Using Your Time Effectively and Efficiently
Having the perfect 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.)
I tried to use the same kind of warm-up I used in elementary school (a word problem to practice a particular problem solving strategy, including a written explanation). Sometimes these took 20-30 minutes. So, that left only 10 -20 minutes to review homework, teach a new lesson, and practice.....but that didn't work well. So I cut these warm-ups down to once a week and let them take the whole class period. But I felt like warm-ups once a week wasn't enough.
Then I bought a warm-up book (because I really wanted warm-ups each day - it's the best way for me to start my classes). These were shorter (though not always as challenging as I wanted), but so short that some students who got to class first finished before others even arrived (and some of the problems were just too simple). Others just took longer to get done.....so those who were done needed something to do while they waited for the others to finish. Eventually I wrote all of my own warm-ups, so I was very happy with what we were covering, but still not happy with the how. (One step in the right direction!)
My next issue was reviewing homework. I wanted to go over all (or most) of the problems. I wanted to be sure that I answered all the questions anyone had (and discussed certain problems even if no one asked the questions). So homework often took a long time to go over.
I struggled with the best balance of warm-ups, homework review, lesson, and practice for a couple of years, I have to admit. And no one that I taught with seemed to have the same issues as me. Part of that was because they weren't using warm-ups like I was, so they weren't losing that chunk of time at the beginning of class. But I knew the warm-ups and our discussions were beneficial to the students in the long term.
Here's what I've finally landed on that allows us to use our math classes as efficiently and effectively as possible:
1) Warm-ups are homework. My warm-ups are only 2-3 questions per day, so is isn't a long assignment. Even when it's added on to other homework, it doesn't take that much extra time. There are times when students don't have the knowledge to answer a warm-up question (because we may not have learned the concept yet), but they have to at least give it an attempt.
2) Warm-ups are discussed in groups for the first 5-7 minutes of class. Students get to class and immediately take out the warm-ups and review the answers with their group members (my students sit in groups of 4-6). This allows for math discussion (love it!); students help each other if someone didn't understand a certain problem. I circulate during this time to listen in, check answers, and help any groups that need help.
3) When the warm-up discussion is done, students self-check homework (another 5-7 minutes, depending on # of homework problems). I put all the answers on the board before they come to class, so that as soon as they finish the warm-up discussion, students can start checking their homework. This again gives me time to circulate, check for homework completion and help students that have questions. I normally pick out one or two of the more challenging problems to discuss as a class.
4) Students prepare for the day's lesson. For those who get done with the warm-up and homework checking before others, I'll have a question on the board or an activity to begin that pertains to the new lesson for the day. I make it something that isn't necessary to the lesson so that those who took longer with the warm-up and homework won't miss something necessary to the lesson.
5) New lesson and practice. Now that warm-ups and homework are down to about 10-15 minutes per period, we have 25-30 minutes for the new lesson and the practice:-)
Do you have 40(ish)-minute math periods? What does your class structure look like?
Making them work in 40-minute class periods
I taught elementary school for 12 years and I loved my centers! They were great. Math class was always an hour, and we had five computers in the classroom, so having a computer center was always an option.
Then I moved to middle school. Math was 44 minutes (minus time for switching classes.....so more like 40 minutes). How could I fit more than two rotations in a 40-minute period?? I longed for block scheduling (our district has never had it)...that would make it so much easier to complete center rotations! For the first year or two of middle school, I kind of gave up on the idea of centers...the activities I wanted students to complete took longer than 20 minutes. So, that would be enough time to finish 2 rotations, IF students started the second they walked in the door and then had no time to clean up/organize at the end of class. But eventually I needed to get my centers back, so I experimented with a few different set-ups before I landed on a structure that works.
I willingly admit that I have not found a perfect solution....40 minutes is just too short a time-period for math! However, I've figured out what works for me, and maybe it can work for you, if you also have short math classes.
My centers are:
* One per day
* 30 minutes a day
* For 3-4 days, depending on the topic.
There are many ways to group and assign tasks, but these are the grouping/activity options I normally stick to:
1) When we only do three days, I create six groups and prepare two sets of materials for some tasks. Students will all complete three tasks over the course of the three days, but they might not all complete the same three...it depends on the topic, their needs, and my goals. The image to the right has two different examples of how I might assign the tasks.
