Classifying 2D Figures and Creating a Hierarchy of Shapes

If you’re anything like I was when I first started teaching 5th grade math, then you probably aren’t too excited about those dreaded geometry standards. You know which ones I’m talking about… The standards that require students to classify two dimensional figures based on their properties and create a hierarchy of shapes.

Let’s break down this standard so we understand the why behind this concept. Watch the video below to see what activities I’ve done with my students to make these standards less painful, more meaningful, and a whole lot more fun for you and your students! When you are done watching the video, be sure to download the Mystery Shape Think Sheet + Bonus Activity for FREE!

If you can’t watch the video, read the transcript below!

So, let’s dive into these standards. If you are teaching Common Core, the standards we are discussing today are 5.G.3 and 5.G.4. Essentially 5.G.3 is a continuation of work students did in 4th grade when they started talking about the attributes of shapes. Attributes or properties of shapes are the things that make shapes different from one another. It can be the number of sides, the length of the sides, the size of the angles, or whether or not the sides are parallel… All of these things make shapes unique. Now this standard expects students to group figures based on their properties and begin making generalizations or statements about all figures in these groups. The standard 5.G.4 takes this a step further and has students create a hierarchy of two dimensional figures based on their properties. This just means that students are using a visual representation to thoughtfully organize the ideas and groupings students discussed in the previous standard.

Now although these standards are not considered core work for 5th grade math, they are still important standards! I think of these standards as the ultimate critical thinking standards for students. The type of reasoning that is required to be able to classify objects and make accurate generalizations about each group is a thinking skill that will serve students well down the road.

Honestly, these standards are heavy thinking standards for teachers too! When I first taught these standards, I had to have a cheat sheet with me because I didn’t fully understand the standards myself which meant I definitely wasn’t confident that I could teach them to students. But don’t worry, I’ve got two activities for you that I think will be really powerful in helping you and your students really understand these standards and bring them to life. And of course, if you’ve followed me for any length of time you know I believe that one of the most engaging math strategies is building true understanding through hands-on work.

The first activity I have for you is called Mystery Shapes. This activity is a great way to kick off your geometry unit by reviewing some of the work students did in 4th grade with identifying properties of shapes. It will be impossible for students to create a hierarchy of figures if they are unable to identify their properties. The purpose of this activity is to break students of the “it looks like this, so it must be this shape” mindset by taking away their ability to actually see the shape. As I mentioned before, we want students to be able to identify figures based on their properties not just by how they “look.”

Most students would not look at a square and call it a rectangle because they’ve been taught since they were very young that a square looks this and a rectangle looks like this. They likely were not taught what specific properties make a shape a rectangle and square. When they can no longer see the shape and can only feel the shape, they really have to focus on describing a shape based on their attributes, which is the goal of this activity!

Here’s how you will set up this activity. You will need bags, some sort of stuffing or filler to put into the bags, and pattern blocks. If you don’t have pattern blocks you can head to your local craft store and pick up a pack of those colorful foam pads. You’ll just need to cut out different shapes from those foam pads and those will serve as your pattern blocks.

Fill each bag with your filler item. The filler item is just to keep kids from easily being able to look in the bag and see the shape. I’ve used tissue paper before and it worked just as well.

Essentially you will create stations around the room with one bag at each station. Students will be working in pairs, so you need half as many stations as you have students, although you may want to create two extra stations so there is always a couple of empty ones for students to go to when they finish. Half of the stations will be A bags and half will be B bags. In all of the A bags you will put two different shapes. So I may put a parallelogram and a square in each of the A bags. In the B bags, you will put another two shapes, so I’ll put a trapezoid and a triangle.

Once the activity begins, students are going to reach in the bag to feel each shape in order to answer the questions on their think sheet. Be sure to print the think sheet that goes along with this activity. It is a free download that you can grab a copy of by clicking on the link in the notes below this video.

As an example I might feel the trapezoid and notice that it has four sides, only one pair of parallel sides, and that two of the sides feel about the same length. I may comment on the angles of the shape as well.

