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7th Grade Geometry can be fun for many students, but it is also very scary and often times challenging! Check out the Georgia Frameworks for Geometry to get a basic background of what students in Georgia will be learning about in 7th grade geometry. There are also a TON of resources and activities that are directly aligned to the standards. After looking through the standards, check out the rest of the links on my page. I have even included which standard it correlates to at the end of each description.

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Let's be real, Flocabulary is awesome. They are at it again with another catchy song about angles! Check it out!
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Angle Relationships - Angle Relationships Video - Complementary Angles - Flocabulary

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Learn about angle relationships with Flocabulary's educational hip-hop song and lesson resources.

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This activity is PERFECT for engagement and introducing students to the four types of angle relationships they will be learning in 7th grade: Supplementary, complementary, vertical, and adjacent angles.
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Give your students an opportunity to check what they know, digitally! Too often we leave assessments to be done with pencil and paper, even thought the standardized tests are done completely on a chrome book! Utilize this AWESOME online quiz!

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Free gamified quizzes on every subject that students play in class and at home. Pick an existing quiz or create your own for review, formative assessment, and more.

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This is always a concept my students STRUGGLE with. I really enjoyed this quick break down of what to look for when determining the unique solution, if there was no solution, and if there were many solutions to a triangle.
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Triangles and Constraints

Standard 7.G.2 reads:

Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

What does this mean? If you had just taught a traditional high-school geometry course, you'd recognize immediately that this leads to understanding triangle congruence and similarity; it's the foundation of a number of bread-and-butter theorems such as SAS, ASA, SSS, and hypotenuse-leg, as well as the "gotcha," SSA, which does not work in general.

At grade 7, then, we want to prepare students so that by the time they study these theorems, they will have had relevant experiences, and will have developed some intuition about how the sides and angles of triangles interact.

If you have not recently taught high-school geometry, or feel a little shaky about why SSA doesn't work, we'll cover all that here as well.

What does it mean to determine a "unique" triangle?

Standard 7.G.2 (above) includes a tricky phrase: "noticing when the conditions determine a unique triangle." Let's build up an example that will illuminate much of what follows.

Suppose Penelope is trying to get us to draw a particular triangle, and has to talk to us on the phone. No drawing, no pictures.

"It's triangle ABC," she says.

But this is of little help; we could label any triangle ABC.

"AB is 5 centimeters long."

Now we're getting somewhere. We draw AB as a segment 5 cm long. Now part of the triangle is all set. But we know nothing about where point C is. It could be anywhere!

Penelope continues: "The angle at point A-let's call it angle A, or ∠A-is 45°."

Now we can construct a 45° angle at point A. We build it so it extends up and to the right. Now we know that point C is on that "ray," but we still don't know where. We have countless possible triangles.

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We tell Penelope we still need more information. She says, "Angle B is also 45°."

We draw the ray from B, and it intersects the "A-ray" in just one point. It must be point C.

We've been given three conditions:

And with those, we can draw Penelope's triangle reliably. The conditions specify a unique triangle.

Wait-Three numbers?

It's interesting that we completely specify the triangle with three numbers. We might think that it would take six numbers to specify the triangle:

the three side lengths and the three angles; or

the x and y coordinates of the three vertices.

And it might-depending on what you mean by unique. For example, here's a different triangle ABC. It also has a side length of 5 cm and two 45° angles. If Penelope saw it, she would say, yeah, that's my triangle.

The triangle is not completely the same-the coordinates of all the points are different, it's lower on the page, and it looks rotated and reflected-but it has all the same side lengths and angles. And that tells us what we mean by unique: that if we follow the instructions, all of the triangles we get will have the same 3 side lengths and 3 angles. When we only had one or two conditions, we could make lots of triangles, but they would be fundamentally different.

The official word for this is that all the triangles we get will be congruent to one another. We often describe congruence as, "they have the same size and shape," or "if you cut one out, it will exactly cover the other."

In this case, the three numbers determined the triangle. Oddly enough, this means Penelope can now give bad information. For example, suppose she told us that angle C was also 45°. That's impossible! We know it's 90°! Correct. If you get too much information, it could create a contradiction. We will try hard to avoid letting that happen to our seventh-graders-but stay alert.

Do three numbers always determine a triangle?

No. And that's the more advanced part of the lesson.

