5 Tips to Help Middle School Math Students
The math homework dilemma – to give or not to give (IF you have the option in your district)? How much to give? To go over it all or only review some of it? What will be most helpful to your students?
Maybe your experiences have been similar to mine: I’ve adjusted my practices from year to year, sometimes spending a lot of time reviewing homework, but other times spending little; some years giving homework related to the lesson, other years giving homework that was basic skills practice; some years lots of problems, other years just a few. There seemed to be pros and cons to each.
Thinking about this topic yet again, I decided to look for some research to see how we can help students get the most out of the homework we assign.
Fall Activities Found!
Middle school students still like those fun seasonal activities:-)
Many years ago (I have no idea how many) I used this pattern coloring activity with my middle-schoolers. I don't remember where the idea came from, and I had even forgotten that I ever used it! However, I was looking through an old "November" file to find some ideas for a fun activity for a sub day, and found the tracers and examples in my file.
When I found it, I DID remember that the kids really enjoy this activity. They had fun creating the patterns and deciding what colors to include. So, I gathered materials (graph paper, tracers, colored pencils, thin black markers, construction paper) and left them for the sub, with these directions:
Using Your Time Effectively and Efficiently
Having the perfectly-run math class....that's been my goal, year after year. Somehow, in middle school, it has consistently tried to evade me!
In other posts, I've shared that I taught elementary math for years, and always had an hour for math class. That hour gave me the time I wanted to have good warm-ups every day (sometimes taking up half the class with one particular problem that led to additional discussion/extension!); the hour gave me the time to go over homework the way I wanted to. And it still gave me time for a new lesson and practice.
But when I got started teaching math at the middle school, with "44"-minute periods, that was all over. (They aren't really 44 minutes - the students get no time between classes for switching, so switching time comes out of the 44.)
Four Ways That Self-Correcting Math Work
Can Benefit Students
I have been teaching for more than 20 years. If you have been teaching for a long time, then like me, you may have used a certain strategy/instructional tool for a period of time, and then for some reason, stopped using it....and then after another period of time you came back to it, and wondered WHY (or when!) you stopped in the first place!
That was me today. I had made 20 copies of my Footloose answer key and had the students correct their own papers (they had worked on the Footloose activity for part of yesterday's class and then finished during today's). I was surprised by the thoughts that went through my brain as they were correcting - the main one being - "When did I stop doing this?!"
I do have students check their homework answers with the answers shown on the board (sometimes), but I don't give them each a detailed answer sheet to use, and I rarely have them grade their own classwork.
Here are my re-discoveries related to students correcting their own math work. Some of these may be particular to the topic we worked on (writing algebraic expressions from phrases, phrases from expressions, and evaluating expressions given a value for the variable), and the fact that the answer keys were detailed (not just the answer), but I'm sure I'd observe the similar things when studying different topics as well:
1) Students asked me more questions when checking their work with my key. Since they were working at their own pace and checking individually, they seemed to be more comfortable with verifying whether or not their phrases were ok (I didn't have every possible phrasing option on my key). Students who wouldn't normally raise their hands to ask in front of the class did ask me questions during this time.
2) Correct work is modeled on the answer key. Because I had several options for phrases on my answer sheet, they had to read each one to see if theirs was on the sheet, giving them a little more exposure to correct options. I also had the steps for evaluating each expression, so they could go line by line and have those steps reinforced, as they compared the work to their own.
3) Students were finding their OWN mistakes, rather than me finding them. I heard things like, "I copied the problem wrong," "I said 3 x 3 was 6!" "Oh, I put division for product." And I realized, as I did years ago - it makes so much more sense to them when THEY see the difference between the correct work and the mistake they made, rather than ME finding it....do they really know why I circle a mistake that they made on their paper if they don't take the time to ask me? When they find the mistake, they know what happened. I don't need to make those types of connections and observations. They do.
4) Students are engaged - they enjoy having the key! It was fun to see them with their pens or colored pencils, pointing at their papers, question by question, making sure they were being accurate in their grading of themselves, and then being sure to write the correct answer accurately (I did make them write the correct answers, using pen or a colored pencil, so the change would stand out).
