Note Passing

Each year is always a little different in respect to the personalities we are responsible for educating for the year. This year happens to be one in which our grade level is experiencing dynamics in our population that are not optimal for the educational environment.
In blunt terms, many are so busy messing with each other in negative terms, that the learning environment is in danger of being lost.
This year has been what I call "The Year of Notes". I have even started a file folder in which to keep them all and have scanned some to send to parents so they are aware that their child is not doing assignments, but involved in a completely different activity during class time.
The children have been very creative in their delivery of the notes, and other children are enlisted through out the class to pass them along.
Some delivery methods:
1. Student asks to throw trash away, and then another student asks to sharpen a pencil (or whatever) and takes the balled up paper (note) from the trash.
Solution: Monitoring of course, but also, I collect trash from a student and put it in the trash next to my desk.
2. Simply throwing a balled up paper or paper airplane through the air.
Solution: This one is difficult as they usually wait until your back is turned or you are helping another student.
3. Student asks to use the restroom. Leaves note. Another student asks to go after, gets note.
Solution: Class bath room breaks, but as we know there will be the child that insists they will have an accident if they do not go, even if you have just taken the class.
4. Other students used to pass the notes across the class, after the great care a teacher has taken to make sure certain personalities are apart.
Solution: Bring it all out. Let the entire class know that if they participate in the passing of notes during instructional time, they will be just as guilty as the note writers and their parents will also be told of their involvement.
If anyone else has experienced any other methods and can let me know, I would appreciate it. This Year the Notes have not only taken from our educational experiences in class, but the effects of their contents have led to fights, bullying, and drama that needs to decrease.

Division of Fractions with Common Denominators

We teach division of fractions using common denominators. The kids have picked up on this easily, but for some reason don't want to change the numerators when they find the common denominator. The don't do this when they add or subtract, just divide. Any ideas on how to remind them to change the numerator as well as the denominator when they are dividing?

Surviving the holidays

I don't know about everyone else, but this week has been an adventure and not the kind that I want to go on again! Trying the keep the kids focused and caring about class discussions have been very challenging. The last two days before our holiday break, I plan to review all I can. I know new material will go in one ear and out the other and if the review is not for a grade, the students will not complete it.

Five of the same...

Something we started last year at King's Fork Middle was beginning each day with five SOL type questions. We use SOL released items, but change the numbers. The five questions come from different SOL's, including some that we have not covered yet. From Monday through Thursday the students see the same five questions with different numbers. I give them about 10-15 minutes to work them out. When they have finished I go over the answers with them on an Interwrite Pad with projector (a transparency can also be used). They must correct their work on their papers which I collect. Student receive a check if they have shown all the work we went over or a check minus if they didn't. On Thursday, they get a classwork grade. Each check minus takes off 10 points.

Friday we do the same 5 again with different numbers, but this time it is a quiz grade. With only 5 questions worth 20 points each they learn pretty quickly the importance of keeping up with this each day.

Last year we started this at the beginning of the second semester. This year we started about 2 weeks ago. It really makes a difference. It's an ongoing review of SOL's covered, plus it gives them some familiarity with upcoming SOL's.

Think Pads & Notebooks

Everyday my students enter the room and work on 5 Math Review problems to continually practice for upcoming tests. I've had problems getting them to organize their work and save it for future use. I started making sure they work by making it a part of their classwork grade and that part worked. However, I would find their papers on the floor, counters, and tables regularly. I just knew they weren't taking my advice on how useful these would be.

A collegue offered some suggestions and I've taken it a little further with this plan. Now when they enter the room they make their "Think Pad" by folding paper to create three columns. One to show their work, one for the solution we come up with as a class, and one for the multiple choice answer. The rows are folded based upon how many problems you have and the front and back can be used. These are easily graded daily by walking around and making sure each block has the appropriate information inside.

In order to encourge the organization of them we've developed the Think Pad Notebook. Inside they are to keep the weekly worksheet that contains all the problems for the week and behind that sheet they are to keep their "Think Pads". These notebooks are to remain in the room for now and they will be graded each nine weeks for completeness. I've made this worth the same as a Test Grade so they realize the importance of it.

I'll keep you posted with the results!

