#July2014Challenge: Guess my graph

Can you guess my graph?

I have done this activity with countless students over the years, in all classes from Algebra 1 to Calculus AB.  I'll admit that it goes better when there is candy involved, but even without the candy engagement is high.  Students need to have a graphing calculator for this activity (Desmos or Geogebra are also fine).  I show them a graph using either my graphing calculator under the document camera, or a premade powerpoint with images from Geogebra/Desmos.  Students take a guess, input into the calculator, and view the graph to check their answer.  If it is wrong, they discuss with a partner or ask a question.  I generally circulate during this time to see how many students are getting the correct answer.  We have a quick class discussion at the end of each round to address misconceptions.

I like to use this activity for review of quadratic functions in factored form.  To start the activity, I would show the graph from above and walk students through the process of writing factors given roots.  The work that I show on the board might look like the diagram below.  We don't worry about the vertical stretch/shrink at this point in time.

I am not suggesting that students show this work.  I am simply trying to model my thinking for students, and I really want to make sure they understand that the roots of a quadratic function are points on the graph.  It is not by magic or coincidence that a factor of (x-4) makes a root of 4.  If I model my thinking for them now, they are more likely to use this language or reasoning pattern later when I ask them to explain their thinking.  I might expect them to write an abbreviated version of this on the classwork or homework, but for the guess my graph activity we are going to use a graphing calculator and our voices to practice with this reasoning.  I really liked the suggestion below for showing work when you find roots.  This is from a TMC14 presentation by Glenn Waddell, which I read about at Misscalcul8.

After we walk through the first problem together, I'll show a few more graphs of the form
 y=a(x-b)(x-c) where a=1.  Then I will give problems with a= -1, and a=1/2 so we can discuss vertical stretch/shrink as well as reflecting over the x-axis.  I let them know that the only a-values that I will pick are a= -2, -1, -1/2, 1/2, 1, or 2.  I save double/repeated roots for last.  This is a favorite, and many students are able to guess the equation for a graph with repeated roots without any help from me on the very first try.  This activity is also great for an introduction to cubic and quartic graphs.

Another version of guess my graph uses mini whiteboards or Wikki Stix.  In this version I tell you the equation, and you show me the graph.  I started using Wikki Stix because I knew it would appeal to my kinesthetic learners, and teachers share mini-whiteboards at my school so it isn't always an option to use them.  I hand each student 4 Wikki Stix.  They form the axes with two Wikki Stix, then they form the parabola y=x^2 with the third.  Then with the fourth stick students can form the correct graph.  Below is an appropriate graph for y=-1/3(x-2)(x-2).

We lose some of the specificity by using Wikki Stix instead of mini-whiteboards, but I kind of like this.  It means that students have to make some generalizations about how to graph quadratic functions.  To make distribution and collection easier, I ask students to make a twizzler (see below) with the Wikki Stix.  (Warning: some students in your next class will think this is a piece of candy.  Make sure they know it is a wax twizzler and not the real thing!)

#July2014Challenge: Dynamic Polar Curve Plotter

In my last post I talked about how to plot polar curves in Geogebra.  As I neared the end of the post I remembered how the use of sliders can enhance this topic.  

Below is a polar graph plotter.  You can try this out now by dragging the slider alpha from 0 to 360 degrees.  Move the slider back to 0 degrees and type in another function such as 3cos(5x), or 12/(2-sin(x)).  A copy of this tool is available from the Geogebratube site here.  


I always have so much fun playing around with Geogebra, but I know it can be time consuming.  In case you have the extra time and are interested, I am also including directions on how to plot the polar curves and add the slider. Some of this is a repeat from my blogpost on how to plot polar curves with Geogebra.  

Let's say I want to plot the polar curve below.

Start by typing the following function into the input bar at the bottom of a Geogebra page:

Hit enter, then hide this function.  Next we will add a slider called alpha that goes from 0 to 360 degrees.  From the toolbar select the button that says a=2.  If you can't find this button, open the dropdown menu from the button that is second from the right (see below).

