Differentiating Assessment

How many math teachers give the same math test year after year?  Make your math tests and quizzes more valuable to students and help them learn in different ways.  Using academic vocabulary and teaching how you want your quizzes and tests done, you can have more creative tests that students enjoy to do.  A few academic vocabulary words you can put on tests that incorporate a different range of student learning are:  draw, estimate, anticipate, suggest, rank, and investigate.  These words help you change your tests so that students have a higher-level thinking about mathematics how they can apply math to different situations.


Academic Vocab

Questions of the Day

Having questions of the day or questions of the week where students can work on harder problems or problems that could be on the test are a great way to get students interested in mathematics.  Giving prizes to first, second, and third places are the best ways to show that knowing mathematics helps you advance not only in school, but in life.  Listed below are multiple sites that offer questions of the day on their website.

Question of the Day

Weekly Problems

Math Buddy

There are mounds of books that incorporate math puzzles and brainteasers that you could use in your classroom to inspire students to work hard to use their brain in higher order thinking and problem-solving.  Another great website is http://www.themathleague.com/ where the math league brings challenging materials to students.  The league includes contests, books, and computer software designed to stimulate interest and confidence for math students.  

ShowMe

Sometimes we know that student or multiple students who take almost beautiful notes in your class, that you couldn't even make them better than those.  Now with a iPad, you can have the notes along with everyone else in your class.  ShowMe is a interactive learning community where you can upload student notes and problems to the ShowMe website where if a student had missed the last class or multiple classes you can have them watch a lesson or problems you worked on in the class.  One of the best things about the ShowMe application on the iPad is that you can record your voice to explain notes or problems in greater detail then writing them down.  Featured below is ShowMe from the website and goes over a very interesting way of multiplying fractions using the value of one.

Area Tricks

Most math teachers have seen how 1=0 and most of the tricks you see in college.  But, math area tricks are easier for middle and lower secondary schools to implement and describe why there are problems with the current picture.  Below is one of the math area tricks, it demonstrates not only triangle awareness but area understanding.  Look at the picture below and tell me where the hole comes from?

The goal for the students is to become masters at interpreting graphs and understanding of the whole picture.  There are many different websites for area tricks and multiplication tricks, one siteMath Tips, Easy Calculation, and Math Tricks.

Multicultural Math

How do you use instruction to grab the attention of all your students, especially if you are in a diverse classroom?  First I am going to give you the big three points in using multicultural teaching strategies in your classroom.

1. Knowledge Construction
2. Prejudice reduction
3. Equity Pedagogy

 The basic three things are all you need to get your classroom culturally aware.  They start by extending the lesson/lessons/unit to offer students the opportunity to make sense of the mathematics for themselves.  Secondly, offering students the opportunities to break stereotypes; develop more democratic attitudes, values & behaviors.  Lastly, are my instructional practices designed to improve the achievement of all students regardless of race, gender, ethnicity, exceptionality, or class?  Now, for a few extra sites that incorporate multicultural strategies directly into mathematics.  A multicultural fair, and math talk.

Trial by Math

Taken from Time Magazine (watch out this article was in the 60's) (Parental Discretion is Advised)!  A quick introduction is that an elderly woman saw a blond girl with a ponytail run from an alley and jump into a yellow car driven by her husband.  The prosecution, impressed by the unusual nature of the matching details persuaded the jury by the mathematical law of statistical probability.  The jury was persuaded by a university professor who determined the probability was 1/10 the car being yellow and the interracial couple being 1/1000 when multiplied you get the odds were 1 in 12 million (somehow).  The California Supreme Court recently turned up serious defects (as you can tell).  That the probabilities were roughly accurate and that they are not fully independent.  In thus the guilty party, is not guilty at all.  Recently turned up evidence is that there was a 41% chance of at least one other couple in the area that might satisfy the requirements.

Trial Article

Math Trails, anyone?

Math trail are a great way to incorporate everyday mathematics in to the curriculum.  Below is a video featured by a professor, it shows him going through geometry, algebra, and mathematics everyone teaches in their classroom in an exciting way.  A math trail is a walk with various stops where you look at math in the world around you, and ask questions about it.  Math trails stimulate interest in math in middle and high school, when classroom math becomes more abstract.  Math trails help students not only get out of the math classroom, but see that math is alive and comes to life when you look at it.

Geometry Playground

The Outdoor Classroom

There are many different ways you can incorporate nature and nature walks into a math lesson.  Building real world meaning and creating awareness for environmental concerns are great ways to get student's interested in outdoor activities.  In an outdoor setting all our senses are aroused and so many natural opportunities for stimulation.  A few ways to incorporate the outdoor classroom in mathematics is are listed below.

• Counting Tree Rings
• Distance across a pond or lake.
• Speed of a river
• Slope of a hill
• Average temperature
• Height of a Tree
• Time of the day.
• Population studies: students, state, fish, plants, trees, deer.
• Competition among animals
• Compass directions.
• Feet in yard/degrees in a circle/area/time/shapes
• Fibonacci Sequence

The Fibonacci sequence is a great tool to use in the outdoors, because the numbers in the sequence are the total amount of petals on a flower, spiral on pine cone, and sometimes leaves on a branch.  You can have students try to find as many Fibonacci numbers as possible outside in 10 minutes and then share their findings.