Once you’ve got all your bags set up around the room and your think sheets in the hands of your students, have students go around the room with a partner and dive into their mystery shape bags. You may want to set a few rules. For my students, I told them that only one pair could be at a bag at a time. Also, they were not allowed to pull the shapes out and look at the shapes until both partners had finished one side of the think sheet. Once they were done at a bag, they could go to another open bag that was different from the one they just completed.

By the end of the activity, students should have explored at least 4 different figures and had time to really discuss and focus on the properties of each shape. Now that they’ve refreshed their brains on what attributes make figures unique, they are ready to begin classifying shapes and creating hierarchies.

Creating hierarchies sounds fancy, but it is really just creating groups based on characteristics. The reason this is tricky is because most students don’t even know what a hierarchy is. I like to begin this standard by doing the Hierarchy of Chips activity so that students get to explore hierarchies with something they know before they add in the additional information that comes with properties of shapes.

There are many ways to do this activity and modify it, but I am going to share with you how I’ve done it.

I brought in regular Doritos, cool ranch Doritos, a cookie, and a fork but you could use whatever items work for you. I asked students what the most general name would be for this object. Students ultimately came up with the word food. Then I asked them to get a little more specific. We agreed on chip. Even more specific would be Dorito. And lastly, the most specific you could get would be Cool Ranch Dorito.

Next we determined where the other items would fall in our picture. A plain Dorito could be categorized as food. It could also be categorized as a chip. It can be categorized as a Dorito, but it cannot be called a cool ranch Dorito so we will leave this item right here.

A cookie can be categorized as food so we will move it inside this circle. It cannot be categorized as a chip so we will leave it right here. Because it cannot be categorized as a chip, we don’t even need to check with any of the further categories because all other categories are chips meaning they have the same characteristics of chips which the cookie clearly doesn’t have.

Lastly the fork. This won’t make it inside any of the categories because it is not a food which means it cannot be any of the subcategories which are all foods.

Now that students have created a hierarchy with their chips, we can constantly refer back to this when students create a hierarchy with polygons. One of the things that is the most confusing for students to grasp is the idea that all squares are rectangles but not all rectangles are squares. This is challenging for most adults to wrap their brain around! Well, let’s go back to our chip hierarchy. Are all Doritos chips? YES! Are all chips Doritos? No. Get students talking about why that is!

Students know that rectangles have two pairs of sides of equal lengths, two pairs of parallel sides, and four right angles. But guess what? A square has all of those same attributes, so a square is just a specific type of rectangle, just like a Dorito is a specific type of chip. There is something additional that sets squares apart from all the other rectangles and that is that all four sides are equal. Doesn’t that just make so much more sense?

Now that students understand what a hierarchy is and can have these types of discussions about the groups within the hierarchy, try replacing the chips with pattern blocks or cut outs of other shapes and begin doing the same activity but this time instead of talking about the characteristics of random objects, they are talking about the attributes of shapes.

You can do this with the big category circles like we did with the chips and other objects, or you can create a hierarchy that looks more like a flow chart. This layout  is especially useful when you have shapes that begin splitting off into different categories.

I’m going to use pattern blocks for this demonstration, but you can use cutouts of shapes which will give students more figures to explore. All of these shapes are considered polygons. I notice that these shapes have different numbers of sides. I notice that these shapes are parallelograms and this is a trapezoid. Fun fact: trapezoids have different definitions depending on what state you are in so be sure to look that up before doing this activity! We can categorize these shapes even further by naming this shape as a rectangle or square.

That’s all there is to it. Now students have just made their own hierarchy of shapes!

I hope this video was helpful in giving you some meaningful and engaging ways to make what could be a really boring and confusing standard more exciting and understandable for students! A few things 1) Be sure to subscribe to my channel so you are notified whenever I post a new video and 2) Don’t forget to grab your free download so you can use these activities with your students! 3) If you aren’t already, be sure to follow me on Instagrm @mixandmath. I love to share ideas and activities to help you make math more hands-on and concrete. Let’s talk math again soon!