This post is transferred from my old blog - I can't believe it's been nearly three years since
I wrote it (Jan 13 of 2015)! I'm glad to say that I'm just as dedicated to my workouts as I was when I wrote this:-)
I don’t know about you, but I love my workouts. They do so much for me, mentally and physically, and I really miss them when things come up that cause me to skip them. I miss them so much that I often get up at 4:30 am to be sure I get some workout in, just in case my day ends up having other plans for me.
Why is it important for teachers to work out (besides the usual health reasons)? These are my top 5 reasons: 1) Exercise is a great stress reliever. How many days do you come home stressed out over the events of the day? Still thinking about things that kids (or parents, or administrators) did that got you worked up? Do you bring that stress home with you or leave it at school? I know I have trouble leaving it at the door, but when I can go jump on the treadmill or the elliptical and pound that stress out, my mind definitely becomes more free. 2) Working out can renew your energy level for the rest of the day. This is especially true if you can do it right after school. I usually have some grading (or planning) that I bring home, or I need to help my daughter with homework during the evenings; when I take that exercise time right after school, I get recharged for the evening. 3) It helps you avoid snacking. I don’t know about you, but when I get home, I feel like eating EVERYTHING I can get my hands on, (and I'm often tempted to choose foods that aren't very healthy!) When I work out, I don't have the same snacking urges. 4) Creativity Research shows that exercise helps memory and stimulates creativity. It's a great time to run lesson/activity ideas through your mind; somehow that extra physical activity gives your brain the boost to make those lessons more engaging/exciting/interesting! 5) Sleep better! Extra physical activity helps me sleep better. What teacher doesn't need to get good sleep? Who else loves their workouts??
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I’m a firm believer that one of the best ways to learn is by playing games. It’s just more fun and students don’t even realize how much they’re learning.
While any game that helps kids learn is a winner in my book, I have some wonderful middle school games and activities I’ve created to use at home or in the classroom. Truth or Dare Math (and ELA) GameRemember playing Truth or Dare when you were younger? I’ve brought the concept to the classroom and incorporated math and language arts concepts (and Google classroom!). Students can choose a Truth, which is a one-point questions about the concepts. Or, they can boost their score faster with a more challenging Dare question. It’s one of my favorites among middle school games and it really gets the students excited. Decimal DiceI’ve always loved the dice game Yahtzee!, so I decided to create my own little spin on it. Students love rolling the dice and creating fraction pairs. The challenge comes when they have to convert those fractions into decimals or whole numbers. It only takes a few turns before students learn the rules. It’s an incredibly engaging game for small to large groups. Footloose Task Card GamesWhy should learning math concepts be boring? I’m always looking for and creating middle school math games to get students more engaged. With Footloose Task Cards, students answer various types of questions about math concepts - sometimes they are basic knowledge questions, sometimes they're word problems, and sometimes they're quite challenging. It's easy to differentiate using these cards:-) Students move around to get new Footloose cards each time they complete one, and they write all their answers and work on their Footloose grids. It's a great way to keep students practicing and moving - and it's amazing how quiet they are during this time! Math Color By NumberColoring for adults is one of the biggest trends at the moment, and it's become a great way to help students practice math concepts:-) I’ve put together a fun bundle that uses the color by number approach to make it more fun to learn and practice probability, algebraic expressions, prime factorization, combining like terms and more. While I do offer each separately, the bundle’s a great resource to have on hand as practice for a variety of math concepts for 6th and 7th graders. I could list my own middle school games and activities, and those of others, for days. But for now, try out the ones above, check out the other activities I’ve created on Teachers Pay Teachers and keep coming back to the blog for more games and great resources.
How often have you taught fraction division to your students only to find them "flipping" the wrong number? You may have taught them to "skip, flip, flip," "invert and multiply," or "multiply by the reciprocal." You may have listed out the steps, or taught them a nifty song, but somehow they
still flip the wrong one or they forget to flip at all.OR they change a mixed number into an improper fraction and seem to subconsciously think that since they did something to that mixed number, the flipping had already occurred...and then they don't flip anything. Why does this happen? I'm going to say that it happens because they don't see the sense in it - it doesn't mean anything to them.
