POTW – Putting it all together with triangles

What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: This was a review problem I gave in class.

What is it: This was a problem to practice and review proof skills.

Why I like it: This involves a few different ideas such as auxiliary segments and you can prove a couple different pairs of triangles. Their is also a couple different ways (as well as ways that would not work) so it was a great exercise for the learners to determine how much proof practice they needed. It made my top kids stop and think for a moment so that is always a good thing!

Let me know if you used this and how it went!

POTW – Fun Triangle Proof

What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: This was a problem on a quiz I gave.

What is it: This was how I tested to see if my kids could prove triangles congruent using more than one pair in your proof.

Why I like it: There are so many different ways to solve this problem so it made it quite interesting. Some saw other different pairs of triangles than others so it lead to some great discussion when I passed it back. Talking about how to prove isosceles and what is enough to show is also interesting to see what they think.

Let me know if you used this and how it went!

POTW – Intro To Tougher Triangle Proofs

What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: I gave this after students finished a quiz to play with before we got back together as a class.

What is it: This was the very first dive into proving a pair of triangles congruent and then using them to prove another pair congruent.

Why I like it: The kiddos were able to complete this without anything from me! I like the way it is scaffolded to lead them to what I desire. This allowed us to jump into problems with much more difficulty (see my next post).

Let me know if you used this and how it went!

POTW – Parallel Lines Strike Again In Proofs

What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: This was an exit slip I gave to the learners before they class one day.

What is it: This is checking to see how they are doing with triangle congruency proofs and whether or not they can match up the corresponding parts.

Why I like it: I had so many kids get #2 wrong. They either marked sides congruent instead of parallel or incorrectly marked the angles congruent. Why do parallel pieces seem to throw even my best honors students off sometimes? This was eye-opening and allowed me to adjust some instruction. I am happy to report on the quiz a couple of blocks later they all rocked the question similar to this.

Let me know if you used this and how it went!

POTW – One Important Proof

What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: This was a problem I gave to students to work after we had practiced how to prove triangles congruent.

What is it: This is the first time kids see a proof that will involve auxiliary segments.

Why I like it: The goal is to tell them nothing! You let them sit there and try to figure something out. Eventually, one kid draws in two radii and everyone at his table gasps and ask if they can do that. I swear my kids are like meerkats and then everyone else wants to know what happened and they want to do it to. News soon spreads and next thing you know we have a great place for a discussion. Seriously, one of my favorite proofs ever.

Let me know if you used this and how it went!

POTW – Transformation Compositions

What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: This was a problem my kids worked on during a review activity in class.

What is it: This focuses on using compositions and checking the order of transformations.

Why I like it: We were able to talk about whether or not something was an isometry and it came out naturally in this problem. It was also great to talk about how the order of a composition can change something. Whenever I can connect something from geometry back to an algebraic standpoint, i believe it is worthwhile.

Let me know if you used this and how it went!

POTW – Reflections With Coordinates

What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: This was a homework problem as we worked on transformations.

What is it: A problem that focuses on finding the equation of the line that can be used to obtain the pre-image and the image.

Why I like it: I have always given problems similar to this in the past and asking for the equation of the line. For some reason, I realized having it in this format can really help the kiddos see that the equation of the line must go through the midpoint. So many students came in and told me next class that this homework problem was super helpful so we spent time talking about it in class then. Since this is my honors level class, the last two problems are not as straightforward.

Let me know if you used this and how it went!

POTW – Deceiving Parallel Problem

What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: This was a problem I threw at my students during class while we were working on parallel lines.

What is it: This tests to see if students are reading carefully and pay attention to their angle pairs.

Why I like it: It caused a debate in all of my classes because half of the students said x = 7 and the other half said x = 8. It is great when you can have them argue with each other and then hold a discussion about it.

Let me know if you used this and how it went!

POTW – Crook Problem

What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: This was a problem I threw at my students during class while we were working on parallel lines.

What is it: This is a classic crook problem but initially stumped a lot of students immediately.

Why I like it: Anytime I can give a problem nobody knows how to solve right away is great. Many of them drew some crazy triangles and could eventually reason it out. I liked that I could draw in an auxiliary line and introduce that idea that since two points determine a line, I can draw one in parallel to the other two anywhere I want in the diagram. It was great because they immediately asked if I could make up another one for them to complete.

Let me know if you used this and how it went!

POTW – First Parallel Proof

What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: This was an opener problem I used the first day after I taught parallel lines.

What is it: This is a proof that practices using formal two column proof with parallels. It forces students to practice their reasons.

Why I like it: I like that students have to first practice the congruent complements theorem because even my honors students want to say substitution. Then, they have to prove the lines parallel using a converse to the original statements we learned the class before. Then, they end the proof using a straightforward statement. I think it is important that students have to practice and wrestle with knowing when to end their reasons with parallel or end it with an angle pair congruent.

Let me know if you used this and how it went!