VERY IMPORTANT!!!  To add the slider to your graphics view, click on the location where you want the slider to be.  I usually pick the top right of the graphics view.  It is a pain to move these sliders once you place them on the screen, so better to get it right the first time.

The default for a slider value is a number from -5 to 5.  We want an angle, so select the angle button on the left, as shown below.  The default values shown below will work for our polar curve plotter, so you can press apply to set up your slider.

After this we are going to use the following command:

Below is what I will enter into the various command parts:

If you read the blogpost from yesterday, you will notice that my end value was 360 degrees.  To make this a dynamic plotter, I changed my end value to match the value of the slider alpha.  Once this is finished, you will be able to plot the parabola below by dragging the slider value from 0 to 360 degrees.  

#July2014Challenge: My Exeter PD Day 1

About 10 years ago I was invited by my district to attend a week long summer institute led by the instructors of a private school on the east coast called Phillips Exeter Academy.  Each day we spent about six hours doing math problems from the curriculum that students use in these courses.  Sometimes we would work on problems alone, sometimes together, with lots of presentations as well as integration of technology.  What a fantastic week!  I attended the same institute the following summer, choosing a different course to focus on, and found myself equally excited about this professional development. 

I haven't run across the opportunity to attend another of the Exeter Math Teacher Institutes, but I have chosen to go back to their curriculum over the years.  They follow an integrated approach which spirals different concepts throughout the year.  They also develop concepts in ways that I am not always familiar with.  I decided to take a look at their Math 4C Curriculum this week, which looks to be a trigonometry/pre-calculus type of course.

There were many topics to choose from in the first ten pages, but one that intrigued me was the introduction of conics.  On page 2, problem 6 asks students to write an equation in polar form for the set of points P that are equidistant from focus F at (0,0), and directrix at y=-2.  They do a much better job of explaining this in student friendly language, saying "Using the polar variables r and theta, write an equation that says that the distance from P to the directrix equals the distance from P to F."  They provide a diagram similar to my diagram below.

I was excited to try this problem since it made use of a definition that I was familiar with, but in a different way.  I'm not sure I've ever thought about how to derive an equation for a parabola using polar coordinates or equations.  My next step was to label my diagrams with unknowns.  I am not sure students would remember how to express the side lengths of a right triangle in terms of r and theta.  This is another step to derive, but one that would not take too long.

After I wrote the lengths of all relevant sides on my drawing, I wrote an equation that matched the problem description.  It is empowering that this equation came from me, not my textbook.  Better yet that I put together information from a written description and a diagram that I filled out according to info from this written description.

The next step in the problem was to solve this equation for r.  A nice review in algebraic manipulation could come from this step.

Students would then graph this equation, most likely using a graphing calculator in polar mode.  I don't have a graphing calculator handy, so into Geogebra this goes!  I always have to look up the directions for how to graph a function in polar form using Geogebra, so I finally wrote a blogpost so I never have to sift through online directions again.  Below is what I see on my screen when I graph the polar curve above.

The next day I skimmed a few more pages and ran into a similar problem on page 5.   This problem asked students to use the polar variables r and theta to write an equation that says that the distance from P to the directrix equals twice the distance from P to F.  I was intrigued because I knew the work would be similar to what I had already worked on, but I didn't know what the shape would be.  The text provided a drawing similar to my drawing below.

I went through the same set of steps.  First, set up the equation.

Solve for r in terms of theta.

Plug into Geogebra, and it is an ellipse!  Totally unexpected.

This intro comes without the barrage of details normally involved with the introduction of ellipses.  I am intrigued because this is not the definition of an ellipse that I am used to, but it is a description that produced an ellipse.  As a teacher, I am full of questions and curious to see how this develops.  More on this soon!

#July2014Challenge: How to plot polar curves in Geogebra

Let's say I want to plot the polar curve below.