2) When we do four days, I create four-six groups (if my class size is the usual 27-30). If I have only four groups, I usually assign them each a different task and then rotate through those tasks over the four days. If I have five or six, then I'll have two groups complete the same task on the same day, similar to the three-day example.
My students are not ability-grouped, so they finish activities at various times. I decided that I have to be happy with some students/groups finishing early and others not finishing (or finishing during a free, non-math period). Doing one center a day, for about 30 minutes allows for some flexibility here. If group members finish early, they can do the following:
1) Finish another center activity, if they had something unfinished.
2) Complete a color by number from our "finished early" resource bin.
3) Use the trivia cards - a set that isn't one of the center activities. (click here to grab this free resource!)
4) Use the pentominoes that we use on the first day of class - there are always students who want to complete this challenge.
5) Use a technology source for additional math practice, if we have extras available.
Before We Use Centers
Before we start using center rotations, I make sure students have a complete understanding of expected behavior AND of the activities they'll be completing. We complete the different activities together with different concepts at the beginning of the year, and then I use those activities in the centers, using some of the same ones each time.
1) Footloose task cards:
Students are up and around the room for this, so I typically assign only one or two groups per day.
2) Truth or Dare Game
(with paper and pencil):
This version is a group game, so I only assign one group per day, for less "noise" in the room. They have to talk, and they definitely have fun with this one!
OR Google Truth or Dare:
I created a digital version. This allows two different groups to complete the same activity, but one group can use whatever technology we have available. This version could be played by group members independently or in teams.
3) Color by Number:
This is a quiet activity that provides some self-checking practice. Students can also check answers with their group members if they'd like. (They often don't finish the coloring during the center time, so I have them complete all the problems first and then color....they can come back to the coloring if they finish an activity early on another day.)
4) Math Wheel:
I use this as a teacher-guided center sometimes, but I can also use the wheels as an independent center for review - students can copy the notes and complete the practice on their own. Coloring is similar to color by number - that part is last and they can return to it later. These get added to students' binders to keep for the year, so they can finish coloring any time they finish something early.
5) Problem Solving:
I make this a collaborative center (I love when students have math conversations!), but it could be independent work.
6) Math Trivia Cards:
This is a fun activity to practice more general knowledge, with less calculation involved. Students can just quiz each other and share correct answers, or they can record their answers to be checked later. I have three sets so far - Numbers and Operations, Geometry, and Algebraic Concepts (link to download them is above.)
As you can see, some of the center rotations require students to work together, while others allow them to work independently. I like to have this mix, so students can share ideas and solving methods but also have time to work with the concepts and skills on their own. I also like to compare the work they did alone with the work they completed with others.
When students complete a center assignment, I have them put that assignment into a specific tray in my classroom. I go through the trays at the end of each day and use my checklist to record who's handed in their work.
I do grade all of the center activities....sometimes it takes me quite a while!!
I have sets of 4-5 center activities for each of the topics below, so these are the ones I use/have used. I don't use all of them every year (because, time!). I pick and choose based on student needs, time of year, etc. If you're interested in trying any of them, click the titles to see them in my TPT store. (I have 2-3 activities for many other topics, but won't bundle those until I have 4-5.)
Area and Perimeter
Fractions, Decimals, Percents
Mean, Median, Mode, Range
Order of Operations
Percent of a Number
Ratios and Proportions
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.
Enter to win one of four $25 TPT gift cards! Good luck!
Surface area is a such a fun topic for students to explore! To really understand what surface area means, students need to interact with three-dimensional actual objects. Before we talk about formulas or how to calculate, we spend time discovering how to find surface area in our own ways.
I give students every-day items to work with. Typically, we use product boxes (rectangular prisms) with different dimensions, and I ask the students to visualize and then draw what the boxes would look like if they were taken apart and laid flat. Most students take about 5 minutes to complete their drawings, depending on how detailed they choose to be, and for the most part, they do a very good job drawing the nets of the boxes. Next, I have them spend a few minutes comparing their nets with group members, deciding whether those nets are reasonable representations of the object (even if they are drawn a little differently), and determining whether anyone appeared to be missing anything (some students will draw only five sides, and their group members are able to help them figure out what's missing).
