Guided Discovery of Geometry: AngLegs - Play Discover Learn 24/7

Guided Discovery of Geometry: AngLegs

guided geometry

Geometry is so much more interesting when you get to discover the ideas surrounding it for yourself and AngLegs is my new favorite tool for guided geometry.

Guided discovery is using specific task that unveil to the student important concepts from geometry to number properties to even laws of science. Today, we look at using AngLegs to uncover geometry concepts. 

3 Key Elements For Success

Stories, constraints and making predictions. With these 3 elements, we will capture the attention of the child, guide them to discoveries and leave them driven to discover more.


Children love shapes but what they really love is making up stories and going on adventures. When you let them build shapes to paint a story, you have a winner.

Introduce this activity after story time. The story will stir their imagination, and get them to make the most of building with AngLegs. I recommend a few great choices at the end that are all about seeing shapes in everyday objects.

The first day just let them build freely using their imagination. Here they will intuitively begin to notice important elements, like three AngLegs always make a triangle. With the right stories, children will also start combining the shapes to make more complex pictures.

During freeplay, connect with the students by having them tell you about their pictures. Let them articulate their ideas in their own words and then provide them the language to help them say their ideas simply, language like triangle, square, quadrilateral, octagon, corners, angles, sides and so on.

Constraints for Guided Math Discovery

Once the students feel confident in manipulating the AngLegs and are familiar with shape building, it's time to add constraints. That is when we give them specific tasks that let them discover specific qualities of geometric figures.

Let's start with a simple constraint. Make a shape using just three AngLeg pieces. Have students compare their shapes. What is the same? What is different. What do we call this shape?

You can continue to expand this activity by adding in an Angleg piece one at a time until you have talked about all the shapes you desire.

Guided Inquiry math

Introducing the Protractor

Extending the students observation, add more constraints like use only one color to make a triangle. Then use the protractors to measure the angles.

If this is the first introduction to protractors, show them what they are measuring, but there is no reason to discuss why. They will see that when they start comparing and observing different measurements.

What do they notice? Hopefully, they observe each angle measures the same. Have them measure the angles of their peer’s triangles? Does it remain true?

You may consider recording their observations in a table for easy comparison and to promote closer observation. 

Challenge students to show you their observation when they articulate an idea that is quite right. This is important in building the habit of self-corrective thinking. Often in showing you, they catch their own mistake.

Making Predictions

inquiry based learning

Making predictions is helpful in improving students' imaginative thinking skills. In this activity, students begin by building 3 triangles.

Each triangle has at least 2 purple sides. The first is all purple. The second has one orange side. The last has one green side. The third side that is changing is growing progressively larger.

Have the students measure the angles of each shape and then make a prediction. If we change the next shape to a yellow side with 2 purple sides, will the angle of the purple corner get smaller or larger?

Predictive activities that use patterns to predict the next outcome help spur students to continue discovering on their own. Will the pattern continue? Student-led is student-driven and capturing that drive is important to maintain genuine interest. 

Taking a Look at AngLeg Task Cards

guided math task cards

We purchased the AngLeg set with activity cards. It was enough AngLegs for three kids. Of course, the more the merrier, I say.  

The activity cards give you a variety of ideas for a multiple grade levels from Kindergarten to Junior High School. It is not comprehensive by any means, but it will give you even more ideas than I have given you in this brief overview of AngLegs.

Also, the task cards aren't oriented around the philosophy of guided discovery. The cards give you good ideas, but if you want guided discovery, you are going to have to adapt them. ​You get though an idea of the awesome potential of these manipulatives.

Of course, just playing​ with the AngLegs yourself will give you plenty of ideas, and that is what I recommend. It helps you to see how to discover certain concepts for yourself and which tasks will guide discovery of those ideas.

Nevertheless, ​I recommend AngLegs as a great manipulative for guided discovery.  Plus, the clicking together of these pieces has the relaxing effect of popping bubble wrap.  I know, totally worth buying just for that. 

Want more ideas for playful math discoveries? Be sure to follow me on Instagram where I am always posting easy activities for spurring math discovery.​

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Lacy | Play Discover Learn 24/7

Knowing the best kind of learning comes from a highly motivated internal drive, Lacy Coker cultivates tools and resources that help to make learning for young children playful and self-directed.

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