Speed Dating is one of my favorite structures for incorporating review in a collaborative, non-kill-and-drill manner. If you've never heard of Speed Dating in math, I suggest that you stop reading this right now and read this post by Kate Novak right now. She explains it much better than I could. Here's what I did to make it work in my 8th grade math class:
Since we've been working on graphing linear equations, I made my cards by printing out some problems from the Chapter 3 Student Workbook from UtahMiddleSchoolMath.org (pgs 10-14). After cutting out the cards, I wrote the equation of the line on the back. Students had already done these problems as an assignment, but they did so poorly on the quiz that I knew they needed to revisit them.
Ideally, every student has their own card. However, when you've got 36 students in a class like I do, that's a lot of problems to come up with. When I did the graphing speed dating, I made 3 sets of 12 identical cards. I then have 3 separate groups of speed daters, which works well since my room is arranged like this:
This also works out well for me time-wise because I only have 45-minute class periods. If you're going to use 3 identical sets of cards, I highly recommend that you number/letter each card in the set so that they are easy to sort out when they get mixed up or lost. I learned this lesson the hard way.
Each student gets their own card, turns it to the graph side, writes the equation of that graph and then checks the answer on the back. The student then is the 'expert' on that problem. Students then trade with their partner across from them and write the equation for that card. If they struggle, they ask the person sitting across from them for help. I set my online bomb timer for 1-2 minutes, depending on the class. When the timer goes off everyone switches cards back so that they are holding their original problem. The students on the window side of the classroom remain seated while the students on the wall side of the classroom move one space toward to the right. Students switch again and begin working.
I found that some of my speed dating groups had an odd number of students. This is quite simple to fix. Just place a card on the empty desk (make sure it is on the non-rotating side) and have students work on that problem when they rotate to the desk without a partner.
After students wrote the equations for all 7 problems (their own problem plus their 6 partners), I had students swap their cards diagonally and turn it to the equation side. I gave each student a set of coordinate grids kind of like this. Students then had to graph the equation that was written and we repeated the whole speed dating process with the same set of cards, but this time going from the equation to the graph.
The results? After a day of practice, when I re-quizzed my students on these topics, they did much better! A few hang-ups still: students forgetting to write a negative for equation of lines with negative slope; students who can't differentiate between y = 2x and y = 2. Any suggestions for dealing with these two issues?
About the author: MaryAnn Moore (@missnarymm) teaches 8th grade math in Davis School District. She coordinates the UCTM teacher blog and is also a regular contributor to the UCTM teacher blog. Please email her at firstname.lastname@example.org if you are interested in contributing to the UCTM blog.
In my last post I discussed some of the things I learned about mathematical modeling at a recent Math for America professional development. At that same professional development, I had a conversation with a few people about modeling and developing great tasks. I mentioned that I have to practice looking for great questions, but until I'm able to come up with all of them on my own, I steal (borrow) a lot of great content that people share online. Over the next few weeks, I will write blog posts to share with you some of my very favorite modeling and number sense resources. Let's get this party started by discussing my all-time favorite number sense resource:
Website url: http://www.estimation180.com/
Author: Andrew Stadel @mr_stadel
Description: "Each day of the school year I present my students with an estimation challenge. I love helping students improve both their number sense and problem solving skills. I'd like to share the estimation challenges with you and your students. Michael Fenton and I have collaborated on this handout for your students. Happy Estimating!
Why I Love It:
Honestly, I first started using Estimation 180 because I was looking for an easy time-filler/warm-up for a class of students that was way below grade level. I needed something that I knew everyone could do no matter their mathematical skill, that would keep them busy for a few minutes at the beginning of class while I took attendance. I'd heard some buzz about Estimation 180 on Twitter and on some blogs, so I decided to try it out. I got a whole lot more than I bargained for! Here's a few reasons why this site is so awesome:
Everyone can estimate. Everyone! That kid who says, "I don't know how to do this," every time you call on him? Yep, he can estimate too. I have 100% student participation when we do an estimation challenge. On some days, it might be the only 5 minutes of class that everyone is participating, but at least everybody was thinking mathematically for at least 5 minutes.
2. High Ceiling
Not only can every kid DO the Estimation Challenges, but every kid can LEARN from the estimation challenges. I find that the best learning often happens when I ask kids the 'why' behind their estimates. Other good teaching moments come from having students calculate their error. For example, I had no idea how difficult it would be for my students to calculate their errors of estimating Mr. Stadel's height and the height(s) of his family and friends. First we had a discussion about all the different ways to correctly write out his height (6 feet 4 inches) and why it couldn't just be written as 6.4. Then we had some interesting discussions on how to calculate error if someone had estimated that Mr Stadel was 5 ft 9 in. Why can't we just do 6.4 minus 5.9? Students brainstormed several strategies to determine the error, including counting up and regrouping to write his height as 5 feet 16 inches. Was this part of my lesson plan? No way! Is it in the eighth grade core that I teach? Not exactly. Do my students need it and does it help them improve their number sense? Absolutely! I consider it to be time very well spent.
3. Kids Love It
I wish I could record for you that moment that I 'reveal' the correct answer! There is often shouting, occasionally there are fist pumps. There are sometimes exclamations of disbelief! "What?! There's no way that is only eighteen napkins!" When a student's estimate is perfect, it's as though he or she had just won The Price Is Right? I usually try to take a moment to acknowledge the person with the smallest error. That's all they get - no candy, no extra credit - just a moment of verbal praise, and the knowledge that for that moment they had been more successful than every other person in the room. You wouldn't believe how motivating that is.
4. Estimating and Problem Solving
As a math student and, until fairly recently, as a math teacher, I always thought that teaching estimating was a waste of time. You know what I'm talking about - those worksheets that teachers gave kids where they had to use rounding to find their answers before they learned the actual algorithm. Students' answers are invariably different from those in the textbook because they'd rounded to a different place value than the textbook had used. In all honesty, I still don't see any value in the 'kill-and-drill' form of teaching estimating. However, I see a lot of value in teaching the Estimation 180 form of estimating. When I give my students a task like Noah's Ark or Styrofoam Cups, I now begin the task by asking my students to tell me something that is too high, something too low, and then an estimate. This starts them thinking about what the answer should be. For my students, choosing the appropriate mathematical operation is often the most difficult part of a problem. If they already have a good estimate in their head before they start to problem solve, the students are able to figure out much more quickly if their strategy is leading them down a wrong path.
About the author: MaryAnn Moore (@missnarymm) teaches 8th grade math in Davis School District. She coordinates the UCTM teacher blog and is also a regular contributor to the UCTM teacher blog. Please email MaryAnn at email@example.com if you are interested in contributing to the UCTM blog.