For Teacher Appreciation week, I created two FREE problem solving math wheels (they are in the same PDF file) - they can be used to teach problem solving strategies, be used as a center activity, or be used as a finished early activity. When complete, they can be added to students' binders/interactive notebooks to be used as references all year.
I hope you can use them! Just click the image to download.
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Have you ever thought about how ping pong helps kids practice math?
I love playing ping pong! I played it a lot as a kid and I play occasionally as an adult....we have a table in the basement:-) I would never claim to be a SERIOUS player, but I'm not bad!
I was playing with my daughter the other day, and it occurred to me that playing ping pong is a great way for younger children to practice their addition facts and some multiples of 5 (good for older kids too, if they don't know these facts very well). Now, this idea is based on the "serving rules" that we used when I was growing up. It appears (after I searched for info) that these are not the official rules any more, but since I'm not a professional, I'm ok with playing by the unofficial rules! The way we played is that the server switches every 5 points, and we played to 21 points.
So, here's where the math comes in....when you're playing, you need to know when to switch who's serving, so you need to know what adds up to the multiples of 5. When the score is 5-0, 4-1, or 3-2, serving switches. To switch servers at 10 points, players need to know that the score would be 10-0, 9-1, 8-2, 7-3, 6-4, or 5-5. When serving switches at a total of 15 points, the score possibilities are 15-0, 14-1, 13-2, 12-3, 11-4, 10-5, 9-6, 8-7. At 20 points, the score would be 20-0, 19-1, 18-2, 17-3, 16-4, 15-5, 14-6, 13-7, 12-8, 11-9, 10-10. The repetition of these facts throughout many games can really help kids learn them.
Over the years, I have noticed that students (in general) seem less aware of, and less automatic with, the digits that will add to 10. Playing ping pong is a great way for kids to practice these facts without thinking that they're practicing math (math in real-life!).
This is great for parents to do with their kids, but also - a mini ping pong table in the classroom sounds like fun!!
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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Do your middle school math students like to play math games? Mine do, but over the past few years I've noticed that many of them aren't familiar with some of the games I played when I was a kid, like Yahtzee, for example. So, as we started working on converting fractions and decimals, I decided to create a game to make practicing the conversions more fun AND give them some more game experience! I based it on the idea of Yahtzee:-)
Here's how it works:
Students roll four dice, and pair the dice up to create "target numbers" that are either decimals or whole numbers.
For example, a student rolls 1, 2, 4, and 6. From these dice, the student may create any two of the following decimal (or whole) numbers:
½ = 0.5 4/1 = 4
¼ = 0.25 4/2 = 2
1/6 = 0.1666... 4/6 = 0.666...
2/1 = 2 6/1 = 6
2/4 = 0.5 6/2 = 3
2/6 = 0.333... 6/4 = 1.5
Once a player has chosen two target numbers, he or she finds the score by adding the dice that were used for each decimal (or whole number). If the player chose to use 1 and 4 to get 0.25, he or she adds 1 + 4 for a sum of 5 to place in the score column. If the second choice used 2 and 6, to equal either 0.333...or 3, then sum of 8 would go in the appropriate column as the score.
On the next roll, this student rolls 1, 1, 3, and 5. This student can pair 1 and 1, to get 1, and pair 3 and 5 to get either 0.6 or 1.666... The score for 1 is 2 (1 + 1) and the score for 0.6 (or 1.666) is
8 (3 + 5).
In many cases, students' scores will be the same, but some of the decimals can be found with different combinations of numbers (1 and 3 = 0.333..., and so do
2 and 6, so students could have a score of either 4 or 8). Some students will notice this sum difference and go for the combination that will give them the higher score....bringing in the possibility of using some strategy, for those higher level thinkers.
The students have really enjoyed playing this game. They do need a few examples at the start, to understand exactly how the game works, so if you decide to try the game, be prepared to go through a few turns together.
You can create a score sheet like this on your own, or go to TPT and use what I've created. Detailed instructions are included, and a complete answer key of highest and lowest possible scores for each target number are included as well. This is handy to quickly check student score cards as you check in on their games.
If you give it a try, please let me know how it goes!
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In my early years of teaching, I didn't always know what to say when students told me they didn't have time to do their homework (other than something like, "You must have had some time between 4:00 and 9:00!). There were all kinds of reasons - they had sports practice or a lesson, or they had to go to their brother's or sister's game/practice/event of some kind; or their parents took them shopping or out to eat. At that time I had one child (who was 2 when I started teaching), so I didn't have the experience from a parent's point of view of making sure I was getting my kids to their activities, getting done all the house-related things, and also making sure they were getting their homework done. This made it a little difficult for me to relate to the students' situations, but I tried to help them think about how much time they did have to do their work.
