere: engineering, architecture, and navigation. All complex ideas are based on simple, strong foundations.

Trigonometry is the study of triangles and all their measurements. When introducing the right angles, trigonometry focuses on learning how to label the triangle.

Focus on Vocabulary

Then, students can understand how to find the correct ratios that the acute angles create. Students must have a firm handle on how to label the triangle. If they don’t, they will struggle with rations.

The lesson plan for this topic should focus on learning and understanding the new vocabulary and ratios. I know the saying is “practice makes perfect,” but wrong practice confuses.

Students will be introduced to the terms opposite, hypotenuse and adjacent as it relates to triangles. Remind them that the hypotenuse is always on the opposite of the right angle. After working through a few examples together, allow students to work in groups or spend some time on independent practice.

The Ratios

When they are ready, introduce sine (sin), cosine (cos), and tangent (tan) ratios. When you see that they understand those three ratios, dive into their respective reciprocals of cosecant (csc), secant (sec) and cotangent (cot).

Every class is different, so it is important to move at their pace. This introduction to trigonometric ratios is part of the foundation of trigonometry.

Lesson Plan

Here is an “Introduction to Trigonometric Ratios” lesson plan that helps break down the key concepts and vocabulary.

It includes a presentation that defines all the key terms, formulas and visual examples of different ratios. Download this free lesson plan that includes a bellringer, activity, practice worksheet, exit slip for assessment and more.

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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.