What's your favorite time of the school year? I'm guessing that it probably isn't testing time, nor the test prep weeks leading up to it! In spite of the fact that we never want to teach to the test or prepare students just for a test, the fact remains that students have to take the standardized tests, and we want them to do the best they can. So, how can we best use our test prep to help them?
1) Spiral Review
The most effective test prep method I've found is using spiral review throughout the year. The warm-ups I use review previous concepts, reinforce current concepts, and introduce new ones. This way, we are always solidifying concepts ("prepping for the test"), and as we get closer to test time, the warm-ups give us a chance to discuss concepts that might show up in the testing, but that we won't cover until after the testing occurs. Using these warm-ups may put me a little 'behind' in the curriculum on a daily basis, because they take time; but it helps solidify understanding and puts my students a little ahead with other concepts at the same time. I'm good with that:-)
Finding the Lowest Common Denominator with the
What's the most challenging math topic to teach/most difficult for your students to ‘get'?
This was my question in a recent Instagram survey. I got a variety of responses, but the one that came up most often was fractions – remembering the ‘rules;’ students finding common denominators when they were multiplying; students (older students) not being able to find a common denominator; and so on.
So, today, I’m going to share how to use the ladder method to find the lowest (least) common denominator, and hopefully, if your students have struggled with this, it will help them (and you!). Before I explain how it works, I want to share that I've used the ladder method for several years, after many years of teaching GCF and LCM the ‘traditional’ way - the way I’d been taught! And during those years, I’d often get frustrated by the fact that students would miss the GCF because they missed factors, or they couldn’t find the LCD because the numbers got too big so they just multiplied the denominators…..or they listed out the multiples, but made a mistake in one list, and so they never found an LCM/LCD. I'm sure you know what I mean!
The ladder method took these issues away, and it also added something I didn’t initially expect – it appeared to improve number sense for many students who struggled with their multiplication facts or with the idea of finding factors and multiples. It helped them understand HOW numbers were related to each other by making the breakdown of the #s more visual (using prime factorization does this as well, but the ladder method provides a little more organization to the process, and I think that’s helpful).
Ways to Improve Problem Solving Skills and Math Communication
Do Students Struggle with Word Problems?
Do your middle school math students struggle with problem solving? Do they get to the end of the word problem and then guess at the operation they need to choose (maybe not realizing that there are multiple operations)? You probably see this with some of your students, while other students do very well with problem solving. What methods have you found to help those who struggle? What methods can you use to help each student at his or her current level?
I’ve used many strategies over the years, to help students sort out how to make sense of word problems and how to approach them. These methods didn't have a specific name at the time (like close reading or talking to the text), but some would fit into these categories.
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.
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.)
This is a post I wrote back in 2013 (now revised), on my other blog, so the observation I refer to was quite a while ago now...how time flies!
I was observed by one of my assistant principals today (a Friday). After 20 years, I don't get super-worried when I'm going to be observed, but I still feel a little anxious. Today, I decided to have the students complete a problem solving activity and then start a "Footloose" activity, even though they wouldn't finish....Footloose normally takes about 40 minutes, so I figured they could do about half and then finish on Monday. (I do this fairly often, to give students flexibility in their work time - they can take as long as needed to complete problem solving, but if they get done quickly, they can move on). Things went so well during the observation...AP commented that there was so much going on in the room, and that the kids were so engaged! I was happy:)
During the class, students worked on group problem solving, (which they have done previously, with other math skills). These particular problems involved comparing and ordering fractions. Our procedure was as follows:
1) Each group received a different sheet with a problem "situation" and 3-4 questions about that situation. (I have five different sheets so that we can do the problem solving several different days with the same concepts, if needed and if time allows).
2) Each group read their situation and each of the questions together.
3) Each student spent 5-7 minutes, thinking/working individually to solve the questions, writing their work on their own recording sheet.
4) When students completed their individual thinking time, they compared their ideas (and answers if they had them), discussed any differences in thought, and worked to agree on final answers.
5) The final answers (with work) were written onto a group answer sheet to hand in.
When we did this type of group problem solving the first time (with decimal problems), we spent about 5 days on the problem solving, with each group working on a different problem sheet each day. The students really like the problem solving, partly because they are able to talk out their answers with each other. It's great to hear their communication about math and how they are able to point out the steps a group member needs to complete or the concepts that they may have missed.
Today, it was great to hear them say "Oh, we're doing this again. I like this!" My AP commented that he listened to hear what they were talking about, to see if they were focused, and he could hear one student explain to another how the work that they had done was different from another student.
The problem solving took about 15 minutes, and then as each group finished their problem, they moved on to Comparing and Ordering Fractions Footloose. This is a great game for keeping students engaged, but moving! Students start out with one card and a sheet of paper with 30 blank "blocks" in which to write answers to the questions on the cards. Each card has a number on it, and students record the answer to each card in the same number block as the number on the card. After answering the question on the card they start with, students put the card on the chalk ledge and pick up another card with another question to answer. Students continue answering and returning cards until they have answered all 30 questions. Students work so quietly when they are doing this activity! My AP said it was like "night and day" when they switched from the problem solving to Footloose - they were talking about the p.s., but as soon as they started the Footloose, it was sooo quiet.....and I didn't have to say anything for it to be this way - it just happened.
As I mentioned, I don't really get worried when an observation comes around, but it was great to hear the positive feedback for these activities that I create for my students!
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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