Start by typing the following function into the input bar at the bottom of a Geogebra page:

Hit enter, then hide this function.  After this we are going to use the following command:

Below is what I will enter into the various command parts:

For my problem I chose the parameter variable to be "t", and my function to be f(x). You can choose another parameter variable, but remember that x is not an option since this is the default independent variable for the program.  If you want to plot in degrees instead of radians, make sure to indicate this on your start and end value.  Hit enter to submit your information.  below is what I see on my screen.

I'm not sure if there is a shorter way to do this, but for now this is what I've been using. Another fun variation on this is to create a slider to represent the end value, and then you can watch your curve appear and disappear.  More on this in the next blog post!

#July2014Challenge: Sketchpad Presentations from Key Curriculum Press

One of my favorite blog finds this past year was Sine of the Times by Key Curriculum Press.  Several bloggers write for this blog, and what I appreciate most from them is how they present math topics in new ways using Geometers Sketchpad.  

The latest post is Dilations Challenges.  The tool embedded on the webpage took me a couple of minutes to figure out, but this was time well spent.  If you have a few minutes to spare, I definitely recommend checking out this post as well as those below.  

Some other great posts from 2014:

CREATE PARAMETRIC CURVES GRAPHICALLY AND KINESTHETICALLY

ITERATION IN THE COMPLEX PLANE

SIMULTANEOUS EQUATIONS IN ELEMENTARY SCHOOL? YOU BET!

PI DAY 2014

What blogposts have you seen this year that present material in new and interesting ways?  Please feel free to share!

#July2014Challenge: The other SBG

I had to work today, so I figured I would go for an easy blogpost.  I am part of a blogging challenge to blog everyday in July, put together by druin.  I figured an easy blogpost would be one where I am sharing one of the many amazing teaching resources or strategies that have been shared with me over the years.  Enter SBG.

No, I don't mean Standards Based Grading.  When I first started reading blogs I saw SBG plastered all over blog links.  This was really confusing, because it was assumed that readers knew what SBG meant.  I finally Googled SBG and found that it means standards based grading, but I'll admit that I spent a week or so wondering if it stood for Silent Board Game.  And I was okay with this, because silent board games (by College Preparatory Mathematics) are fantastic and deserve their own blogpost.

My first teaching job was 7th grade pre-algebra, and we used the CPM curriculum that year.  Silent Board Games are one of the many engaging activities provided in the teaching kit to help students learn and practice mathematics.  We introduce this activity when students are learning about linear equations or functions.  Suppose I give you the table below:

The first rule of this game is that you have to be silent.  I will initially give 60 full seconds of think time for students to think about what the rule is that relates the input numbers in the top row to the output numbers in the bottom row.  I will then start taking volunteers to add entries.  No one can give the rule or the equation until all other numerical entries in the table have been filled out.

After a couple more entries, give about 30 extra seconds of think time.  Adding fractions or decimals is an easy way to reinforce number sense, and it is an easy way to differentiate for the students that need an extra challenge.  Once you get to this point in the game (below) there will be many wiggly students itching to give you the rule.  They love that part!

 The completed table is below. 

Some things to consider as you get ready to play Silent Board Game with students:

-The first time you play, you may need to go through a round with students to explain your thinking.  
-You can leave some of the input numbers blank so that students can work backwards from the output.
-For errors, some teachers erase the incorrect answers.  Other teachers let students know ahead of time that there might be mistakes, and if so you can erase the error when it is your turn.
-CPM used this activity a couple of times a week for an entire unit.  I don't recall the including non-linear rules until the end of the unit.  They chose simple quadratic and square root rules.
-This game is also fun to play in Algebra and Algebra II!

Links with SBG resources:
-Blank copies with examples
-Silent Board Grid with top row filled in (you pick the rule and tell students what to add to the bottom to begin the game)
-MathRecap blogpost by Dan Meyer on silent board game and a couple of other related activities.  

#July2014Challenge: Coordinate Algebra and Transformations

I was recently reviewing workshop materials from a transformational geometry session and was directed to the Georgia Deparment of Education website for a unit called Algebraic transformations. This is the fifth unit in their first year (9th grade) course titled Coordinate Algebra.  I found the activity/assessment below on page 109 (answer key on page 103).   The task was to draw some shapes on a coordinate grid, and transform them using 8 different coordinate rules.   Below is a list of similar problems.