So, I have another way to teach fraction division - perhaps you've heard of it, or you use it. I never learned it this way as a child, but I like it and it makes more sense to some students. I learned this method when I had a student teacher a few years back. She was teaching the fraction unit, and when her supervisor came in to observe and discuss, she asked if I had ever taught fraction division using common denominators. Having only learned (and then taught) to multiply by the reciprocal, of course I said no.
The next time she visited, she brought me a page from a textbook that explained dividing fractions using common denominators. These are the steps: Step 1: Find common denominators, just as when adding and subtracting and then make equivalent fractions (students are already used to doing this - hopefully). Step 2: Create a new fraction with the numerator of the first fraction over the numerator of the second fraction...this is your answer. Done (unless you need to reduce)!I was shocked - it seemed SO simple!
Check out this example - it's a simple one, for starters:
5/6 divided by 2/3. 1) Find the common denominator of 6 and 3, which is 6. This gives you 5/6 divided by 4/6. 2) The first numerator (5) becomes the numerator in the answer. The second numerator (4) becomes the denominator. Then reduce.
Let's look at another one, with mixed numbers:
1 and 4/7 divided by 1 and 3/4. 1) Convert the mixed numbers to improper fractions, which gives you 11/7 divided by 7/4. 2) Find the common denominator of 28 and make equivalent fractions. This gives you 44/28 divided by 49/28. 2) The first numerator (44) becomes the numerator in the answer. The second numerator (49) becomes the denominator. No reducing, in this case.
I've shown both methods to my sixth-graders. Some really like it. Others stick to the flipping method - but I don't know if this is because they like it better or because it was the first way they learned it.....most of them had been taught something about fraction division in 5th grade.
As far as teaching multiplying by the reciprocal - if students are going to use it, I think it's important that they understand WHY it works. It may be tough for them to understand, but if they learn the common denominator method first, the proof may then make more sense to them. I found a great article on the NCTM website that uses the common denominator method to prove why multiplying by the reciprocal works - check it out!
Recently I made two math wheels, to use to teach both methods of dividing fractions -taking notes will be more fun!
What do you think? Do you see any advantages or disadvantages to teaching fraction division using common denominators?
I love teaching fraction multiplication--particularly multiplication of mixed numbers. Why? Because I have fun explaining why multiplying mixed numbers DOESN'T work a certain way.
Inevitably, when we start multiplying mixed numbers, some students want to multiply the fractions by the fractions and then multiply the whole numbers by the whole numbers. And I can see why they might think that's ok - after all, when you add and subtract, you deal with the whole numbers and fractions separately. Sometimes, I think they don't want to be bothered with making improper fractions, because it's "easier" to just do 2 x 3 and then 3/4 x 1/2, haha.
So, every year, we end up having this discussion about why that just doesn't work. I enjoy showing/explaining that multiplying 2 3/4 by 3 1/2 means that ALL parts of 2 3/4 must be multiplied by ALL parts of 3 1/2. On the board, we make a list of the problems that would need to be completed: 2 x 3, 2 x 1/2, 3/4 x 3, and 3/4 x 1/2.
- Once we complete those problems, students can see 6 and 3/8 in that list of products (which would be the answer if they multiplied fraction by fraction and whole number by whole number), but there's also an additional 1 and 9/4 in there that are part of the final answer.
Now that we have all four products, we go through the process of adding them all together (finding common denominators, equivalent fractions,etc) and then reducing.....quite a bit of work to get to the answer:-)
Then we compare that to what we get when we convert the mixed numbers to improper fractions. The detailed example of completing four multiplication problems and adding the products proves not only that converting to improper fractions is necessary, but also that it's a lot faster! So,
Tip #1 is to show students WHY what they're doing isn't correct...show what the multiplication really means.This may also mean bringing out the graph paper and showing what 3/4 groups of 1/2 looks like, etc, in addition to doing the computation.
