One of my goals this year is to involve the students in the creation of assessments. Last year I got this started by giving them a rubric and having them score themselves against it. I’d also grade the item in question and we’d compare scores and discuss the differences if they arose. This year I wanted to up the stakes by involving them in both creating the assessment rubric and contributing assessment items.

About once or twice a week after our investigation and practice, the last question will be to create a problem related to the days work. Students author a question and either an answer key  or suggested solution paths if it open ended.   These questions often make up the quizzes or parts of the assessments. We’ve even had a few student led debates or Would you Rather sessions. I’ve also had students switch questions and use them as a review session.  When we started this work, most were lower level skill questions, but as they’ve had more exposure to the types of questions I ask, they have stepped up their game. There are obviously lots of less well thought out questions still too, but I’m happy with my first attempt of getting the students more involved.

A few examples of questions I’ve received and then used on an assessment or quiz:

From a 1st semester Algebra class – Systems of Equations:

• Find the value of circle, triangle and square and explain how you know.

From a 2nd semester Algebra class and a 3rd Year Class – Quadratics:

• Which form of a quadratic function is most useful? Defend your choice.
• Create  two (or more) quadratic functions for each situation:
  • Same two roots, no other points shared.
  • Same y-intercept, no other points shared.
  • Same vertex, no other points shared.
• Team A is the Gray circle. Team B is the blue circle. Graph Team A and write the equation for Team B. If Team A won, what might the contest have been? What if Team B won? Is there a contest which they would tie?

From a Geometry Class – Probability:

• There are 10 students. 3 names are chosen. Write a situation that would involve:
  • A permutation
  • A combination
  • Where each pull is independent.

Most of the time, its a quick 5 minute end of class task. Sometimes I give them more time to create more involved problems, solution guides, and rubrics. It still doesn’t take up much time, gives me an idea of how confident the students are with the material, and gives the students more ownership of the class.  The first time a quiz was all student submitted questions, they were grinning while doing the quiz. I don’t think they believed I’d use them. For most students its a point of pride to see his or her question used and I’d careful to make sure they’ve all been chosen a few times.

I’d love to hear from others that have students help with the assessment process. Ideas, resources, readings… I want to go into next year and be even more intentional about student led assessment.

This is quite a few weeks overdue, but I saw Jon Orr’s twitter and blog post about using the clothesline to do a slope activity. I ran mine (files at the end of the post) much like he did, but with a few modifications. He does a great job sharing all the background thought that went into designing the activity so its worth checking out.

Here is a basic run down of what we did. I had two pieces of yarn taped up which ran the width of my classroom. Kids entered and were immediately curious and ready to start.

Each student got a pair of two points and was asked to calculate slope. They wrote the slope on the card and then would go up and add it to the number line. I used no anchors at first, instead letting students adjust others as needed to fit their card on correctly. This brought out some great student to student dialog when both trying to place cards. I had more cards than students, so they’d grab a few card and repeat until all the pairs were placed on the line. One of the cards had an undefined slope.  We had a quick whole group discussion on where to put it. They decided to set it on a cart off to the side.

When the point stack was exhausted, they each took a graph card and drew a graph of a line using the two points. I had them place the graph on a second number line over the corresponding points. Rinse and repeat until all had a graph.

Each student walked along the line as was asked to jot down what they noticed, what they wondered with each line and the connection between the two number lines.  Again, I had them think about the graph of the undefined slope and where it looked like it would fit. They shared out their notices and wonders with a small group and any lingering questions were brought up to the whole class.

Finally, each student a blank card and graph and had to create their own ordered pair and graph to place on the line that would lie in between two assigned points on the graph that were currently right next to each other. I actually  let them pick the two points, but the key is to pick a target interval first, not create some points and see where it fits. For students that needed more support I was able to quietly suggest intervals that they would have more success with. Another way to make it their own, they could keep the (0,2) as a point or try to find two points where (0,2) was not a point, or do both. 

Overall, it was a fun way to practice the slope between two points and reinforce the visual picture of changing slope.  I noticed fewer errors between a slope of 0 and an undefined slope after the activity, and we had the bonus of some number sense practice when trying to figure out how far apart of place cards and readjust them as we added numbers. It would have been quicker to provide anchors, but they extra few minutes was worth it to see the thought process and conversations.