What would happen to your shape if you transformed it using the given rule?
1.  (-x,y)    
2.  (x,-y)
3.  (x+2,y)
4.  (x, y-3)
5.  (x+1,y-4)
6.  (2x,2y)
7.  (-x,-y)
8.  (3x-2,y+1)

In case you've never seen these rules before, the process is that you take your preimage point (x,y), and substitute the values for x and y into the given coordinate rule to find the image point.  If your set of preimage points creates a shape, then it is easier to see the transformation given by the coordinate rule since your image will form the transformed shape.

In case you want to check your answers:
1.  Reflect across the y-axis
2.  Reflect across the x-axis
3.  Shift (translate) right two units
4.  Shift (translate) down 3 units
5.  Shift (translate) right 1 unit, down 4 units
6.  Dilate from the origin by a scale factor of 2
7.  Rotate 180 degrees counterclockwise about the origin (or reflect across both axis)
8.  Horizontal stretch and shift, and shift up one unit.  (I am guessing this was an extension of what they learned, so not a precise description).

I am thrilled that the Common Core allows for more time spent on coordinate rules. These rules are somewhat intuitive, and easy to verify using a diagram.  Activities can easily involve multiple representations of knowledge.  This study of coordinate transformations is even included in the 8th grade standards:

8.G.A.3.  Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

My hope is that all of this study of coordinate transformations will help with the understanding of function transformations.  Many of the newer textbooks and resources still teach function transformations via observation.  You might see an introductory activity that asks students to graph each of the following functions and to notice the similarities and differences between each graph.

Students easily make the correct observations, and they can even memorize the rules for vertical translations in this case.  But once we teach students all of the rules for function transformations, it starts to make less sense if the introduction is based on observation instead of reason.  I'd rather review the rules for coordinate transformations each time I introduce a function transformation.  In this case we are transforming a set of points instead of just moving a graph around.  This will also help students see functions as a set of points instead just a graph with a shape.  In my work over the next year I will be looking for textbooks or online resources that utilize this method of teaching function transformations.  

I made the following tool to use when practicing coordinate transformations.  To use this tool, enter a coordinate rule for point B that depends on the coordinates of point A.  For example, if Point B= (-x(A), -y(A)), then point B will be rotated 180 degrees about the origin from point A.  You can use the tool below to try this out.  Once you've entered coordinates for point B, drag point A across the semicircle to see the transformation created by the trace of point B.


I'll admit that this tool isn't as polished as I would like it to be. I wanted to share anyway because this is a concept where the use of technology can enhance instruction and practice.  The updated version will be added to the Geogebra Tools list at the top of this blog when available.  For now you can access a download of this tool from the Geogebratube website, and from there you can open with Geogebra and resize the window and turn on the option to view coordinates, etc.  

#July2014Challenge: Google Auto Awesome

Yesterday while in the middle of a Google search I noticed my Google bell flashing, meaning that I had a Google notification.

This rarely happens, so I went to check it out and was presented with the movie below.

Very little information was available about this movie, but it did indicate that it was created by Google Auto Awesome.  I was immediately amazed, flattered, and a bit confused.  I had recently posted my daily blogpost about modeling with trig functions, and this movie had taken all of my pictures from the blogpost and animated them!  I wondered if someone had read my blogpost and made the movie using Google Auto Awesome.  It was an intriguing idea, kind of like having a secret admirer!  But surely if this was the case then I should be able to figure out who made the movie.

After about two minutes of searching I realized that my secret admirer was in fact Google.  Auto awesome can automatically take a series of photos and make an animated .gif file.  This webpage gives more details and says you will receive a notification if Google automatically makes a video for you.  This really is both awesome and amazing!  If you use Blogger to create your blog then all of the photos you upload to the blog will also be copied into your Google Photos page.  I can't tell you why Google chose the photos from my most recent blogpost to make an Auto Awesome video, but I suspect it has something to do with the photos already being on my Google Photos page.  You can make your own Auto Awesome videos if you have an Android device.