Canceling, or "Crossing Out"Tip #2 - Teach students to cancel, or "cross out" (or whatever you might call it), and show them why it makes life a little easier.I love teaching this aspect of fraction multiplication. It's hard for some students to grasp at first, but when they repeatedly see that if they don't cross out, they have to reduce at the end of the problem (with larger numbers, like 168/12), they start getting excited about finding how much they can cross out. In recent years, I've found that students aren't learning this in earlier grades as often as they used to--for many, the discussion we have in my classroom is the first time they've encountered it. Once I teach them the idea of reducing first, and we explore why it works, there are some that still want to stick with what they learned in earlier grades and reduce only at the end, while others get super-excited about the concept of making the numbers they're working with smaller at the start. I may be wrong on this, but it seems that the students who embrace it first are those who know their multiplication facts better and can more easily find the relationships between the numbers in the problem....a student who knows that 15 and 24 can both be divided by 3, for example, is more likely to go ahead and divide them by 3 than the student who can't see it because they can't remember/don't know what 15 and 24 are divisible by. Multiplying Fractions and Mixed Numbers WheelTip #3 - Give students a graphic organizer to help them remember the process. Some will need this and some won't, but it's handy to have in their binders to reference throughout the year. I recently created a fun math wheel, which is a great way to have students take notes about the concept, practice it, and then add their own personal, artistic touches.Do you have any special methods you use to teach the multiplication of fractions and mixed numbers?
I’ve heard this debated, and both sides make great points. So, do students need the fundamentals to be successful in math?
The answer isn’t quite black and white. Overall, the answer may be no, they actually don’t. However, it also depends on the fundamentals in question. The Bare BasicsIt’s not so much that students need to know math before doing math. It’s all about their thinking processes. These are the fundamentals that students need. For instance, it’s what Common Core is based around – learning the processes for thinking through math versus just memorizing.While some students already have those processes, others may still need some guidance. For example, a child that struggles with counting isn't quite ready to comprehend addition. Or, a child struggling with language skills may not be able to reason through a word problem just yet. This is where the bare basics come into play. Studies have shown that it takes multiple areas of the brain to do math. I love telling students this, so I can prove that math helps make the brain stronger – which is a great reason to learn it. It takes language, memory, temporal-sequential ordering, spatial ordering, attention and more to reason through math problems. Much of this is learned at an early age. For instance, when kids are stacking blocks by color or talking to you about the book you just read together, they’re building the fundamentals they need to do math and of course, a wide variety of other things. Building Upon The BasicsAdam Sarli showcases the perfect example of why children don’t need more than the bare basics before doing math. While it does help students to know more, they usually reason things out. It may not be the approach you and I would use based on what we know now, but for the kids, it’s a learning experience that helps them figure out why and how math works. Sarli talks about one student, Yarieliz, and how she learned to go from addition to scaling up by addition to multiplication without learning the fundamentals first. This happened as she reasoned through word problems. Students were encouraged to find their own way, and it worked. Fundamentals are important, but perhaps not always necessary. With the right problems, games and activities, kids can do math by using logical thinking to get from Point A to Point B, or in Yarieliz case, addition to multiplication:-)
I know the knee-jerk reaction answer to this might be no. After all, there are millions of distracting videos to make students forget all about school.
Yet, I do believe YouTube has a place in middle school. While it’s full of distractions, it’s also filled with educational videos. When used for educational purposes, YouTube is an invaluable resource for students, parents and teachers. Pick Out Videos Ahead Of TimeAsking students to just search for a video is a major mistake. I’ve been there. My advice is to find the videos you want students to watch. Give them the links or just show them in class to help get a point across. Middle school students love watching videos, so it’s more engaging to let them see concepts in action in a YouTube video. To them, it may be much cooler than their teacher. Of course, incorporating YouTube helps make you the cool teacher. Show Concepts In A Fun WayAs you know, I’m 100% for finding fun ways to educate students. I’m always on the hunt for games and activities. YouTube is filled with those. Even if I don’t show them the video, I learn new ways to teach to better engage my students. It’s always amazing to me how people on YouTube are able to create such entertaining videos about things that most middle schoolers would consider boring. Finding The Right ContentThis is where I struggled most at first. After all, there’s a reason so many schools actually ban YouTube. I did have to do a bit of searching to find the type of content I wanted, but it was well worth it. I was thrilled to run across the Education category. It covered everything and set me on my way to finding unlimited resources for teaching middle school. The NEA has a great resource on using YouTube in the classroom, even advice on creating your own videos. I could list numerous YouTube channels to help you get started, but this post simply isn’t long enough. Here are few sites to start your search: - 20 Excellent YouTube Channels For Math Teachers (kind of a personal favorite)
- 197 Educational YouTube Channels You Should Know About
- 10 Best Channels For STEM Education On YouTube
I’ve always thought language and math skills go hand-in-hand. After all, without strong language skills, solving word problems (and sometimes even understanding directions) is rather difficult.
