# Systems of Equations Unit Plan

During this years MTBoS blogging initiative, I used the share the love prompt to capture some of the things I wanted to use and remember for teaching the quadratics unit. I am going to try to continue doing something similar to keep links and ideas for other units as well. I am really terrible about keeping all the activities I have used in the past or new things I want to try so this way I have an electronic record and I can share idea with other math people:

We are knee deep into a systems of equations unit in one of my Algebra classes. So far we’ve done the Systems of Equations Launch which I wrote about here. Which led into graphing systems. At the bottom of that post I wrote how I would adapt it next year by adding in some lines that never cross or end up being the same. Since I hadn’t done that with the launch, I used that idea for the warm-up the next day.

I projected a Desmos graph with a few different lines and told them that the battleship path was the red line. They were tasked with estimating mine placement for the other 4 lines.

This quickly brought up the “missing” orange line and the inability to lay a mine on the green path. We discussed possible numbers of solutions to a linear system then I had them sketch ideas for a system that could have two solutions.  Afterwards they did some more practice with graphing to find solutions. And ended by having the students create scenarios were you’d care about the intersection and then write up a problem which would fit that story. I collected them. Some will turn into warm ups or lagged review and some will end up  on quizzes or the end of unit assessment.  I’ve been working over the last few years to incorporate student generated problems. They seem to get excited about the possibility and its improved their problem writing because they want me to use theirs. Continue reading “Systems of Equations Unit Plan”

# Pythagorean Theorem and the Distance Formula: Live 3 Act

I was reading twitter when I found Mr. Orr’s 3 Act Task Corner to Corner task. I had just taught the Pythagorean Theorem the day before and the distance formula was on tap for the day. I had a giant thing of string from Algebra’s battleship task, so I thought….why not recreate the scenario in class.

I taped a piece of string from one corner on the floor to the kitty corner  one on the ceiling.  I have tables and a relatively small class ~15 students so I was able to push tables to the sides for the day. When I greeted the class at the door, I asked them to watch their heads. That got a few chuckles until they saw the giant string. Instead of giggles, I got excited chatter. Many were variations on”What is Ms Micaela up to now?”,  but many students were asking each other math-y questions as well. The bell hadn’t rung, I was still greeting in the hall, and already I overheard the question I wanted.

# Systems of Equations Launch

After wrapping up our linear functions unit, the students had one day off. When they returned to class on Thursday, each table had been turned into a mini command center. Big sheets of graphing paper were stuck down to the table and an assortment of string, scissors, tape, rulers and three colored dots were at each table.

When students were sorted into teams, they were handed the mission sheet:

I told them they could only use the supplies on the table and at the end of the activity, I’d need a report on where the mines should be laid in the form of coordinates.  And they were off! (Side note, the original question had more information, basically telling them how to solve, so I just erased it which is way the type is a bit crazy. I’ll type up a nicer version for next time with the additions I add at the end of this post).

After we stopped, I took the coordinates and posted each teams on the board. No groups had the exact same answers. They wanted to know if they “won” but I told them they’d have to wait. Continue reading “Systems of Equations Launch”

# Measuring Angles (Plus a Little Dancing)

Geometry A is working through a unit on definitions and introduction to proof, with a good dose of reviewing key ideas that may or may not have been learned in middle school math. Our topic today was recognizing: vertical angles, linear pairs, corresponding, alternate interior, alternate exterior, and same-side interior and how to use that information to start building proof.

I put up a set of lines and a transversal and had student call out angles that fit the above terms. Then I had them all choose a set of taped lines that were spread around the room. We went through each location again, trying to find as may pairs that fit said relationship. After students were comfortable with each, I hooked up “Dance, Dance, Transversal.” I have no idea who I first saw the idea for “Dance Dance Transversal” from or I’d give credit, but there are lots out in the inter-webs of math land, so if you want more, Google returns many hits. We played a few rounds to warm up. Basically, I had a PowerPoint set up to cycle through the terms (I limited it to vertical, AIA, AEA, and corresponding) and students had to jump to the correct location. We had music going and in later rounds, judges. We crowned the class champion and I let them know they’d have to dance on the unit exam.

Then, each student was tasked with getting a protractor and measuring the eight angles formed by the transversal. I had purposefully used both parallel and non-parallel set ups (About 2 parallel for every non-parallel). After measuring, they walked around and had to write down at least two notices and two wonders. (Examples “I noticed all the vertical angles were the same.” “I won
der why some gro
ups have only two different angle measurements and others 4.”   “I noticed an error, or what I think must be an error in set B.”   “I’m wondering if my tape was messed up, because it doesn’t look the same as most of them.”)

We were running short on time, so we shared out a few of the Noticings and Wonderings as a class and we’ll pick back up there tomorrow. The plan is to agree upon, prove, and then practice with the key ideas.

# Time Distance Graphs

Algebra 1A is reviewing parts of a graph, writing stories from graphs, and graphing based on situations. I ran across a really fun idea from Mr. Orr where he had students create motion videos, create an answer key (i.e. a nice graph of the scenario) and then gallery walk and try to create graphs based on each pairs video. I knew I wanted to do it with my class. I am not one to one, or even close to that, though, so I adjusted the activity to fit. Instead, we all had to share the one iPad I did have.

Each student got a set of steps and a place to sketch what they thought the steps would look like on a graph. I didn’t give them much direction here. As they finished, I pulled students out into the hall to film there series of steps. I asked them to think about the distance they traveled over the course of doing the activity and re-sketch the graph if doing it changed their minds. (So in the worksheet below, most students had two sketches for #1).

