## Thursday, October 25, 2012

### Transversals, Tape, and Stickies

Today in Geometry, we're discussing two lines, a transversal and the angle relationships formed. We did a few minutes of word wall pics and direct instruction of Corresponding angles, Alternate Interior angles, Alternate Exterior angles, and Same-side (or Consecutive) Interior angles. Then students were presented with the following setup on my walls. I used three strips of masking tape to create the lines intersected by a transversal and numbered stickies. I was able to set up 3 stations since I have a small group of 8th grade Geometry students this year.

Students worked in groups and were instructed to start with the two parallel lines and the transversal. It's a lower entry point as opposed to the three lines intersecting to form the triangle (which my textbook chooses to introduce this concept. Silly publishers). Groups are given the following handout and need to place the stickies in the correct places, based on the given clues. Work together, GO!
Handout and solutions here.
If you have limited space, create 1-2 stations and have groups rotate as other students are completing a task at their desk. Put a timer on the board and tell the students to get as far as possible within the allotted time. When the timer finishes, I'd take a picture of their work, reset the stickies, and let another group tackle it, resetting the timer.
Here are possible solutions. Let me know if you find any errors.

It went well. There was a lot of tension in the groups. Some kept moving stickies around because they disagreed. They disagreed because of the overall connection, not because of getting the relationship wrong. It was so fun to hear them get so excited about this activity. We ran out of time and the quote of the day came from a girl, "That's upsetting me." She wanted to finish. She wanted to know the answers. She wanted to figure out the puzzle. Many other students had similar feelings. I love it!

What I learned: Don't make the groups too large. Go with about 2-3 students (4 max) per group. Use really good stickies. The orange ones you see in the pictures were old and had lost their stickiness. If groups are struggling too much, encourage them to find a set of angles that has the least amount of possibilities.

Transversals,
1239

1. Love this, especially the non-parallel example. I have had students in the past who assume that alternate interior angles are always congruent, and this activity lends support to the vocabulary. Also, the transversal become the star of the show, as some some of the pairs are alternate-interior RELATIVE to the transversal they share.

Do you have any magnetic boards in your room? For me, this would be idea for small magnets to make it easier to move the numbers around. Would also make a nice puzzle computer app.

1. Good call with the magnets idea!

2. Good call with the magnets idea!

3. Yes, magnets would be awesome here.

2. Awesome idea!! Definitely going to share this with our Pre-Algebra teachers (which is when our kids are first introduced to angles formed by transversals). Great way to learn the vocabulary and really get at the relationships involved - thanks!

3. This is wicked Andrew! I wish I was teaching it, definitely saving for one day.

4. @Bob Magnetic boards would be a great idea. I agree, it would make a fun puzzle computer app.
@Anna Glad it might get you some use.
@Timon Thanks man!

5. Thanks for stepping this out, Andrew. I'm going to try this with high school Geometry. Would you make any other changes if you had a class of 40?

6. I loved this, and tried it with my Geom kiddos. It was a blast. I set up yarn and post-its all over the room: on walls, bulletin boards, on the sides of filing cabinets, on the back table. When the kids came in, they were SO curious! I had to get them through being able to name the special angle pairs first. They practically jumped out of their seats when they finally got to do the activity!

As an extension to this activity, I had them making their own puzzles like this. A lot of fun to go through them: had them realizing one clue per angle pair wasn't enough!

1. I'm gad it worked out Mrs. Palmer. I agree, there has to be some direct instruction to front-load this activity. Glad it worked out and I appreciate you sharing.

7. For me, this activity is too much about learning words. I can solve angle problems without knowing the names for pairs of angles.

1. Really great point, Katrin. You're absolutely right that students can solve angle problems without knowing the names for pairs of angles. I would like to think that students tend to see the numerical relationships over the vocabulary relationships here, because of the visuals and interaction. The more I do this activity, the more I value the discourse students have when working together to solve these challenges. Furthermore, I think it's important to prioritize the name recognitions for the angle so that students become familiar with the names of commonly used angles in geometry. For example, I would rank vertical angles and linear pair pretty high on my list. It's a lot easier for us to communicate by saying vertical angles instead of a student pointing and saying something like, "this angle and that angle across from it."
The mathematical goal here is to not solve angle problems, as I'm sure you see. This activity's mathematical goals has evolved into student discourse around angle relationships where students construct arguments, use logic, and become more familiar commonly used angle names in preparation for many geometric activities, including (but not limited to) proofs.

I'm curious, if you had to prioritize the names of the angles, which would be your top two?

8. Just completed this activity with my Algebra one class and absolutely loved it. My kids started with little background, I front loaded with two column notes (warm up) then I quickly went over...then stated the objective of the activity was for the students to use the vocabulary to solve the puzzle. The conversation was awesome. Loved it. The second puzzle is a big jump and we did not have time to explore it completely, however I will return to it! Thanks!

9. I have been doing this activity with my geometry classes at all levels for three years now. In my opinion it is the best possible vocabulary practice for angle pairs. The students love it, and they think they are just doing a logic puzzle. At the end of the activity I congratulate them on their persistence, point out the ambiguity of the transversal in the second situation, and have them focus on the types of relationships that are most restrictive (and therefore helpful) when they are starting the puzzle. Then I point out that they are now completely fluent with the vocabulary, because they have been using it to argue with each other for the last half-hour. Since I have been using the activity, students very rarely have difficulty identifying the types of angle pairs in figures later in the year.

A little extra bang for the buck, and a way to ensure all group members are solid on the vocabulary: When a group asks me to check their solution, I simply make them put the puzzle away, and I go down the list calling out the angle pairs, and the members of the group have to name the relationship between the angles (rotating through the group). If they name all the correct relationships, then they know their solution is correct!

1. Hi Dawn,
I'm so happy to hear you've had success over the years with this task/puzzle. I like your "extra bang" idea. Thanks for sharing.

10. Hi Andrew,
Thank you so much for this idea! I made a similar puzzle for my geometry class today, using less of the vocab, and taped the intersecting lines onto large whiteboards where they could use markers to label angles. They worked in groups of 2 (ok) or 3 (better). It worked really well :)

11. I really enjoyed the idea in this and thought it was really nice! I have used this many times!

Thank you alot!