Plus, language lends itself to logical reasoning. But, I wondered what effect knowing two languages might have on learning mathematics. Currently, the conclusion as to whether it’s helpful or not is still up in the air, but I did find some interesting ways bilingual students and adults use their skills in math. Potential Brain BenefitsIn such a diverse society, I can’t help but feel that being bilingual gives students an extra edge in life and helps them connect with a wider variety of other students. But, there are also studies that show the brain itself benefits from knowing two languages. One benefit I zeroed in on was improved attention. When bilingual kids and adults switch between languages, they also enhance their executive function skill set. In layman’s terms, they’re able to stay more focused and switch tasks easier without losing their train of thought. This also means they may be able to better switch between different mathematical concepts too. Language Does MatterOne in five kids in the United States speak two languages. However, this doesn’t mean they’re as great at math in both languages. Studies show varying results in this area. For instance, I discovered a study that disproved the original theory that students learn math better when it’s taught in the first language they learned. The study was actually performed with teachers, but it showed that the teachers responded almost equally in both languages. They answered slightly faster, though, when the problems were in the language they taught in, not necessarily their first language. So, my belief from all this is students learn math equally in both languages. However, they may work through problems faster and potentially grasp concepts better when math is taught in the language they use most. Overall, there’s little evidence that being bilingual has any real impact on learning mathematics. But, I say if a child is able to learn the intricacies of two languages, they just might be able to better understand a third language – math.
During my second year of teaching, in the early 90s, our state testing began to include a greater focus on problem solving and writing in math. Over the next couple of years, we used standard sentence starters to help students practice explaining their problem solving process, so they would be well-prepared for the test. These were starters like:
“In this problem, I need to….” “From the problem, I know….” “I already know…” “To solve the problem, I will…” “I know my answer is correct because…” Using these starters, students ended up with several paragraphs (some short, some long) to explain how they approached and solved the problem and how they knew they were correct. Sometimes this took quite a long time, but it was helpful, because it made many students slow down and think a bit more about what they were doing. They took a little more time to analyze the problem (rather than picking out the numbers and guessing at an operation!). I was teaching 5th grade at this time, in elementary school, and we had a full hour for math every day. So, fitting in problem solving practice a few times a week was easy, after students understood the process. I really liked spending the time on these problems, because they often led to discussion of other concepts, and they reinforced concepts already learned. I used problems from a publication that focused on various strategies, like Guess and Check, Work Backwards, Draw a Picture, Use Logical Reasoning, Create a Table, Look for a Pattern, Make an Organized List. I LOVED these… I really did (do)! And the students I taught during those years became very good problem solvers. When I moved to 6th grade in middle school, I tried to keep teaching these strategies, but our math periods are only 44 minutes. I tried to use the problem solving as warm-ups some days, but it would often take 30 minutes or more, especially if we got into a good discussion, leaving little time for a lesson. I found that spending too many class periods using the problem solving ended up putting me too far behind in the curriculum (though I'd argue that my students became better thinkers:-), so I had to make some alterations. I liked the format of the sentence starters, but the biggest time-consumer was the writing part. We had to decrease it. Instead of writing so much, we started to:* highlight/underline the question in the problem * shorten up the writing to bullet points * highlight/underline the important information in the problem Problem Solving StepsNow, when I teach these problem solving strategies, our steps are: Find Out, Choose a Strategy, Solve, and Check Your Answer. Find OutWhen they Find Out, students identify what they need to know to solve the problem. They underline the question the problem is asking them to answer and highlight the important information in the problem. They shouldn’t attempt to highlight anything until they’ve identified what question they are answering – only then can they decide what is important to that question. In this step, they also identify their own background knowledge about the concepts in that particular problem. Choose a StrategyThis step requires students to think about what strategy will work well with the question they’ve been asked. Sometimes this is tough, so I give them some suggestions for when to use these particular strategies: Make an Organized List: when there are many possible answers/combinations; or when making a list may help identify