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1/27/2015 17 Comments

Grading Math Notebooks

Getting your students to take good notes can be quite a challenge. 

I have noticed that giving a notebook grade greatly increases the number of students who are engaged in the note-taking process. 

I give plenty of freedom for students to decide what works best for them, but I do require the following structure:
  • a section for vocabulary
  • a section for class notes
  • a section for homework
Grading Procedure for Math Notebooks
I have tried doing a section for warm-ups in the past, but ended up switching to printed paper warm-ups.  I found that it was worth printing them, because the kids took it so much more seriously.  They tended to just give up and wait instead of trying if they knew that the warm-up would not be collected right away.

Setup

I think it's so important to set the stage and show that the notebook is a valuable resource and should be well structured, well maintained, and well used as a reference.

On the first or second day, take time to walk students through the setup.  It can be a 3 subject notebook where they label the sections, or it can be a regular notebook that they separate.  I like to hand out the firm, clear post-it tabs.  They can stick these in the sections, then easily move them around as one section grows larger than the others.  This prevents wasted pages when one section does not get filled up.

Be sure that students label the outside with their names and class periods, and the inside with the section names.  I do not require dates.

Be clear from day one that these will be graded.  Students need to know that you take the notes seriously.

BIGGEST TIP:

After carting 150 notebooks home in enormous plastic bins every quarter as report card time approached, I made a breakthrough.  I decided to do notebook checks DURING A TEST.  This was such a simple change that made all the difference.

It really does not matter if the notebook check comes two weeks before the end of the quarter, so I just choose the unit test that is closest to the end of the grading period.  This spreads out the checking dates for different classes.  I just have students leave the closed notebook right under the desk and I walk around and grab each one and scan through it while they quietly take their tests.

This way, students never have to part with their notebook when they may need it, and I never have to spend time outside of school with the grading process.

Vocabulary

I assign vocabulary for each lesson BEFORE any instruction.  This becomes a standard part of homework.  I require the term, definition, and an example.  The example can be a picture, a sample problem, or a sentence.  Students make different choices for this depending on the type of word.

Read about teaching vocabulary using root words here.
Grading Math Notebooks

Notes

During any direct instruction, I expect students to take notes.  They must record the examples and other notes that I give.  Later during practice for a lesson (or even a week later), I say "check your notes" when they ask certain questions.  Middle and High School students really need reminders to use their notebook as their first resource.  I try to train them to reference it whenever they get stuck.

Homework

Homework is checked daily, so although it lives in the notebook, it is not part of the notebook checks.  See my post on grading homework for details.

GRADING

I give a total of fifty points for the notebook each quarter.  I let students know that this is a way to get points for doing what they are supposed to be doing.  It can either boost the grade at the end of the quarter or hurt the grade.  This really does keep them pretty motivated.  I keep a list of each section of notes that should be present in the notebook and quickly flip through to verify that the notes are there.  After looking at the first three notebooks, the rest usually take only about two minutes per notebook.  I can quickly tell if something is missing.

If a section of notes is missing due to absence, I jot down what is needed and subtract two points.  I allow that student to bring it to me any time before X date to show me that they worked with a friend to make up the notes for the lesson.  (I know this is generous, but when students miss a day, they tend to get behind and make up the homework while neglecting the notes.  I prefer that they go back and look over the lesson they missed and add these notes.)  If they take the time to fix it up and come show me, I erase the old grade and add back the missing points.

As far as vocabulary, each student is generally either conscientious about doing it, or is missing almost all of it.  I subtract points for this accordingly, and give lectures about how this affects the grade.  We talk about shaping up for the next quarter!
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17 Comments

1/20/2015 1 Comment

Resource Vault: Polynomials Collection

Don't Spend Your Sunday Hunting for Lesson Materials

Resources for Teaching Polynomials in Algebr
I've rounded up resources that you can use as supplements to your polynomials lessons. 

I've done the searching and collecting so you don't have to! 

There is some great stuff here.  Most is free, but a couple of these resources cost a few dollars. 

Enjoy!

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Classifying Polynomials

Polynomial Classification Game
This FREE game is available to download for your class.  Students play in small groups and try to get four boxes in a row marked off.  With each card a student pulls, he/she has the option to mark the classification by degree or by number of terms.
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This free PDF download from "Grade A Math Help" is available for all students and teachers to use without any login.  Click on the image for a link to the PDF file with a worksheet on classifying polynomials and more!