After drawing their nets, I assign the groups two tasks - to find the surface area of their particular box and to determine a formula for the surface area of rectangular prisms. At this point, we have already studied area, so the only thing we discuss before they set upon their tasks is the actual meaning of the term surface area....we brainstorm the possible meanings and agree on the defintion. Then they set off measuring and calculating.
Most groups determine the surface area of their by the end of the class period, but normally none of the groups are able to decide upon a formula (we only have 40 minutes). So, we continue for a second day. While some groups are able to write a formula that reflects a correct understanding of the concept (though not written correctly "variable-wise"), others often remain stumped. Even though they are stumped about writing a formula, the "stumped groups" are usually able to explain to me HOW they found their surface area. Most of them explain that they found the area of the front and multiplied by 2 because the back is the same; they found the area of the top and multiplied by 2 because the bottom was the same, and the same idea for the sides; then they added those three sums together. Other groups find the area of all six surfaces and add them all. Some groups will find the area of the 3 different sides, add them and then multiply by 2. Based on our conversations, I know when they have found a correct way to find the surface area (or can then guide them if they are off track - the conversations are so important!). When it comes to writing a formula, some groups get very close, but have to be guided toward naming the length, width, and height with different variables.
For those groups that are able to finish fairly quickly (correct formula and all!), I have them work on determining the surface area of a triangular prism (I keep a Toblerone box on hand to use:-)
In the end, we share and discuss the formulas as a class. The students really enjoy this activity - it's challenging but achievable:-) Giving the students the chance to explore the concept and to construct a formula based upon their understanding of surface area is a great use of class time!
Once the exploration is complete, we can move from the concrete to the more abstract notes. I created this Surface Area Math Wheel for students to keep in their notebooks. I included the nets on it so the visuals are always there for them, in addition to the formulas. They love it!
Box-and-whisker plots are a brand new concept for my 6th-graders, and when students are first introduced to them, they seem a little scary. However, with some structured directions, students catch on very quickly.
I break down the box-and-whisker plot into 5 steps, in order to plot the 5 points needed to create the box and whiskers:
1) Order the data set from least to greatest.
2) Identify the smallest and largest values; place those points on the number line (above the number line).
3) Identify the median and place that point on the number line.
Students need to remember that if there is an even number of numbers in the data set, the median will be the mean of the two middle numbers - even though they've found median in the past, many students tend to need this reminder.
4) Find the first and third quartiles and place those points on the number line. This step can be tricky for students...I've found it to be the step that most often throws off their box. Here's what I've noticed: when there is an odd number of numbers in the data set, it's a little easier for students - the median is not included in the upper and lower halves of the data, so they are ok with circling the halves on either side of the median and then finding the median of each half, as in figure 1.
However, when the data set has an even number of numbers, students need to remember that the median is between numbers and that exactly half of the numbers are in the upper half of the data and half are in the lower, as shown in figure 2.
The common mistake that students make is to assume that since the two middle numbers (in this case 6 and 7) were used to find the median, they aren't part of the upper and lower halves. This throws off their 1st and 3rd quartiles. I've found it's important to spend extra time on the different scenarios possible in this step. I've also found that drawing that middle line to represent the median is a very helpful visual.
5) Draw the box and whiskers:
a) Draw a box, with the end lines going through the points of the first and third quartiles.
b) Draw a vertical line through the median.
c) Draw lines from the box to the least and greatest values.
I created this notes/fold it up a couple years ago, to help guide my students as they began creating box-and-whisker plots on their own.
I created two versions - a blank one for students and a completed one for me:-) Using the blank version, I walk the students through their creation of the box-and-whisker plot. And when we're done, they have the notes for their independent work.
The only folding part of this fold it up is the section at the very bottom that has the definitions of the vocabulary. Students will need to cut the vertical lines along the bottom, fold them up, and then write the vocabulary words on the outside of the flaps (quartiles, first quartile, third quartile, variation, interquartile range).
When students miss the instruction due to absence, I give them a copy of the completed version on their return.
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!!
I know the first thoughts many people have are the ability to work well with preteens and a degree in education. However, those are just the basics.
I’ve discovered to be successful as a middle school teacher, you need a certain skill set. While I learned some of this in school, most of it I learned through experience.