A big thanks to Google for giving me an awesome video (automatically), and for making my blogpost for the day so easy.  While we're on the topic of awesome, below is a short list of awesome resources that I have used recently as my district transitions to Common Core.

Phillips Exeter Academy math teaching materials.  These are updated yearly by the math teachers.  If you ever have a chance to attend a summer institute, I highly recommend.  

Mathematics Assessment Project MARS website.  Check out the tasks if you want to learn more about assessment, and the lessons if you want to learn more about math pedagogy or instructional strategies.

Emergent Math Problem Based Curriculum Maps.  These align to the Common Core Standards and are organized using the Pearson Foundation Pacing Guides.

Illustrative Mathematics.  Also aligned to the Common Core Standards, and are easily searchable.

Clovis Unified School District SBAC math page.  They have organized all of the Smarter Balanced Assessment Consortium (SBAC) released test items by claim.  The released performance tasks are under claim 4.  There are four items for grade 11 and three items for grade 8.

#JulyChallenge2014: Modeling With Trig Functions

Link to Geogebra Book with all 4 applets

Last year was the first year we taught trig graphing in Algebra II, and so it was a brand new teaching topic for a couple of our teachers.  Perfect opportunity for collaboration!

We decided to introduce the topic using Dan Meyer's Ferris Wheel.  This introduction built on intuition and gave students a day to practice reasoning with a context that involved sine and cosine graphs.  The equation for a sine graph was introduced at the end of the lesson, and students used sliders in Geogebra to fit the sine graph to the ferris wheel data of time versus height.

Towards the end of this unit students were asked to model real world situations using trigonometric functions.  We picked a few problems involving tides and ended with a problem from Illustrative Mathematics called Foxes and Rabbits 2.  We used a series of scaffolded Geogebra presentations to help students get started.  The first presentation is below, and is an embedded applet that you can play with.  Type a function into the f(x) input bar and press enter to see it on the graph.  You should try this right now. It is fun! The goal is to get the sine graph to pass through all of the data points.  



We introduced this to students by first talking about the data and how tides are measured.  You can talk about how the moon impacts tides and how the data is roughly periodic.  At this point students should know the amplitude and period for y=sin(x). Next, have a class conversation about how to transform this graph to pass through the given points.  The power of a premade interactive model is that you can pause during the conversation to allow students time to process.  I make use of the think-pair-share structure with the expectation that students may be called on to explain what they know or discussed with a partner.   One of the teachers on the Algebra II team started writing and sharing the questions that she used with these presentations, and the other teachers found this to be very helpful.  Below is a list of questions that can be used with this presentation after the initial conversation about the data.  Feedback  on this list of questions would be great!

1. What is the midline for the Santa Cruz Tides data? (Discuss first, then reveal the midline by selecting the midline box.)

2.  How can I change (transform) the function f(x)=sin(x) so that it has this midline? (Discuss, then type in the correct function and reveal the change in the graph.)

3.  What is the maximum value of this function?  What does it represent with respect to the tides?  Find the minimum value as well.  Discuss and then reveal the max and min lines by selecting the appropriate box.

4.  What is the difference between the highest and lowest tide measurements?  Does this help me find the amplitude, period, or vertical shift of my function? 

5. Now that I know that the amplitude is 1.5, how can I change my function f(x)=sin(x)+2.5 to account for an amplitude that is not 1?

6.  Discuss with your partner what one period of y=sin(x) looks like.  My current graph has been shifted horizontally from the parent graph y=sin(x).  Can you find a new starting point?  How can we change our function y=1.5sin(x)+2.5 so that it has been shifted horizontally to your new starting point? (There are multiple answers here, which can be discussed now or later depending time.)

7.  What about the period?  Note: Most classes will have a formula to use to account for a change in period.  I haven't taught trig in years, so I just use horizontal stretch/shrink reasoning.  y=sin(x) has a period of 2pi, and Santa Cruz tides has a period of 12.  Since 12 is larger than 2pi, I will multiply x by a factor of (2pi)/12.  My new function is f(x)=1.5sin(2pi/12(x-9))+2.5.