Giving them the answers!

I really try to emphasize in my class that I'm not that worried about the answers. I want to see the process they go through to get the answers. I've tried a couple of things to help them out. One is that I give them a set of problems and just hand them the answers. They have to spend time figuring out how I got the answers. Another is to pair up students. Each person in the pair has a different set of problems, and their partner has the other person's answers. So, one person does a problem, and then the other checks if they are correct. If they aren't, this generates discussion as the students try to figure out how to get the correct answer. The kids really enjoy checking and helping each other.

Reducing Fractions

I find that sixth graders really struggle with reducing fractions, so I have them come up with the 3 characteristics of a reduced fraction themselves. I put 15 to 20 reduced (simplified) fractions on the board. Some of them have 1 in the numerator, some are consecutive like 3/4 or 8/9, and then the rest have a Greatest Common Factor (GCF) of 1. I put the fractions with 1's in the numerator in circles. The consecutively numbered fractions go in squares and then the remaining fractions go in triangles. I then have the students work together to come up with what each shape has in common. Obviously they have no trouble with the first 2 rules, but they tend to struggle with the "GCF is 1" rule. Once they have thought about it awhile, I have them list the factors for each numerator and denominator. From here I have them find the GCF. By this point they are able to give me the three things they need to look for to see if a fraction is reduced: The numerator is 1, consecutive numbers, the GCF is 1. The fact that they came up with the three rules themselves tends to make it stick a little better.

While teaching dividing fractions this year I started with a paper activity to capture their attention. I held up 4 peices of paper and asked what 1/2 of 4 was. I then wrote the step that 1/2 x 4= They reminded me to multiply the numerators and the denominators. And the last step to simplify. They redidly gave me the answer that 1/2 times 4 was 2. The students were then ready to restate that mutiplying by 1/2 and dividing by 2 were the same thing. The point was made that dividing by a fraction was the same thing as multiplying by it's reciprocal.
Ex. 4 divided by 1/2 (four sheets of paper torn in 1/2 gives you 8 sheets of paper) therfore it is the same as 4 times 2 (multiply be the reciprocal!)

I Can Learn

This year, my middle school has invested in a computer software program called I Can Learn. It is highly recommended to be fully integrated into the classroom nearly all day, every day. My school chose, however, to integrate the program partially, at only 2 days a week for 60-90 minutes. This software is well rounded with problems of the day, pretests, warm ups, lesson videos and notes, examples fully explained, tutorials, quizzes, section tests (pre-made and teacher made) as well as almost full SOL correlations. The program has a list of best practice strategies that add to its 20% increase in student test scores such as students wear headphones continually, notes are taken very methodically and thoroughly, a mastery level is to be set so students can not move on to the next lesson until, for example, a 70% quiz score is achieved, students write out all examples and quiz corrections, etc.

This year I have attempted full integration for 4 of my students from each block. There was criterion for selection, but to my amazement, the students are writing notes, focusing on their own computer screen, keeping their headphones on, and passing quizzes with scores I wondered if they could achieve. In speaking to these students about their math experience, more math vocabulary is being used and student engagement is increasing. I encourage everyone to take a look at the link to the website and watch the tutorial. Complete computer teaching is a futuristic sounding concept, but I have found success with it in my class for a select group this year.

http://www.icanlearn.com/default_new.asp

I am concerned about how I have been teaching percents this year. The district I work in no longer wants us to use the cross product method of finding percents. The preferred method is for students to use benchmarks when solving consumer application type problems. I have tried the Singapore method and some of my students really take to it and like it, but many students say they find it tedious and refuse to use it. I currently teach Pre-Algebra at the 8th grade level and from diagnostic testing a large percentage(about 40%) are at a 4th or 5th grade level of math proficiency. During testing we have done at our school, the teachers who have ignored our districts recommendations about how to teach percents have achieved significantly better (30 to 40 percent better)results in student achievement, making students write out the steps necessary to solve percent type questions using the cross products method. My concern, and I would like to hear any input and advice I an get on this, is that perhaps since so many of my students are 3 to 4 grade levels behind where they are supposed to be, does it make more sense to try and drill them using cross products type solutions or should I continue forcing the students to use benchmarks. What have other teachers seen as the learning curve for students using this technique?

