Blue Constructive Triangles

If you’re a Montessori teacher and you’re anything like me, there’s probably a little box sitting on your sensorial shelf that has remained untouched for quite some time. This little box might look something like this:

I have obviously always known this is the last box in the Constructive Triangle series, but never really knew what its purpose was or how to properly present it. However, I recently learned from another Montessori educator about a beautiful presentation of this lesson. I will give an overview of this presentation here, but also highly recommend that you watch the video lesson I sent out to my students this week:

This box contains 12 identical right angle triangles, painted the most magnificent shade of royal blue. What is beautiful about this lesson, is that it inspires the child to explore. The other constructive triangles have literal black guidelines painted on the edges, encouraging the child to construct specific geometric figures. The blue triangles are much more ambiguous, allowing for more creativity and exploration.

Here’s how I would present it.

First I would use only four triangles to show how you can make two very basic shapes: a rectangle, and a rhombus.

Now is where it starts to get a bit more complex with the introduction of right angles. Again, using only 4 triangles, you point out the right angles and connect the 4 right angles together. Once this shape is constructed, you can show the child how to slide two triangles at a time to create a shape with an open square in the middle, as well as around the outside!

You will need 6 triangles for this next shape. Point out the second most acute angle (i.e. the angle in between the right angle and the acute angle). You will make the next shape by putting this angle of each triangle together. Then again, you will carefully slide the triangles to reveal a new shape, with a hexagon in the middle and a hexagon on the outside.

Finally, you will need all 12 triangles. Point out the most acute (smallest) angle of each triangle, and put them together. Very carefully slide the outer corner of each triangle so that they are aligned, revealing a brand new amazing shape: a dodecagon!

This lesson is gorgeous. Because of the complexity of the shapes created, and the concepts of right and acute angles, this lesson is not intended for the younger child. I would say this is best for ages 4 1/2 – 6 years old. It definitely should be introduced after the child has worked with and mastered the previous constructive triangle boxes.

I have two reasons for sharing this blog post today.

First, simply to share this lesson presentation with you. I know in all classrooms there tend to be those lessons that are not presented frequently, because the teacher has not become familiar and comfortable with them. This was one of those lessons for me. But now that I have learned more about it, I cannot wait to share these beautiful patterns and concepts with my students.

Second, to emphasize that even as a teacher, I am eternally learning. Even 6 years after completing my training, I am always going back to my albums and seeking advice from more seasoned Montessori teachers. I will never be a perfect teacher, and neither will you. But it is this never-ending quest for improvement that enables you to continue growing spiritually. It is this fire burning inside – a deep, intrinsic love of learning – that shines through to your students and ignites in them the desire to seek knowledge as well.

DIY Montessori Cards and Counters + FREE Printable Number Cards

Cards and Counters is an essential Montessori mathematics lesson. And unlike many other Montessori materials, this one is extremely easy (and CHEAP) to DIY at home. It also happens to be an excellent avenue for practicing quantities and their corresponding numerals. I literally made a version of this lesson to share with my students for FREE.

All you will need are my FREE printable numeral cards (see below for link) and 55 pebbles. The reason I say pebbles, is because this version of Cards and Counters was intended to celebrate Earth Day. I had my students first go on a nature walk outside to gather the pebbles, and then use the pebbles as counters. If you want to use another object for the counters, go for it. You can use pretty much anything as a counter (pom poms, beads, beans), just make sure you have 55 total to be able to count out the quantities 1-10.

Here is the video I made for my students:

It is important to note the placement of the counters under each numeral. They are placed in pairs, with the odd counter placed in the middle, below the pair directly above it. The purpose of this is to teach the concepts of “odd” and “even” numbers. Pointing to the quantity below two, you ask the child “does this one have a friend to walk with?” When the child answers “yes”, you say “two is an even number”.

Moving on to three, “does this one have a friend to walk with?” (indicating the last lone counter under three). When the child answers “no”, you point out “three is an odd number”. You move through all the numbers in this way, pointing out which ones are odd and which are even.

Most children pick up on this concept very quickly. The counters simply provide a concrete, visual representation of the abstract concept of odd and even.

Enjoy this free printable! Hopefully this will help aid in the development of your child’s Mathematical Mind at home! Home learning truly has never been more relevant than it is now.