Adding and Subtracting Polynomials


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This wonderful site has a great set of videos on adding and subtracting polynomials.  Check it out at Home Schooler's Resources.
WebMATH has a nice applet that will simplify the expressions that you input.  The nice thing about this one is that it also shows the steps instead of just giving an answer.
This fun activity helps students practice adding and subtracting polynomials.  Answers are checked using QR codes.  Download this activity from Tina Hamlet for FREE by clicking on the image.
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Multiplying Polynomials

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This is a really great little animation to show polynomial multiplication.  It goes through tiny steps and is very clear.  Show this to your students for free!  Click the image to download (from 4 the Love of Math).
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The "Free Math Worksheets" site has plenty of worksheets available as PDF downloads.  These will help your students practice multiplying polynomials.  Three difficulty levels are available (easy, medium, and hard).

Dividing Polynomials

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This set of task cards includes practice on long division for polynomials, synthetic division, and finding zeros by dividing.  The cards (from Mrs E Teaches Math) have a variety of difficulty levels - great for differentiating! ($3.00)
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This applet does a variety of polynomial operations.  It would be great for working with finding zeros.  If you have not yet covered division, but want to discuss zeros, or are confident in students' ability to divide by hand already, try using this to cut down on the division work when you are looking at the bigger picture of what the results mean. 

Factoring Polynomials

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This YouTube video is a great one to show your students when introducing factoring trinomials.  The process for factoring with algebra tiles is explained clearly.  Pull out a set of Algebra Tiles and let your students practice factoring using manipulatives.  This can really help build the concepts and make connections in their brains!  There are a few videos in the set (by Tom Horn).
Factoring Polynomials Fun Practice
Factoring Polynomials - Fun Practice
These fun worksheets help students practice each type of factoring.  On each sheet, students shade/color the factors in the grid to reveal a "GridWord" for quick checking.  Each "GridWord" in this set is the name of one place that the Golden Ratio can be found in nature.  Can your class figure out the connection between the words? ($6.00)

Polynomial Functions

End Behavior of Polynomial Functions - Card Sort Practice Activities
This activity includes two Card Sorts for identifying End Behaviors for Polynomial Functions.  Quick-folding pockets are included to be kept in student notebooks.  Cards are a mix of graphs, equations, and word phrases.  Answer check cards can be tucked in the pockets as well so the activity can be re-done at any time as a study guide.
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This interactive page from GeoGebra allows students to manipulate the coefficients in the polynomial and see the effects on the graph.
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These free charts from Less Than 3 Math are great for students to place in interactive notebooks or use as a reference sheet.  The chart is included in different formats so you can choose which set of given information you prefer.  The charts identify each type of end behavior for polynomial functions.

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1/12/2015 5 Comments

Introducing Derivatives

Teaching Derivatives in High School Calculus
The day that you first introduce derivatives is the most exciting day of Calculus!! (Well, at least WE feel this way as teachers!)  Here's how to spread that joy to your students.  Maybe they will discover why you love teaching this stuff so much!

To start out, take a day or two to just focus on the main idea.  You do not have to jump right into chain rule right away.  Give your class plenty of time to soak up the concepts.  Focus on "the slope of a tangent line" and "change of rate" vocabulary and main ideas.

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Let your Students be Surfers for the day.

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Dress up! (a fun surfer hairdo and a bandana will do!  Maybe throw some flowered shorts on over your pants.)

Decorate your classroom.  Spend two minutes finding a beach-themed or crashing waves screensaver to project onto the wall or whiteboard as they walk in.  Spend another two or three minutes drawing a huge surfboard on the whiteboard, or better yet, bring a real one to use for the lesson if you have access.

Making Derivatives Fun
Get the class excited.  They are at the age where teachers do not bother to do this for them much anymore.  It will not take you much effort to make this really memorable for them, so go big!!

When you are ready to jump into the lesson, start with a large graph.  A quadratic function works well.  Draw or find a graph of a parabola that opens downward, since that is the easiest to compare to a wave.  Demonstrate how the surfboard can travel along the curve.  Explain that its slope at any point is the derivative of the function at that point. 