12/5/09
by Don Lloyd
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Patty Paper Proofs

I have been using patty paper in my geometry class to help students understand concepts. It has been a huge help especially with students who have a hard time visualizing. I usually have an easy time knowing when to pull out the patty paper in geometry but not so much in pre-algebra. I am sure this method could be helpful in pre-algebra as well in areas other than geometry. I would appreciate any ideas. I also really like using foldables for note taking. They are a great place to store the patty paper.

"Unwrapping" 1-step & 2-step equations

Last year when teaching this I saw that the students were having a hard time solving 1 and 2 step equations so when this was introduced to me I immediately fell in love with it. It has worked marvelously. Attached are two worksheets I made to help the students with solving 1 and 2 step equations. The first is two step equations. (Of course we started with 1-step but I accidently attached 2-step first oops). For example 2x - 4 = 12. The variable always starts in the first triangle (x) (then follow the arrows) then the first bubble you put what happened immediately to x (multiplied by 2) and second bubble you (subtracted 4) and the answer always goes in the star (12) after the star you follow the arrows around. The opposite of subtracting 4 is (adding 4) and the opposite of multiplying by 2 is (dividing by 2). If you have the students start at the star and do the operations they will get their answer in the second triangle. So have them take 12 add 4 and then divide by 2 to get the answer. They should be able to "substitute" the answer they got in the second triangle and for the variable in this case x and perform the operations to get the answer in the star.

It works the exact same way for 1-step equations.

Hope this helps you like it did me.

Word Problems

Word problems are a constant struggle for my students. I have searched for different ways for students to interact and conquer this skill. I found a wonderful activity that our math coach shared with us called "Silent Pass." In this activity there are 6-8 problems that you place on the back of numbered note cards. Students are asked to divide a paper into 8 sections (by folding). They are then asked to solve each problem in the corresponding box. When they are done with one problem they hold the card up and silently pass it to another student and obtain another card to solve the next problem. This continues until they have answered all 8 problems. I was very impressed with the number of students who were actively involved all the students were. Even those who normally find it out difficult to participate or refuse to do the work assigned.
This activity can be modified to accommodate any level and any subject involving problem solving.

Scale Factor

Since I teach Geography as well as Math I incorported practicing map skills when teaching scale factor. The students had to plan a trip from Norfolk to L.A. making three stops along the way. They had to calculate their distance from each stopping point as well as total distance of their trip using the scale on the map. It was a great way to make an interdisciplinary lesson and make it relevant for the students.

APEX LEARNING

My school district is encouraging us, the Math teachers, to use the Apex Learning for Algebra and Geometry courses. Apex Learning is educational software that offers online courses in mathematics, science, English, Social Studies, Romance Languages, and Advanced Placement. The curriculum is organized into semesters, units, lessons, and activities. A typical semester includes 5 to 7 units, each with 3 to 6 lessons. A typical lesson comprises a number of activities including studies, practices, readings, journals, labs, discussions, projects, explorations, reviews, and embedded assessments. Although each Apex Learning online course provides a complete scope and sequence based on national and state standards, it does not align perfectly with the educational framework (SOLs) in the state of Virginia. Therefore, I need to pick and choose lessons on Apex Learning for my Geometry classes.

Overall, my students like the Apex Learning digital curriculum because it has a lot of interactive activities within each unit. For me, as an educator, I like Apex Learning because it changes my role in the classroom. Since I usually have my students work with Apex before I actually teach a concept, it allows my students an opportunity to become a self-learner, which in turn, allows me to be a facilitator/resource for them. Furthermore, I like the fact that students are allowed to use this program at home once a login ID is created for them.

Perfect Squares & Square Roots

I love to use color tiles to teach perfect squares and square roots! I pass out baggies of color tiles and then ask the students to work with a partner to create as many different squares as possible. The students are allowed to create the squares showing the area or the perimeter. I then have each team share one of the squares they created and I put it on the overhead for the class to see. (I always put up the area model so the perfect square is easy to see.) We discuss what makes each of the shapes a square before we discuss the perfect square. We then work backwards to see the square roots. Once the children have seen perfect squares and square roots like this, they usually remember it!