Organizing Student Notebooks with Dividers

Today I’m sharing my newest step towards improved organization in the classroom: notebook divider tabs.  (I got the idea from a blog post by Sarah Carter and knew that I wanted to modify them to work for me in the upcoming year).

Notebook Divider Tabs: math-in-the-middle.com

I decided that this year I am going to make notes worth 2 points per day.  Students need to include a summary/explanation and completed worked-out examples for each lesson (which is where the 2 points are coming from).  In the past I made notes worth 20 points per unit, but in reflecting on it, it doesn’t really make sense because some units are 10 lessons long while others are only 6.  I collect and grade notebooks on days that students are taking the unit test.

So, here’s where the divider tabs come in…before each unit I will give students a divider to glue in their notebooks.  A little tab sticks out the side with the name of the unit on it.  On the divider I listed all of the lessons that are included in the unit.  I figure that will be an easy way for students to make sure that they aren’t missing the notes to any lessons (which will be especially useful for students who were absent).  It will also serve as a checklist for me while I’m grading.  Next to each lesson I can write 0, 1, or 2 for however many points students earned for that day’s notes and record their final grade for the unit on the bottom where I left a space for it.

Notebook Divider math-in-the-middle.com

The beauty of the tabs is that I can flip right to the correct unit without wasting time trying to find their notes.  I also think they will be useful to students, as if I ask them to refer back to an earlier topic, they should be able to find the lesson pretty quickly.

I made the dividers small enough that they won’t waste a page of the students’ notebooks.  I think I will have students write the vocabulary for the chapter on the first page (next to the divider) and then start with the first lesson’s notes on the back of that page.  The divider doesn’t cut into any of the useable space on the back of the page at all, which I am really happy about since I hate wasting paper!

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I made my dividers print 3 per page, so I just print them, cut on the two dotted lines, and hand them out to the students.  They fold on the solid line and then put glue on each side and make sure to leave the tab sticking out the side of the notebook when they glue it in, and that’s it!

If you’d like to try out similar dividers for your class, I set up a 3 per page divider template in PowerPoint that you can use.  Just click the image below to download the editable pptx file.

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Other school-related things I have been thinking about/working on recently:

Have you used dividers before with your class?  Are you thinking about trying them out this year?  Please share in the comments below – especially if you have any tips for using them since this will be my first attempt!

Thanks for reading,

Christina

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Unit Analysis in the Middle School Math Classroom

After a long break (due to craziness in my personal life and some technical difficulties with the blog)…I’m happy to be back blogging!

I’m going to jump back into blogging with a post about Unit Analysis…

unit analysis in the  middle school math classroom

I hate teaching customary system conversions the traditional way!  No matter how many times you explain to students that you multiply when converting from a larger unit to a smaller unit and divide when converting from a smaller unit to a larger one, there are always students who mix the two up.  And then when teaching students to convert rates, it’s a whole new process…

So, I prefer to teach Customary conversions with unit (or dimensional) analysis.

Here are a few of the reasons why I love unit analysis:

  • It’s ALWAYS multiplication (no need to figure out which operation to use)
  • It reinforces fraction multiplication skills
  • The same process can be used for converting rates (no need to learn a new skill)
  • Students get it (and like it)!!

 

Here is an example of a simple unit analysis problem:

Convert 7 miles to yards.  (This example is done with the assumption that  students do not know that there are 1,760 yards in a mile;  If they do know this, it is only a one-step unit analysis problem).

basic unit analysis

 

When I teach unit analysis I always have a discussion with the students on why it works.  It sometimes takes some encouragement, but students are eventually able to come to the realization that each fraction (other than the starting one) equals one since the numerator and denominator are equivalent.  Therefore, unit analysis ‘ works’ because they are just multiplying by 1 over and over again, which doesn’t change anything (as we know from the multiplicative identity property).

I typically start the lesson with a simple fraction multiplication problem to review cross-simplifying.  That makes the transition to cancelling out the “yd” in the numerator with the “yd” in the denominator easy for the students.

I always tell them that they know they are done when the only word remaining is the one they are asked for.

When I give the students rate conversion problems the next day they are able to solve them using unit analysis, as well.  It just sometimes takes some gentle reminding that every fraction should equal one (the numerator should equal the denominator) and then they are good to go, even for “hard” problems like the one below!

converting rates unit analysis

Thanks for reading,

Christina

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My Spin on Symmetry

Today’s 6th grade lesson was on rotational symmetry.  I have found that students tend to be less familiar and less comfortable with rotational symmetry than they are with line symmetry (and sometimes mix the two up), so I try to find ways to make it more clear and understandable to them.

I had several different shapes cut out ahead of time: an equilateral triangle, isosceles triangle, rectangle, square, rhombus, regular pentagon, irregular hexagon, etc.  I had the students each pick a couple of different shapes and trace them on a piece of paper.

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After tracing the shapes, the students were told to use their pen or pencil to hold down the center of the shape.  I had them rotate the shapes and count how many times the cut out shape lined up perfectly with the traced shape (until they got to a full turn around).

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I asked the students to try to figure out how many degrees they were able to turn the figure to have it line up with their tracing.  They were able to reason that since a full turn was 360 degrees, they had to divide the number of times they could turn the shape into 360.

Their finished notes for the day looked like this:

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As an extension, I gave each of the students an angle measure.  They have to draw, color, and cut out their own figure that has that rotational symmetry.  (For example, the student to which I assigned 120 degrees is not allowed to draw an equilateral triangle.  They have to create their own, original figure that also has 120 degree rotational symmetry).

I am excited to see what they come up with!

Thanks for reading,

Christina

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A Little Sum-thing about Triangles

I started my unit on Geometry with my 6th graders before Christmas break.  We got as far as the basic vocabulary and different types of angles.  I decided to begin with polygons after break, so my first post-Christmas lesson was on triangles.

We started off by discussing the different ways to classify triangles – by their sides and by their angles.  The students made a chart in their notebook listing the different types of triangles and we did some example problems.

[Before the lesson, I had made up little slips of paper with different triangle types on them.]  After going over the basics, I had each student pick one of the slips at random.

triangle types

 

They had to draw whatever kind of triangle they picked on construction paper and then cut it out.  This served two purposes – it showed me if they understood the first part of the lesson, and it provided me with a wide variety of triangles.  I had each student number the angles in their triangle (1, 2, and 3).  I then asked the students to rip off each of the angles of their triangle.  Finally, I asked the students to line up their three angles so that they were adjacent to each other, and asked them what they noticed when they arranged their angles in that way.  A few students noted that they formed a straight line.

triangles wholetriangles cut

 

 

 

 

 

angle sum

When I asked the students how many degrees the three angles must be in all if they are forming a straight line, the light bulbs went off!  Since everyone had started with a different triangle, the students were able to conclude that the angle sum of ANY triangle is 180 degrees.

All in all the lesson went very well.  We finished by going through an example of finding the missing angle in a triangle.  The students’ notes for the day ended up looking like this:

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At the beginning of the class when we were first going over types of triangles, one of the students had asked why an acute triangle has 3 acute angles, but a right triangle only has 1 right angle and an obtuse triangle only has 1 obtuse angle.  I posed the question back to the class and their original answer was that the triangle wouldn’t close if it had 2 right angles or 2 obtuse angles.  At the end of class, however, one of the boys in my class said “Oh, that’s why there can only be 1 right or obtuse angle…there’s only 180 degrees in all so if you already have 90 degrees, if you had another 90 degree angle you wouldn’t be able to fit another angle!”

Don’t you just love it when students can reason out the answers to their own questions?!

 

Thanks for reading,

Christina

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