a pattern.Guess and Check: when you can make an educated guess and then use an incorrect guess to help you decide if the next guess should be higher or lower. This is often used when you’re looking for 2 unknown numbers that meet certain requirements.Work Backwards: when you have the answer to a problem or situation, but the “starting” number is missing.Make a Table: when data needs to be organized; with ratios (ratio tables).Draw a Picture or Diagram: when using the coordinate plane; with directional questions; with shape-related questions (area, perimeter, surface area, volume); or when it’s just hard picture in your mind.Find a Pattern: when numbers in a problem continue to increase, decrease or both.Write an Equation: when the missing number(s) can be expressed in terms of the same variable; when the information can be used in a known formula (like area, perimeter, surface area, volume, percent).Use Logical Reasoning: when a “yes” for one answer means “no” for another; the process of elimination can be used.SolveStudents use their chosen strategy to find the solution. Check Your AnswerI've found that many students think "check your answer" means to make sure they have an answer (especially when taking a test), so practice several strategies for checking: * Reread the question; make sure your solution answers the question. * Redo the problem and see if you get the same answer. * Check with a different method, if possible. * If you used an equation, substitute your answer into the equation. * Ask - does your answer make sense/is it reasonable? Teaching the StrategiesI teach problem solving strategies as a unit, teaching and practicing each one, and then incorporate the strategies and our 4-step process as students approach problems throughout the year. They keep reference sheets in their binders, so they can quickly refer to the steps and strategies. Some strategies are used more frequently than others (Draw a Picture, Write an Equation, Make a Table), but it's important to know that others are possible. During the unit, I like to show them the same problem, solved with different strategies. For example, I often find that a 'Guess and Check' problem can be solved algebraically, so we’ll do the guessing and checking together first, and then we’ll talk about an algebraic equation - some students can follow the line of thinking well, and will try it on their own the next time; for others, the examples are exposure, and they’ll need to see several more examples before they give it a try. Doodle NotesThis year, I'm trying something new - I created a set of Doodle Notes to use during our unit. The first page is a summary of the steps and possible strategies. Then I created a separate page for each strategy, with a problem to work through, as well as an independent practice page for each. I also created a blank template, so I can create homework for students throughout the year, using the same format. I'm hoping that using the Doodle Notes format will make the strategies a little more fun, interesting, and easy to remember.
If you want to check out the Doodle Notes to see if you'd like to use them, click either of the Doodle Notes images.
Teaching math isn’t easy, but with the right resources, it’s much easier to connect with your students and improve your teaching practices.
I know you already have the basics, but I’m talking about things to actually help you teach, such as ways to make learning fractions a little more fun. As long as you have these five resources, you’re all set as a math teacher. You might even find your students enjoy learning math (at least some of the time!) 1. Pinterest BoardsI know Pinterest is often about recipes and wedding planning, but I can’t tell you how many great resources I’ve found on there. I'm sure you've found some too! Entering search terms like “math” or “teaching” or specific topics like “equivalent expressions” or “dividing decimals” brings up numerous pins and boards. Fill up your own boards with related resources so you have a place to turn when you're in need of a quick idea. From teaching tips to games, there’s a little of everything. 2. Lesson PlansSometimes it’s hard to come up with a great lesson plan....you just get stuck. When I started looking online, I was surprised to find so many great lesson plans for all grades and subjects, including math. For me, it’s a great way to get ideas, even if I don’t follow the exact plan. I love sites like PBS Learning Media and TeachingMath.org, which have a variety of lesson plans and activities to help inspire all of us teachers. 3. Teaching Groups/CollaborationThere are many groups of teachers from different parts of the world who have found each other through social media and have created or joined Facebook groups. These groups share teaching tips, discuss teaching methods and philosophies, and offer support and advice. One group I'm part of is called Let's Talk Teaching Teens - this one is for teachers of middle and high school teachers. It's exciting to share with, learn from, and help teachers around the world! 4. Games, Puzzles and MoreMy favorite resource for math teachers is actually a bunch of different resources. I’m talking about activities, games and puzzles to keep students engaged. A few great places to start include: - Problem of the Week and Free Resources from yours truly
- Big List Of The Best Websites For Teaching Math (massive list of great resources)
- YouCubed (my absolute favorite site!)