I don't know what prompted me to copy the keys to use today, but I'm so glad I did. It's wonderful to be reminded of forgotten/lost practices that help students to think just a bit more.
Have you re-discovered any strategies/practices recently?
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Using the Date to Encourage
More Math Thinking
2) The other way I used the dates was to write the date so that students have to solve an expression for each number in the date.
It's been fun to see some students writing these in the corner of their notebooks during class! Others have asked to write their equations or expressions on the board during the last period of the day.
What I love about these ideas are that they are quick, can be done at any time (beginning of class, finished early time, closing of class, or in homeroom) and they help kids to expand their number sense and use some "out of the box" thinking. The "date as an expression" idea can also be expanded to challenge students: students can create their own expressions, students can solve the expressions (using the bar as a division sign - a student did this on his own one day!), and if you happen to make a "mistake," students can find it correct it!
I also look at the date-writing as a way to introduce notation my students haven't seen before, like the cube root, as well as reinforcing some concepts, like exponents. I don't know about your students, but mine often forget that 2 cubed means 2 x 2 x 2, not 2 x 3. Using the exponents in the date keeps bringing that concept back for review.
Update: I've started posting math dates at the beginning of every week on Instagram (always on Instagram) and Facebook (most weeks on FB), so if you'd like to use them, I hope you'll follow me on one of those platforms (if you aren't already).
Another update: I've created Math Dates resources for you to use throughout the year - these have been published by individual months and as a year-long resource.
Early last week, I was trying to think of a different kind of activity to help my middle school math students who needed more reinforcement with order of operations, and I decided to make a sequencing activity. I hadn't tried this before, so I wasn't sure about the best way to design it, but the activity ended up working quite well. Here's how I put this math activity together and used it with my 6th grade math classes:
Order of Operations Activity Design
For this math activity, I created 8 different
expressions, and then typed out the steps to simplify each expression. I copied the expressions and steps onto different colored papers, so that two expressions would be on the same color. I cut the steps apart into strips, and then put two expressions and their steps (of the same colored paper) into a baggie...I figured if I put only one equation in a baggie, the activity would be too simple. If I put two expressions of two different colors, it would be too easy. So I went with two expressions in the same color. That way they'd have to do some sorting of the expressions.:-)
Using the Order of Operations Activity
I put 3 baggies (6 different expressions and their steps) into a manila envelope for each group. Groups were mostly just partners, with an occasional group of 3.
I typed directions to include in the envelopes, and asked students to do their best to follow those directions before asking for clarification (some of the students worked on this activity, while others completed different activities, so I needed them to try to work through the directions themselves before I got to each group to discuss with them). Some students needed additional instruction, while others did not.
After students put the steps into the correct sequence (shown in the image above), they had to write those steps onto a recording sheet, pictured below.
In each of my math classes, students worked on this activity for about 15-20 minutes. Some groups completed all 6 expressions, while others completed only 2-3. A few more minutes would have been helpful for those students who didn't complete as many expressions, but I can revisit the activity with those students this week.
I will definitely use this again next year:)
To Read Next:
The other day I shared the Metric Matching activity that I used to help students work on their metric conversions (free activity found in that blog post).
We worked on this for a second day, using decimals in the meter category more often than we did with the first set of numbers the other day (these more challenging numbers are on the second page of the activity). It did take students longer to place the numbers appropriately this time, because they wanted to put all of the whole numbers in the meter category. It was fun to watch them try to figure out how many cm and mm these would be equal to, decide the numbers didn't work in the categories, and then rearrange them. It was also very difficult to be quiet and give help only if really necessary! However, some groups did need some redirection, and a little questioning, like, "If 4 meters is equal to 400 cm, can 4 meters also be equal to 0.4 cm?" was helpful.
As groups finished up with their matching, I gave them problem solving to work on together. This problem solving required students to complete metric conversions to reach their solutions. This is the first time these classes have worked on problem solving together, and the students did well explaining their thinking to one another and using the resources in the room to help them.