Let's back up a bit: there are six possible numbers we're interested in: the three side lengths and the three angles. Imagine a board with six slots (shown). We put numbers in the slots one at a time.

With one number-side or angle-we can make lots of different triangles.

With two numbers, in any combination, we can usually make lots of triangles.

With three numbers-well, it depends.

Our example was a situation with one side and two angles. Importantly, the two angles we knew were on either end of the side we knew. Angle A and angle B are adjacent to side AB. This is the ASA (angle-side-angle) situation in high-school geometry, though we want students to come to their own understanding without relying on somebody else's labels for now.

We might also have had one adjacent and one opposite angle. Suppose we knew AB was 5 cm, and ∠A and ∠C were both 45°. Angle C is across from AB, so it's the opposite angle. And that fundamentally changes the triangle.

This triangle is the same shape as the former ABC, but it's bigger. If we fill in the numbers, we see that this triangle can't have the same side lengths: AC is more than 5 cm here, but it was clearly less than 5 cm in the original triangle ABC.

Still, the three numbers (two angles and one side) again determined the triangle. And there are no other ways to arrange two angles and one side.

Does that mean that you can always determine a triangle if you pick two angles and one side? No! Suppose the two angles were 90°. You can't make such a triangle.

Four Situations

When you think about it, there are really four types of situations for three numbers:

Three sides.

Two sides and one angle.

Two angles and one side (that's what we just did).

Three angles.

And all of them have special conditions to be able to make triangles at all, or to determine a triangle uniquely. At this point, I'm going to tell you the "answers," but if they're not familiar, you should play with the materials in the poster problem Triangles to Order , and make triangles until it's obvious why the following is true.

Three sides. These determine a triangle, provided they satisfy the triangle inequality. Having said that, it's not easy to construct the triangle without using a compass (and that would be asking too much in Grade 7). Kids should guess and check and just do their best.

The triangle inequality says that, to have a triangle, the longest side must be shorter than the sum of the other two sides. So, for example, you cannot make a triangle with side lengths 1-3-5.

Two sides and one angle. If the angle is between the two sides (SAS) you definitely get a triangle every time. This is the easiest way for confused students to see how a whole triangle is determined by three numbers.

If the side is not between the two angles (SSA; avoid calling it ASS for obvious reasons) you get zero, one, or two triangles. In the "one" condition-a unique triangle-the "other" angle is 90° and the two sides are the hypotenuse and a leg. This is the subtlest of all the possibilities; do not expect all students to get this!

Two angles and one side. This is what we did with Penelope, above. As long as the angles add up to less than 180°, you get a unique triangle. Having said that, the ASA situation is easier to construct than SAA. (If you know that the sum of the angles is 180°, though, you can compute the other angle in the SAA situation and get the easy ASA again.)

Three angles. First, the sum has to be 180°. And in that case, you get similar triangles, not congruent ones. That is, you can have an infinite number of triangles, all the same shape, with the same set of 3 angles. But they can all be different sizes. No unique, same-shape-same-size triangles.

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Triangles and Constraints Standard 7.G.2 reads: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. What does this mean?

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Okay, almost all students assume any three side lengths can form a triangle... WRONG! Check out this link for a detailed breakdown, and proof of this concept, the triangle inequality theorem. (There is also a quiz)
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About This Quiz & Worksheet

This quiz and worksheet will help you judge how much you know about the triangle inequality theorem. Get ready to apply your knowledge to find the solutions to the problems within this quiz.

Quiz & Worksheet Goals

Use your knowledge of the triangle inequality theorem to answer questions about:

Possible lengths for the line-segments of triangles

Whether it is possible to make a triangle from certain lines

Statements about triangles

Skills Practiced

This quiz is an excellent opportunity for you to practice the following abilities:

Reading comprehension - ensure that you draw the most important information from the related lesson on triangle inequality

Interpreting information - verify that you can read statements regarding triangles and interpret them correctly

Information recall - access the knowledge you've gained regarding what the triangle inequality theorem tells us about the sides of a triangle

Additional Learning

Keep building on what you know about this subject with the help of the lesson entitled Triangle Inequality: Theorem & Proofs. Complete this lesson to learn more about:

Limits on the creation of triangles

How the triangle inequality theorem can be satisfied

The method for proving this theorem is true

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quiz & worksheet - triangle inequality theorem | study.com

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Quiz & Worksheet - Triangle Inequality Theorem | Study.com

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This quiz and worksheet will help you judge how much you know about the triangle inequality theorem. Get ready to apply your knowledge to find the solutions to the problems within this quiz.