One of the teachers from this team made a worksheet for students to use as we modeled the thinking.  I find this to be an important step so that students can refer back as they practice and study.  Please let me know if you are interested in having this worksheet, and I can get you a copy.  

Below is a list of all the tide problems that students worked on.  

Santa Cruz Tides
San Mateo Bridge Tides
Bay of Fundy Tides

Students also worked on Foxes and Rabbits from Illustrative Mathematics.

Illustrative Mathematics Foxes and Rabbits 2 Problem
Illustrative Mathematics Foxes and Rabbits Geogebra Tool

#July2014Challenge: Saturday morning coffee (with a side of math)

I began this Saturday morning in the same fashion as most mornings, with a cup of coffee at the table and my children by my side. Usually I read the news, but today I wanted to try some of the problems from the Open Middle website.  As I played around with a geometry problem, my 5 year old asked me if I could give her a math problem to work on.

I gave her some number line problems like the one below.  

Next my 6 year old nephew wanted some math problems. He kept coming back for more problems, so finally I gave him the problem below.  To complete the table you take the corresponding number from the top row and the left column and you add to get the answer. 

I didn’t take long for my second grader to ask for some math problems.  I gave him a similar table but added in some negative numbers for an extra challenge.

The older kids finished their tables and came back for more.  I drew inspiration from a problem posted on The Sine of The Times blog a few months ago and gave them each a table like the one below.  For this table you still add the number from the top row and left column to fill in 9 boxes on the bottom right, but now you have to find some of the numbers for the top row and left column.

This type of thinking was new to them, so we spent some time talking about how to find the numbers missing from the top row and left column.  I’m not sure they appreciated the challenge, as the next request was for a subtraction table. 

 After making about 8 of these tables and countless number lines, my nephew came back for yet another table.  This time I told him to make one for his cousin to complete (coffee was getting cold).

 Very impressive!  We did math together for more than an hour this morning.  The next part of our day included a hike, a picnic, a playground, a drive home, and then MORE requests for math.   What a great day!

#July2014Challenge: My Favorite Unit Circle

Today is only my 4th day of the July blogging challenge (initiated by Druin at http://statteacher.blogspot.com/), and I already feel like I need a break.  One of my goals in starting a blog is to improve my writing skills.  Writing does not come naturally to me, so this takes time and effort.  I wanted a short and sweet blogpost for Friday, and after checking out what others were writing about I found #MyFavFriday.  So here it is!

This is a unit circle made from 4 pieces of cardstock and a brad.  The special right triangles rotate around the origin so that you can see the reference angle that you need for each of the angles listed on the circle.  I used to make this unit circle with all of my trig classes, and I found that many students still had it the next year for calculus.  I always make a few extra and stick them on the whiteboard with a magnet, and they get used constantly by my calculus students.  It is hard to tell from the picture, but each special right triangle has all of its angle and side measures printed, and the red circle is about 7 inches in diameter.

You can buy a kit to make this circle for $12 at Facing Math. The kit includes directions for making the circle as well as two practice worksheets with trig ratios that are way better than what I found in my textbook. Cardstock and brads not included, but still worth every penny!

#July2014Challenge: Tech Thursday and Community Building

There are plenty of ways to collect data about student interests that do not require technology, but most of them involve lots of little slips of paper, which I personally don't deal well with.  For this Tech Thursday I wanted to write about using Google Forms to collect data as you build community in your classroom.

One of the most important parts of a positive classroom culture is safety.  Students need to feel safe to participate, to fail, to ask questions, etc..  One of the first surveys I send out to students each year asks students who they can work well with and where they prefer to sit.  Getting student feedback on these two items can help alleviate some of the anxiety caused by all of the changes a new school year can bring. This is also a good time to ask about vision and hearing impairment.  While most students will let you know if they need to sit near the front, there will always be a few that are too shy to speak up.  I let students know that all seating arrangements are tentative, and that changes will be made if needed to support the learning of each individual and the class as a whole.