After all, working with middle school students for years teaches you a few things.
Honestly, I think this is a key skill for every single teacher, no matter what age group they teach. Students aren’t always happy to be in class or eager to learn. This means I have to be persistent and keep working with my students, no matter how stubborn they might be. Of course, sometimes persistence also means taking the time to figure out why a student’s having problems.
Patience and persistence go hand-in-hand. Naturally, working with a group of preteens that are just starting to deal with all kinds of new hormones is going to take patience. This is the age where kids start to act out more and push boundaries. It’s easy to just lose your temper, but I’ve developed more patience than I ever thought possible. Trust me, it’s well worth it.
3. Engaging Teaching Style
One of the main purposes of my site is to promote a more engaging and active teaching style. Students learn better when they’re engaged versus just sitting and listening. I’ve found the more I let students interact during a lesson, the more they remember later.
I know it sounds cliché, but every day is different as a middle school teacher (yes, for any teacher:-). As I mentioned, students are going through numerous changes during this time. I think one of the most important skills for teachers to have is adaptability. Being ready for any situation is crucial. It also means you don’t let your students take you by surprise (if possible, haha).
5. Social Awareness And Empathy
As middle school students deal with new emotions and social situations, middle school teachers need to be socially aware and empathetic. In fact, empathy actually helps to engage students. I’ve found it makes it easier to relate to students and figure out what they need. With the increasing amount of bullying, teachers also have to be socially aware of what’s going on in students’ lives and look for any signs of problems.
Formal education is important, but cultivating the above skills takes you from a teacher to an incredible educator and role model.
Here's to the skills of middle school teachers (and all teachers, of course)!!
I know lots of people use beach balls in the classroom, but I haven't used them in such a long time that I thought I'd share my excitement about finally getting around to getting new ones! I have a little bit of a beach theme in my room this year, so that motivated me to get some beach balls again. I ordered a pack of 12 and am writing different math skills practice on them - so far I have multiplication facts, exponents, fraction/decimal conversions, and common measurement conversions. I have 12 beach balls to fill with math, so I need to decide on more topics. I think I'll do square roots, division facts, math vocabulary...I need to keep thinking:-)
Our math classes aren't that long, but I figure I can squeeze in 5 minutes at the end of class once or twice a week to toss the beach balls around for some quick facts. With so many different beach balls, I could even differentiate and have 3 groups tossing at a time, depending on their needs!
Do you use beach balls - if so, how?
This post is from my old blog, and was written in April, 2015, but I thought it was worth transferring here and sharing:-)
Today, as my students were working on a color by number in math class (which I thought was a fun, different way to practice math), one of them asked "How does coloring help with math?" The question was asked with a "there's no reason I should have to do this" attitude. I explained that it helped with motor skills and helped one to use the brain in a different way, and that exercising the brain in different ways could help in all things that require thinking (not just math). I don't think he really appreciated my answer:)
So, I decided to do a little research, to see what I could find. Most of what I found (not a super-long time of searching, because I didn't have that much time!) was related to the benefits of coloring for young children (and did relate to math skills) and for adults. Here are a few things that I found, as coloring relates to adults:
According to the Huffington Post (10/13/14), coloring benefits adults (and I would assume children as well) because it "generates wellness, quietness and also stimulates brain areas related to motor skills, the senses and creativity." In addition, psychologist Gloria Martinez Ayala states that when we color, we activate different areas of our two cerebral hemispheres. "The action involves both logic, by which we color forms, and creativity, when mixing and matching colors. This incorporates the areas of the cerebral cortex involved in vision and fine motor skills [coordination necessary to make small, precise movements]. The relaxation that it provides lowers the activity of the amygdala, a basic part of our brain involved in controlling emotion that is affected by stress."
According to PenCentral, coloring benefits adults in helping them to maintain fine motor skills -this requires extra work by your brain to coordinate your actions and muscle control in your hands and arms. Coloring can help delay the loss of fine motor skills as people age. Coloring may also help fight cognitive loss, especially
if challenging pieces are completed every so often.
I didn't necessarily find research to answer my student's exact question, but what I found was quite interesting! If anyone knows of other articles or published research to support the role of coloring in improving math skills, please let me know!