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I love math antics! The video really breaks things down, and students enjoy watching a video to explain what something is!
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Pi and circles are actually very confusing for many students. Check out this link for a break down of pi and its relation to circles!
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The circle. The definition of pi. Topics in trigonometry

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The definition of a circle, the diameter, the radius, and the circumference. The definition of pi.

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Because who doesn't love a good rap song to get your students engaged?! Check out this flocabulary!
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Circles: Circumference & Area - Find Area of Circle - Online Math Curriculum - Flocabulary

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Teach or review how to calculate the circumference and area of a circle with Flocabulary's educational rap song and lesson plan.

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Check out this blog for teaching area and circumference in your classroom! There are a ton of great resources and activities that are FREE to print, fun, and engaging! Great for differentiation
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Area and circumference of a circle often gives our students their first taste of geometry during the year. Also, it seems like students see formulas for the first time when learning this topic. Usually, they don't come to us understanding how to plug values into formulas. That means that we have to teach the idea of using formulas to them as well as how to find the area and circumference of a circle. Even though that can feel daunting, though, the great thing about circles and geometry is that they lend themselves to application pretty easily. We definitely have the opportunity to let students see area and circumference in a hands-on way. This post is full of engaging, fun area and circumference activities for secondary math students.

Sometimes I hear teachers talk about whether they should teach area first or circumference first. Personally, I believe you should teach them together and that student really need to understand the differences. Too often we have our students do things in isolation and later on they don't know what to do because we go in a different order, or they have to apply their knowledge without knowing that a problem is an "area problem" or a "circumference problem". The following list of activities will give your students lots of opportunities to practice working with and solving problems related to finding the area and circumference of circles.

The list of area and circumference activities:
Area and Circumference Bingo Hands-on Circle Cut-out Activity Mnemonic Lesson and Activity Online Circumference Memory Game
Let's dive in

As you read through this list you'll notice that some activities work for bell ringers while other activities are whole class review games. You'll find a wide range of activity types and possible uses for your classroom. Have fun exploring these engaging activities.

Students love mazes because they don't have high stakes attached to them. It gives them a chance to practice in a relaxed way. We use mazes in my room every day as a bell ringer and I love the tone that it sets for the class.

This particular set of 3 mazes is one of my favorite. I love the fact that circles have pi in their formula and that pies are circles. That gives me a chance to use pies in my activities and kids love talking about pie. So, I get to use my pie clipart in these mazes. In one of the mazes students find the area area, in the next they find circumference, and the last one they find both area and circumference. Some of the answers are in terms of pi and other answers are using 3.14 as an approximation for pi.

Want even more FREE mazes delivered right to your inbox each month? Join the Math Idea Galaxy Maze of the Month Club and you'll get exclusive math mazes like the one above in your email each month.

Yes! Sign me up for the Maze of the Month club.

If you're not already in the club, hope to see you there!

One of my favorite things to do is to inspire my colleagues to try new things. I work at a school where my 12 years of teaching is less than all of the other teachers in the math department. We are a veteran core. We all have a traditional streak in us and we have all tried to break out of that streak to get our students more engaged. One of my colleagues in particular used to tell me that she hated bingo. Then, just the other day when I went into her classroom she was playing bingo with her class. She even gave out some little prizes. It was amazing to see how even reluctant 8th graders worked hard for the prizes.

This area and circumference of circles bingo game is full of word problems. Students have to find area and circumference with different measurements and sometimes in terms of pi. Some of the questions are a little bit easier where they just have to find the diameter or radius. Each question is based off of a picture, like a guy holding 10 boxes of pizza, a dog catching a Frisbee, or a girl counting coins. I like to use this game for whole class review at the end of the unit. Try this game you'll have your students practicing in a fun and engaging way.

This Area and Circumference Discovery Lab is one of my favorite. Discovery labs are a great way to introduce students to a topic and let them find patterns and draw conclusions. This helps them do the learning and have it more strongly anchored in their mind. What I've realized with discovery labs is that they have to be very focused and the students should not be trying to learn too many things at once. This lab focuses on identifying what the differences between area and circumference. Students will work to build their conceptual background of how circumference is one-dimensional and area is two-dimensional.