Resource #1: "Function Surfer" Applet for Derivatives

Project this "Function Surfer" applet on the board or let students explore in pairs if you have the technology for everyone.  This applet is great for them to play with while they explore the surfing analogy.

Resource #2: Printable Surfer Dude 

Printable Surfer Dude for Teaching Derivatives - Slope of Tangent Line
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Here is a little surfer man I put together for students to use.  Ideally, you want to print this on a transparency so that he can "ride" along the graphs on worksheets and students can still see the curve.  If you cannot do that, just print on regular paper and have students cut along the straight line at the bottom of the surfboard.  Click on the image to download the PDF.  Four surfer dudes print per page.
These guys are great to use along with Resource #5 below as the "straightedge" needed in the inquiry activity.

Resource #3: Derivative Infographic

Derivatives Infographic
This Derivative Infographic is available in my store and displays the main ideas for understanding derivatives. 

For one dollar, you can print it forever for all of your students every year until the end of time.  Click the image to check it out.  It prints two-per-page with an option of color or black and white. 

It is great to hand out as a bookmark and can be laminated or three-hole punched for binders.

Infographic for Main Concepts of Derivative
Derivatives in Calculus
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Connect With Physics

If all your students happen to be taking Physics, try collaborating with the Physics teacher to make the connections.  If not, just incorporate it in your own classroom.  I think the best way for students to really understand the relationship between each derivative and the rate of change is to work with position, velocity, and acceleration.

Show a position graph and explain what it represents.  Write "position" on the board.  Ask students to come up with a word for how quickly position changes.  Write "velocity/speed" below the word "position."  If they need help, act it out.  Walk slowly, then fast across the room.  Then ask "Ok, is there a word for how fast the velocity changes?  Have them think about slowing down and speeding up when driving.  Write "acceleration" below "velocity" on the board.  Display or hand out graphs for position, velocity, and acceleration.  You can even talk about "jerk" as an opportunity to go one more level to incorporate a third derivative.

The key here is getting students talking out loud or writing in complete sentences.  Try to get a real discussion going.  Encourage students to clearly verbalize the relationships.  Have them look at the position graph and talk about it.  You need them to speak out loud and hear classmates say plenty of statements like:

- "The car must be going faster here because the position is changing more quickly than it was." 

- "When the velocity starts increasing more quickly, this means that the acceleration is increasing."

- "The car is driving at a steady rate (constant velocity) when the position graph is linear.  The slope is constant, so the position is changing at a constant rate."

- "The car is stopped when the slope is zero.  The position is constant."

Have students take time to really look in-depth at each graph and point to the different intervals and explain out loud.  Make connections by labeling the position graph f(x), the velocity graph f'(x), and the acceleration graph f''(x).  Start using the words "first derivative" and "second derivative" to introduce the new vocabulary.

Resource #4: Position, Velocity, and Acceleration Graphs

This PDF has graphs for distance, velocity, and acceleration for your students to analyze.  Print one strip for each of them (two will print per page).  Once they have looked and talked through the graphs, they can run their surfer dude along the curves to investigate the slopes. 

When they are ready, you can try giving them the second page of the PDF, which has a distance graph to start with, but blank velocity and acceleration graphs.  Challenge your students to complete the graphs.

Click the image to download.
Teaching Derivatives with Distance, Velocity, and Acceleration Graphs
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Resource #5: Inquiry Activity: Graphing the Derivative of a Function

Graphing the Derivative of a Function - Inquiry Based Discovery Activity Sheet
Graphing the Derivative of a Function in Calculus
This three-page worksheet guides students to graph the derivative of a function.  The activity is set up as a guided inquiry.  Students do not need to know how to differentiate.  This is a great introduction to the graphs of derivative functions.

When your students do the graphing in a hands-on way and make discoveries about the relationships, they will understand and remember the concepts.

In this activity, students answer critical thinking questions in complete sentences and make discoveries about the degree of f(x), f'(x), and f''(x).  They use a straightedge and find slopes of tangents along the curve to graph the derivative function.  The PDF for the "Graphing the Derivative of a Function" inquiry activity is available in my store.  Click the images to check it out.
I hope your students love the derivative lessons! Enjoy!!

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