Here are my files for Clothesline Points and the one for the Clothesline Graphs that I used. my class is small, so I had 15 of each card, plus the blanks for the end activity. It would be easy to add a more points as needed for a larger class. Nothing too fancy, but it did the trick.

I have been busy planning out a unit on trigonometric ratios for my Geometry B course. I have been trying to balance the open ended exploration and project based learning that I prefer with the more typical questions that students will eventually see on state tests or future math classes.

Here is the standard I’m addressing with this lesson: G-MG.3 Apply geometric methods to solve design problems (with a focus on constraints).

I introduce trig with the slope ratio, proportions, and physically measuring before I ever tell them the word tangent. I’m leaning toward using Kate Nowak’s Introduction to Trig and then running a few Labs where calculate heights and distances of physical things outside before offering this:

My File Available Here: Constraint Problem

Afterwards I might show a few ramp fails before giving them a more open ended design problem. I’m still working on the actual formatting piece, but it will be a blueprint showing a door/stoop 5 ft high, but due to size of parking lot also has a restriction on length. Students will figure out it is not possible to use one ramp in that space and will have to figure out how to use two or more ramps to fit the constraints.

Nothing too mind blowing or exciting here, but I figure it gets at what I’m hoping they understand. Any suggestions are much appreciated.

Last year I introduced systems of equations with Trashket-Ball. It was a big hit and the students were definitely engaged. I wanted to do it again this year, but I also wanted to spiral in some older material. So we played trashketball Day 1 to wrap up the linear unit and after the flight lab we’ll go back and I’ll ask them to try Day 2 where they have to try and tie to continue on the idea of systems).

I ran into a lesson by Mr Ward over at Prime Factors (the link includes his version of the task which is great, thanks!) which has students gathering data to answer the question: When is it cheaper to drive? I liked that systems could be used to solve, but it also brought back scatter plots, lines of fit, writing equations, interpreting points and more. I used his idea and adjusted it to use Desmos and include some reflections back to the original predictions. You can download my version here: Drive or Fly Lesson. (Sorry about the crazy graph color, I can’t print in color so I had to make the map very different from the circle for a black and white print).

The attached lesson is more guided than I actually used, but I wanted to provide a complete document that might be able to be used without reading my mind. Here is what I actually did:

Kids walk in and see the prompt: Is it cheaper to fly or drive? Choose and be ready to defend your answer.  I wouldn’t answer any questions or give more information at that point. We took a poll and had students from each side lay out their case. We came to the super insightful conclusion: “It depends.” On what? We listed out the possibilities and factors we might need to consider and distance was by far the most common response. That led to page one in the document with the map and the three distance choices. Again, kids had to choose a picture and be ready to explain as well as come up with all the other things they’d want/need to know to actually mathematically decide.

Student Requests: Cost of the flight. Gas. Food. Time. Type of Car. Destination.

Pretty much the info I asked them to fill out in the chart. I asked them to pick a date a month or more out for airplane tickets as well as a type of car. Then they started gathering data. They were in pairs or small groups to make the data gathering take less time.

**Extension/Change I had all the students use the same flight date and car. it might have been interesting to have each group choose a different date or a different car to see the differences in final answers. I didn’t so that we could combine all the different city data to make a class set and compare their lines/intersections with the class set of lines/intersections. I liked the final compilations, but it would be interesting to have them explore how much gas mileage or how much notice for the plane ticket would change. **

Desmos was great for creating the scatter plot. I had them print the graph so they had to come up with the line of fit themselves, but we also went back to compare theirs with the actual line of best fit via Desmos regression would be to see how close they were and whether or not that error was acceptable. 

Finally, after the reflections we focused on the last questions about tying back to the original guess and checking cost for more cities in and out of the “final” range. Most found they were good predictions, but some did not. We had a quick, but I feel important discussion on why that might be. (Distance is not the the only/major consideration with flight costs). We brought up strength of correlation and how that fir into the two lines. Most students came to the conclusion that the model was good, but that they might want to double check if flying into a really small town.

On the way out, I posed the question… should time to get there have another cost. (We factored in food for both and hotels, but not the value of time itself). We had a quick debate on what our time might be worth and when it would matter more. That might also be a great extension place.