Being involved in activities definitely reduces time for schoolwork, but it
doesn't mean that schoolwork can't get done. Students can learn to manage their time, but they need to be shown how. There are many of us who, as adults, may not manage our time very well. And if a parent is not great at managing time, how will he or she teach their children to manage theirs? Even when adults are good at managing time, they don't always think to teach their children how to do what they do.
Because their parents might not talk about time management, I've spent many years teaching students (5th and 6th graders) how to find their available work time. I make these planner-type pages and have students fill in a sample week, so they can see where their available time is. When they fill in the practices, games, lessons, sibling practices, etc, they can then see what time is left in the day. If homework is assigned Monday and brother has practice, the student can see that they have a chunk of time from 3:30-6:00 (when they probably also eat dinner) and then 8-9:00. If homework completion can fit in those time slots, great! They can plan to use that time wisely. If it's not enough time, then they need to use another strategy to get things done. One of the fun parts of using the calendar/planner is the color-coding! When I used this for my own planning, I color-coded according to person (my son was green, oldest daughter orange, youngest purple, and I was blue:-).
If their chunks of time aren't big enough, students need to find other ways to complete their work. One of the strategies I share with students is to take backpacks and homework supplies in the car with them. When one of my three children had practice (they're all beyond this point now), the others brought any work they had to do. Sometimes homework was completed sitting on a blanket in the grass or sitting in the bleachers. Sometimes it was completed in the car while we waited. Do distractions occur when homework is done this way? Yes, they sometimes do. But, to me, using that time to work was better than losing an hour or two (or more, depending on travel time!) and then having to do everything after we got home (especially if we still had to have dinner!)
I also suggest that students try to study while they're driving to an event. They can read over notes and quiz themselves. If there are several people in the car, one person can quiz another. The student can quiz their parent as well, or explain information to mom or dad....this is a great way for a student to be sure his knowledge is solid.
I always suggest that students put upcoming tests on their calendars and then work backwards to schedule their study time....so they could label the driving time as study time. Projects should go on the calendar too, so students can again work backwards to fit in the necessary time to complete them.
The great thing about a week at a glance like this is that students don't have to depend on someone buying them a planner or printing out pages for them. They can write out their own schedule on their own paper and design it any way they'd like. Then they can post in it their room, on the frig, or keep it in a school binder.
As I mentioned, in the early days, I didn't quite know how to respond to students who didn't have time to do their work. But now, this is something I teach every year, to help avoid those "I didn't have time because...." statements :-)
First Day of Class
For several years now, I have used this pentomino activity on the first day of math class. I've written a few posts about it (on my old blog), because each year I find more benefits to using the activity.
It's a seemingly simple activity, and when I first explain it, students think it'll be a piece of cake. BUT, they find it to be quite challenging. And I find it to be an excellent way for students to start working cooperatively at the very beginning of the year.
How it Works
Students work in small groups of 3 or 4 to create a rectangle using all 12 of the pentominoes. That's it - make a rectangle, with no gaps or overlaps. Students are given a frame to work within (as shown in the photo). As I said, it sounds pretty simple, but if you've attempted it yourself, you know that it's not as easy as it sounds.
It takes the groups quite a while (and some never finish if I don't give some hints), which is great, because they are really thinking, talking to each other, sharing ideas, speaking their thought processes, working together, and being persistent. In the years that I've been doing this, I have yet to find a student who wasn't engaged. This is the type of activity that allows all students to persevere, regardless of their background knowledge in math. All students can manipulate the pentomino pieces and offer suggestions, and while some students are strong in certain areas of math, others are stronger spatially; this introduction activity allows them all to have success.
What Teachers Learn/Observe
While this activity is great for the students, it's also great for me! It gives me the opportunity to observe the students and start learning about them - how they approach tasks, how they interact with others, who will try to take charge, who will sit back and watch/listen. It's a fantastic learning time for me.
In my classroom, I only had 12 by 5 inch frames, which I inherited from someone along the way. I decided, though, that I wanted to make frames with different dimensions (10 by 6 and 15 by 4), so I made those on the computer (on 8.5 x 11 pages).
So the pentominoes would fit into these frames, I had to make the pentominoes smaller. So, now I have 3 different sizes of pentominoes (once I cut them out and laminate them!)
Having the different sizes and different frames allows me to give groups slightly different tasks, if I choose, or will give the groups who finish a new configuration to figure out.
If you'd like to try using these pentominoes, click on the Pentomino Exploration picture below to download.
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