Differentiate Math Homework

If you want to differentiate your math homework, here's a good way to make it work.

Start by creating your normal set of problems. For this example, we'll create 15 problems. The problems should be of increasing difficulty. Problems 1-10 will be called set A and problems 6-15 will be called set B. Students can choose whether to do set A or B on their own. If you don't think students will be motivated enough to choose set B on their own, you can either assign students to the two different groups or offer a bonus point for students who choose to try set B.

Anybody have any other methods for differentiation?

Update: I received a comment about this post on Twitter via @vtdeacon:

"How about instead of choice actually giving out two or three different homework sheets with problems set at each students level?"

 I think this is a perfectly good way to do differentiation, but I think most teachers would scoff at doing this because it means extra work. It means making two or three separate sheets per concept, making copies of each of these sheets, and keeping track of how many copies to make for each group of students. If I had to do this for 6 classes a day, I wouldn't do it for long. The way I presented only needs one sheet and the students can keep track of the groups they are in.

New Teacher Advice

Back in the fall of 2006 when the NCTM Regional Conference was in Chicago, my college professors gave my peers and me the chance to attend for a fraction of the normal cost. It was a great experience and I acquired some useful information. One session was a speaker giving advice to new and preservice teachers. I found the file from the speaker recently and thought I would share it. I remember looking at these slides quite often during my first year.

Here is the link to the file.

Weekend Shopping Gem

I picked up a few of these while shopping the other day. Should be useful during the percent of change lesson.

Here's the good info.

Note to Self

This is my best Norm MacDonald impersonation.

Note to self: Next year, do not plan on teaching any concepts on the first day back after a long break. You did this today and flopped. The kids were still sleeping the first three periods—so were you—and the other classes did not want to be at school yet—neither did you. To top it off, the students seemed to forget everything that was learned the two weeks prior to the break. Instead, do some sort of active learning/review game. Maybe even do one of those trash can basketball games that everyone is talking about.

School Year Resolutions Checkup

It's that wonderful time of the year when everyone makes resolutions they will never keep. That reminded me I made some resolutions back in late August for the new school year. Plus, it's almost the end of the first semester so I think I should see how I'm doing.


1. My first goal was to reward students for doing a "good job" more often. I think I have done a pretty good job of this. I've created an award called the Spartan Circle and I choose one student from each grade level every other week. I use the same criteria as this picture shows. I give them a pretty cool looking certificate with my signature on it - which is the best part of the award in my opinion. The also receive a coupon for a free pass on a test/quiz question. On top of that, I take their picture and put it on my Spartan Circle bulletin board for the whole class to see. I think I could do a better job of promoting the Spartan Circle because it might be losing some of its luster, but many of the students are definitely proud and excited to be picked.

2. The second goal was to make math more real-world applicable. I have done much more in this area than I did last year, but I still have a lot of work to do. I spent some of my break reading through Dan Meyer's blog. Now that is relating math to the real-world. I still feel that in many ways I did this better in my first year as a teacher. Back then, I didn't have a textbook to work with and I also had a math teacher mentor who guided me with unit plan outlines. At my current school, the thought is to use the textbook as the curriculum rather than a resource. To top it off, the textbook is Saxon. I am slowing developing materials that stray from the kill-and-drill ideas of the textbook, but it's going to take some time. I have to keep reminding myself that Dan stayed up until midnight on many days to create that stuff. I need my precious sleep.

Enough ranting. What have I done to meet this goal? The 8th graders have done a cost of living project again - which reminds me that I still need to share that idea. After the classes are done with quizzes or tests, sometimes I show videos from The Futures Channel. We have some good discussions. I also created the Careers in Math project. All of these are general ideas though. I'll keep working on it.

3. The third goal was to keep my composure through my busy schedule. I made it through the fall, which was going to be the toughest part. I juggled the beginning of the school year craziness with completing my first year as the 7th grade football coach. Piece of cake.

I'm still on the school's Leadership Team. Not too much extra work other than planning for subs every once in a while. However, we are planning a Math Night to get the community more involved in our school. Since I'm the only math teacher in the middle school, guess who's planning all the activities? That might be a little tough.

Being the Staff Tech Support person isn't a lot of work, especially when you like doing that stuff. In fact, I like it so much that I will be starting my Master's Program in Educational Technology. This will be another test for me to meet this goal, but I have no doubt I'll pass.


I hope some other people that made these resolutions take some time to reflect on how they've done. Even if you haven't kept your resolution, it would be good to reflect on why you haven't been able to meet your goal. Maybe you can even make a New Year, School Year Resolution.

Converting Units of Measurement Using Connectors

I'm sure most math and science teachers at the secondary level cover dimensional analysis at some point, so this lesson might be very useful to you. In the past, I taught it by moving left to right like in this example. I've even used NLVM's interactive converter to help my students out. They worked ok, but I still had students slightly confused and they made small errors that caused them to get wrong answers.

This method is called Connectors and it can be compared to playing Dominoes.

Directions:
1. The students all start with this handout. I will use the example of converting 90 mi/hr to ft/sec.
2. Begin by writing the starting rate in the bold, center "domino." In the upper right diamond, write the target rate.

3. Take another piece of paper and cover up either the top or the bottom of the original rate. This helps students focus on one specific unit. I will cover the bottom first.
4. Find an equivalent measurement that helps reach the target rate. Notice that the "mile" units align with each other, just like matching numbers align in Dominoes.

5. Since we have our units in feet, we can slide the extra piece of paper to cover the top portion of the original rate. Just like in step 4, we want to find an equivalent measurement that helps us reach the target rate. In this case, your students might not know the conversion from hours to seconds, so I will do it in two steps.

6. Slide the extra piece of paper down one row to focus on the "minutes." Find an equivalent measurement.

7. Take off the extra sheet of paper and you will be left with a good visualization of the 4 fractions needed to multiply.

8. Write the fractions, cancel the units, and multiply and divide like normal. There's your answer.


Ideally, your students might only use the paper template a few times and then they'll get the hang of it. The key thing that is different is starting with the original rate in the middle and working outward.

One thing to do that might be a little more hands-on is to use note cards instead of the template. This way the note cards can slide to be aligned to make the fractions even easier to notice.

Snake Game

A while back, I created a popular dice game called Snake (others call it Skunk) using Scratch. Scratch is a type of programming language created for young people or novice programmers. If you search through their galleries, you will be able to find lots of other math related activities.



Original link to this project