For this activity students color in the area and then use wikisticks or yarn to measure the circumference. They approximate the area using squares that are on the paper. We don't use the formulas, yet. By counting the inch squares, students actually see why area is measured in square inches. This gives them a chance to really see what is happening when we talk about area and circumference. Then you always have an experience to lead them back to when they get that look on their face like, "Which one is area and which one is circumference, again?" You can read more in this step by step guide of how this activity walks students through this discovery process in this post.

I found this circle cut-out activity over on Middle School Math Rules, but it didn't have any circles to use. So, I created my own set of circles that you can. Students get to measure the circles with a ruler and calculate different parts of the circle. It's great for a math station or for partner practice.

You can either have the students cut the circles out, which takes them longer than it should, or they can just measure them on the paper. Also, you can have them label the circles with the different measurements or they can use a graphic organizer (included in the circles download) to analyze the various shapes.

Mnemonics work because our brains like structure. I don't use a lot of them, but when I find one that helps kids remember something like the formulas for area and circumference of a circle, I'll use that. Even though I've been finding area and circumference of a circle for a very long time, I still get the two formulas mixed up and have to stop and think about them.

Many students are in the same boat. Not to mention how important things like mnemonic devices are for students who need extra support. The students who struggle with executive function and organizing information in their brain really thrive when they have a way to remember. That's where this great mnemonic strategy from Janine Huldie over on Owlcation comes in. I took that idea and created an insert for my students' interactive notebooks.

The saying that students remember is:

Cherry pie is delicious!

Apple pies are too!

If they can remember that, then they can keep the two formulas straight. We use a graphic organizer (dowload FREE here) in our interactive notebook for this. Everyday, for a while, we practice writing the formulas on our whiteboard while saying this statement until they all have it. Sometimes it's the little things that make a big difference.

This paper plate activity from The Reading Buddies brings in a little bit of art and a visual activity to your classroom. Students struggle sometimes to remember the parts of the circle. Creating their own colorful circle can help them remember. This activity walks through how to use paper plates to review the vocabulary and formulas we use when talking about area and circumference of a circle.

Also, you can have students share their plates with other people and get some math talk going. At the end of the activity they can hang their creations on the wall and do a gallery walk to look at other people's plates. The blog post where I got this idea used this activity for Pi Day and has them decorate the plates like a pie. I think it can be used during Pi Day or any time of year when you have your unit on area and circumference of circles.

If you need an anticipatory set you might want to use this online circumference memory game. Students can play by themselves or with a partner. They have to find the circumference of 6 different circles and then play a memory matching game. It's cute and it adds a little fun to their practice.

I love this online circle tool from Illuminations. It has three functions and you don't have prep anything. It has an introduction screen, an investigation screen, and finally it has some practice problems. You can have it open on your computer and show the students what you want them to do on the screen in the front of the room. Then, students can work independently or in partners to to do the investigation and some practice problems.

When they finish the activity I would have them write a reflection of their experience using this tool. This is a great opportunity to find out what students understand about finding the area and circumference of circles. In addition, you can see some misconceptions, as well.

My kids love to review using whole class games. Jeopardy is one of the games we play periodically. This game of Jeopardy gives students practice in finding the radius, finding the diameter, and finding area and circumference. I don't play Jeopardy in teams. When I play all students write their answers on a whiteboard or SmartPal. I find that if everyone has to write down the answers then they are more accountable. This activity is great for the day you introduce the topic or the day before the test.

Try one thing

We've presented a lot of ideas in this post. These activities can be used practice or review and will get your students engaged in practicing finding the area and circumference of a circle. My challenge to you is to just try one thing. Look through the list and try something new. I find that when I try something new it gets me more involved in the teaching. The students will appreciate it because they get tired of doing the same things over and over. So, good luck in your teaching or reviewing of this topic. Just remember, great teachers are always refining their craft. I hope you've found some activities or tools here that will help you take your area and circumference unit to the next level. Thanks for reading! Until next time.

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10 Activities for Finding Area and Circumference of a Circle

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Area and circumference of a circle often gives our students their first taste of geometry during the year. Also, it seems like students see formulas for the first time when learning this topic. Usually, they don't come to us understanding how to plug values into formulas.