The screenshot below is from a Google form that I have sent out to students in the past.  There are plenty of programs that make surveys, but I prefer Google forms because the results live in my Google Drive so it is easy to refer back to later in the year.

Setting up group norms is also key in successful groupwork.  I like to brainstorm class norms for groupwork with each class, and use these lists as a starting point to agree on a final list for all of my classes.  I start with a prompt such as, "What do you think are the three most important rules for working in groups?" .  Give students a few minutes to make their own list, then narrow down the list in pairs or groups, then share out with the class (Think-write-pair-share).  We pick four or five for the class, and then after doing this with all 5 classes I will pick 5 common ones to post.  I will also add in important norms that students may have overlooked, but generally high school students do a good job of generating them through this process.  Google forms is also great for collecting input during a brainstorming process, though I haven't specifically used it during the group and classroom norms process.

After we start working in groups I will send out surveys to help students self assess how well they are working in the group, and whether or not there are any issues with the group.  Getting feedback on group set-up and progress helps students feel safe, and gives them a voice.

Another use of surveys for community building is a quick beginning of class icebreaker (favorite movie, favorite breakfast food, favorite song, etc.).  Icebreakers can be done without technology of course, but if you have access to technology for each student then it is a quick process, and a great way to help students get to know each other.  If you are not familiar with Google forms, there are online tutorials and videos to get you started.  Socrative is a another program that works well for this type of activity, and definitely worth checking into.

What types of activities/supports do you implement during the first week of school to help build community in your classroom?  Please share!

#July2014 Challenge: 5 Things

5 Things I can't live without in my classroom

Seating Charts

In 2014, this method feels pretty low tech, but it soooo works for me.  I made these seating charts in excel about 10 years ago, and I use them every year.  I make copies for the entire semester at the beginning, staple them together, and take a new packet out each Monday.  I can record attendance, classwork, and homework scores in the same place, and there is space in the margins to write notes about late work.  

Computer paper in different colors  
I haven’t tried interactive notebooks yet, but we make foldables in my class at least once per chapter.   Sometimes we will make a sophisticated foldable such as a flipbook, and other times we’ll just fold the paper into fourths or eighths and put a problem in each box.  Students like foldables for warmups because they can easily find the paper at the beginning of each day, and if you spiral the problems from the chapter it can help students study.

Flipbook Envelopes 
Not sure where I got this idea from, but I have used these envelopes for many tasks.  I keep a set of index cards in one of these with group progress grades to place on tables during group work (though I’m seriously considering changing to red-yellow-green cards after reading several posts this month).  Another is for name cards organized by period so I can randomly call on students.  A third is for sets of problems to use during groupwork activities.  

To make a flipbook envelope you first make a flipbook. Take several sheets of paper, and align as shown in the picture below.

Fold all the sheets over so that your papers look like the picture below.  If you want a flipbook you put three staples across the top.

If you want a flipbook envelop (mini-filer) rotate 180 degrees and staple along the sides.  

My smartphone  
This device replaces many of my must have tools from a decade ago.  I use the timer, the camera, name picking apps, just to name a few.  I even made a Google form to use as a to do list, and I put the icon on the front page of my cell phone.  The results of the Google form are recorded in a spreadsheet, which makes it easy to edit and prioritize at a later point in time. I can also open the spreadsheet from any computer or device, making it easy to keep up with all of the little items

Geogebra 
Need I say more?  I use this as a demonstration tool, and also to make lots and lots of diagrams for worksheets and class activities.  Having access to quick visuals really gets the students talking, and helps me to check for understanding.  One of my favorite discoveries was that you can take the tick marks and numbers off of the axes.  I’ll do this and graph several functions of the same type, such as parabolas.  Then I’ll write the equations for the functions on the whiteboard and ask students to match equations to graphs.  Without numbers on the axes the conversations tend to be richer, and we can generalize by naming other functions that could potentially represent those on the graph.

Definitely looking forward to reading more of these 5 things we can't live without posts, AND taking more notes on my reading so that I don't forget.