5. Books! I love reading books to find ideas and improve my teaching, and there are a couple that I think are absolute must-haves. These are by Jo Boaler; I've read others that are good, but I think hers are amazing: When you’re armed with the right resources as a math teacher, it's so much easier to help students learn to love math.
Sometimes, when I tell people that I love teaching middle school, they look at me like I’ve grown several new heads. They just can’t fathom what could be so great about it. I've taught middle school for 12 years, so I've had a bit of time to figure out what I like so much. It’s tough sometimes, but the challenge is part of what I love. Other teachers (middle school teachers?) agree: middle school is completely different from elementary and high school, but in a good way. If you don’t believe me, I’m not surprised. Read on to learn what I think are a few of the best things about teaching middle school.
It’s Always Something NewIn The Young Adolescent Learner, Fran Slayers and Carol McKee, both former middle school teachers, talk about the middle school mindset. Those tween years are chaotic at best. Middle schoolers are going through so many changes in their lives, and that is reflected in their behavior in class.It’s a fun challenge to figure out how to keep their attention, appeal to their changing minds, and keep them engaged. Most middle school students like to play games and do activities that let them get up and move. They're independent and great thinkers and questioners; many of them feel free to make suggestions about how to change or improve an activity, which is wonderful, because I’m always looking for new teaching methods and activities. My students help me continue to become a better teacher. They’re HilariousHigh schoolers can be just too cool to laugh at a corny joke and elementary schoolers are too young to get certain jokes. Middle schoolers are the perfect age for teachers to crack jokes. They have a great sense of humor and it makes it easier to joke around a little and play fun games as part of the teaching process. Many of them love to share their own funny stories and jokes; it's a great way to connect. I Help Shape the FutureYes, middle schoolers are going through plenty of changes with their minds and bodies, but middle school is the perfect time to help mold them for the future. Students in this age group still have the optimism of a child, but they are starting to think more like adults. They’re forming opinions of the world and thinking about their futures. I love being able to be a part of this process. For instance, if I can instill the importance of math in terms of their future career, they may learn to embrace math as part of achieving their goals. Of course, it’s always nice to hear from a student years later that something I said or did gave them the confidence to go for what they dreamed of. I Get to Teach EmpathyNo, empathy itself isn’t a class, though our school does have a program that gives us the opportunity to meet with students every week and discuss issues they may be having, especially as those issues relate to bullying. Middle school is the time that the bullies can really start making life hard for their fellow students. Our weekly meetings give students the chance to talk about these issues (and others). We have time to brainstorm ways to approach issues, talk about possible situations before they occur, and even role play how to deal with these problems. I think creating a culture of empathy in the classroom is vital to middle school development. It’s a chance to teach them to think about others and consider their actions. It also continues to help me be more empathetic. This is part of why I like to use games and puzzles in the classroom. It’s a chance for my students to work together and better understand each other. I’m A Role ModelMiddle school is an impressionable time. It’s also a time when students start to question authority. My students know that I’m firm, but fair. I'm empathetic, but I have high expectations and I make them clear. When they do something wrong, I call them out. Depending on the particular situation, I don’t simply tell them to stop; I explain why they need to stop. I tell them stories about myself and others. It makes me hold myself accountable, knowing that I’m a role model during a time when good adult role models aren’t always easy to find. Honestly, the best thing about teaching middle school is growing with the kids. They’ve helped me throughout the years to better understand myself and become a better teacher. For that, I’ll always be grateful. |
To find more posts you might like, check the Blog Table of Contents.## AuthorHi, I'm Ellie! I've been in education for 25 years, teaching all subject areas at both the elementary and middle school levels. |