After the videos and sketches, we talked about what a time distance graph shows. I projected a completed graph and students try to come up with a story. Each student then graphed there own graph on a full sheet of graph paper. I checked over them for accuracy, asking students to explain areas I wasn’t sure about and re-draw until we both agreed. They stapled a blank piece of paper on top and wrote the letter of their story on the outside.

Overnight, I collected all the different clips and arranged them by letter. I also taped up the graphs around the room, with only the letter showing. We opened the next day by watching all the clips as a class. Each student sketched what they thought each graph would look like and labeled it with the correct letter. After the clips, students walked around the room to check their answers. I also asked them to write down any “Notices or Wonders,” especially if the graphs didn’t match they had drawn.

Here is a sample video and solution:

We got back together as a class and took a poll on which graphs had matched or not. We re-watched the most troubling clips and discussed what made them harder to draw. We also talked about how the graphs might not mach exactly, but still be considered correct. Without having actual measurements on the ground, “fast walking” might always be steeper than “slow walking,” but by how much would vary.

Then, students were given a reflection/exit ticket. Instead of creating graphs, they were given a graph and had to create the story.

The whole thing took about 1 class period, but split into two days. (The end of one class and the first half of another. I have 50 minute classes, but they are small. With a larger class it might have taken longer, or with more iPads it could have been shorter as we wouldn’t have had to watch all the videos together before the walk. Mr. Orr had the iPad videos sitting around the room, one video at each poster.)

It was a fun and active way to introduce motion graphs. I will definitely be using it again. Hopefully next time with more video devices.

# Spaghetti Challenge

I wanted to start the year with a project. I value discussion, team work, and creating and I wanted students to know this from day one. I threw around some grand ambitions, but settled on the spaghetti/marshmallow challenge mostly because the supplies were cheap and easy to jump right into. I was worried that students would have done it already or be bored, but I was definitely wrong. Students were thrilled. My favorite comment of the day “You aren’t tricking us right? I hope math class will be good all year and not just today.”

I had students fill out reflection forms and I got all fives, with the exception was of two fours. (1-5 scale). All groups begged to stay longer after class. Two groups worked through lunch hour, and one group tried to stay into their next class.  I’d call that a good opening. I also got pages of notes of individual students learning styles, ability to work together, communication skills, etc.

One interesting note was the responses to the question: What worked well? Students  tended to choose their own contribution to the tower. For example for one group, one said “adding something to pull back the wobbly parts” (her idea) and the other: “making a triangle at the bottom to make sure its even/balanced.” (again, said students idea). Their tower was successful at 26.5″ and there was no way to tell tell which one made the difference, if both were needed, or something else entirely. On the flip side, the “What would you change” was usually more supply or group oriented. “Be neater” “Use material smarter” “Be less wobbly”. This may be normal, but we started doing community circles this year and the students had been really critical about themselves earlier in the day, so I was excited to see them proud of their contributions.

In most of the groups they started out two people working on totally different ideas for same tower and it slowly turned into better team dynamics. A few groups hit it off right from the start and only would do work if both agreed. A few assigned tasks and then came together at the end.

We had some good discussions. What assumptions can we make? How long does it have to stand to count? (The absolute highest was 30 inches. it stood alone for about 1 or 2 seconds and fell. Another at 26.5 inches stood until the group karate chopped it down at the end of class). Is height really the most important part? What are we learning?  “We can go higher!”

Also, I forgot string was a material, so they only got tape, spaghetti and a marshmallow. Three separate groups came back later to tell me a brilliant new idea that “Would for sure be the highest.”  One of the the more inventive ideas was to make a long thin strand and tape the marshmallow to the top of the spaghetti and the ceiling so the long, thin strand didn’t have to actually hold weight.

# Puzzling Minds

Keeping with our problem solving short Wednesdays, we did math station puzzle rotation today. Certain students really dislike when I assign one problem that takes the whole 40 minute block, so I thought I’d give out a few shorter activities today.

First station: Arrange all five pieces into a square. All the students found the 4 piece version and more than half tried to get away with sticking the little left over square on top. Most students were eventually successful with the five piece square although I know a little hint giving was done. I like this puzzle since every student walked in and said “This is easy!” and then quite quickly, “This is impossible!” After finishing, they’d sketch it in a notebook for me to check off.

<— All the pieces

A tricky Student —>

Second Station: Logic Puzzle Fun. Students could choose any of the varieties of logic puzzles I put out and solve it. They have seen each one of the choices at least once during the year.

Third Station: Four 4s. Basically, using exactly four 4s and any mathematical operation, create expressions to represent all the integers 1-100. This was the biggest hit. Students were whining and complaining at the beginning, but as soon as they got into it, they really got into it. I had multiple students try to skip their next class and stay in to do four 4s. I told them they could take them with them, but most replied “But I want you to know I did it myself.” I told them I trusted them, but still something about doing the problem while I’m in the room was important to them, so I told them it could be something they pull out as pre-class work or end of class work if they ever finish early. I feel so corny saying it, but it was so fun to watch them work in this one. They’d light up when they found a ‘hard’ number or used a funny operation. I got to introduce a whole lot of math vocabulary that we never get around it using. They loved this so much, I should have spent the whole hour on it. I had figured it would be the least liked activity. I was very wrong.