Pre-Friday Lesson

Since most teachers lesson plan over the weekend, or the end of the week.  Everyone knows how hard those beginning classes are to get your students to accomplish tasks and pay attention.  One way you can take back their attention is bingo-cards.  From http://www.bingocardcreator.com/ a bingo card creator you can put your own words and once you cover topics they can cross out and once they get bingo and shout it out mid-lesson or once you finished talking, you can give them their prize.  In the morning classes I love giving either apples or granola bars, something healthy and will wake them up.  Later in the day I vary my prizes.

The students I have seem engaged when the bingo cards come out and they are easy to change and come up with bingo cards that directly relate to my lesson that I am teaching for the day.

"Pocket Mods"

Infusing Technology into the Classroom: "Pocket Mods" for Education: This is a great way to introduce math journals in to the classroom, by instilling thinking and reading in the classroom. The students can make the pocket mods at home and bring them to class, my favorite is using them as review notes that the student can take home and study.

The best thing about the pocket mods is that it can incorporate graphs, grot paper, and dot paper. The pocket mod application also includes formulas and morse code for the math people in us. :)

Happy Teaching!

Reading Theatre

Every teacher needs a little time off and the reading theatre is the way I take my time off.  You have the student's read a portion or part of text and then apply either a guide or writing prompts to guide them through the rest of the lesson.  A few of my favorite math texts to read in class is Math Curse by Jon Scieszka it is a great way to incorporate not only reading skills but helps develop recognition with word problems. In the story a teacher tells a student that everything can be a math problem and has trouble sorting math from his life.  Other great stories are featured here, and a place to get free pdf's of these books can be found here.  The reading theatre is a great way to incorporate real world applications and have an engaging classroom in which everyone can learn. 

Math Journals

Math journals are a great way to not only incorporate writing in the classroom, but to also include higher-order thinking and an easy way to test for prior knowledge.  Math journals can be a simple bell ringer from what they learned from the math class before or you can have your students share your math journals with each other in a gallery walk.  Student's math journals need to be seperate from their notes so they can easily be turned in to you and the teacher must model writing in a journal and how the teacher wants the prompts written down.  One rule of mine is that the student must write at least 20 words or enough to clarify what they are writing about.  A few prompts are listed below in the 101 Math Journal Prompts.

Prompts


Journal prompts can be an easy way for teachers to show interest in the students and get to know more about the students and how they are understanding math.  Happy Teaching!

Friday Super Freebie

Teaching algebra from a book can be boring, especially for the teacher sometimes as well.  Another way to incorporate algebra in a fun and new manipulative is algebra polygons.  Students come up with patterns they see in the polygons, they can share them with the group, then the rest of the class.  You end up getting a linear equation with two variables when you follow the directions on the screen and using higher-order thinking students can come up with possibilities for the final one, or one that could even be past the octagon, a decagon.  There are many different ways you can use this manipulative, but featured below are the algebra polygons.  Have fun and happy teaching!

Algebra Polygons

Compound

It seems like all middle school level kids are reading or have already read Compound by S.A. Bodeen is a well written novel about the brink of nuclear war and the compound underground in which they live their life.  I know you are thinking this is not math, it reading.  But, it is easy to adapt any lesson plan to fit the book your students are reading.  I'm going to give some of the mathematical side of compound, without giving away any of the details for those reading or wanting to read the book.

• Prologue: Area of a circular room, rate*time=distance, running on the treadmill.
• Chapter 1: Free-throw percentage.
• Chapter 2: Ingredients, using proportions for life underground.
• Chapter 3: passwords, number of books.
• Chapter 4: seating for 16, volume of a stove, "How much toilet paper you will use in 15 years."
• Chapter 6: Dilution rates.

 It is a fabulous book, it is a quick read, I finished it in about a day.  Happy Teaching!

Origami Geometry

In high school geometry students examine the types of geometrical operations that can be performed by using only a straight edge and a compass.  Origami has similiar and sometimes origami's axioms are easier to understand since in some origami there are a base principle of 6 axioms.

1. Given two points p1 and p2 we can fold a line connecting them.
2. Given two points p1 and p2 we can fold p1 onto p2.
3. Given two lines l1 and l2 we can fold line l1 onto l2.
4. Given a point p1 and a line l1 we can make a fold perpendicular to l1 passing through the point p1.
5. Given two points p1 and p2 and a line l1 we can make a fold that places p1 onto l1 and passes through the point p2.
6. Given two points p1 and p2 and two lines l1 and l2 we can make a fold that places p1 onto line l1 and places p2 onto line l2.

Origami is finding new applications here on earth and also orbiting earth in satallites and spaceships.  Origami is a new way of finding simple concepts in algebra and geometry and expressing these ideas in an abstract, yet real-world way.  There are some lesson plans out there for origami, but very few on complex origami and detailed mathematics.  (Here is link for one lesson plan on origami in mathematics Origami ) 

Using Apple

Using technology in the classroom optimizes student learning and since most of the people reading this are Mac users and most teachers are Mac users (this one is for you).  I'm going to start with iTunes, there is a podcast called A Brief History of Mathemaics with BBC America that a good background knowledge about the history of mathematics.  Other great podcasts including mathematics is Bite-Sized History of Mathematics and much, much more.  There are also great iPad apps such as free ones like powerOne Scientific Calculator, Sketchpad Explorer, and Math Terms. (Look up Super Formula as well) There is are also free books that include mathematics such as Amusement in Mathematics by Henry Ernest Dudeny and others.  At iTunesU there are many different webcasts you can have students play and download to either catch up or have for gifted students in your classroom.  Apple includes websites for uses in mathematics, one of the links I include here is about Origami and the mathematics behind it.  (Origami)  Apple provides many opportunities for teachers to be included in technology in their classroom, I know for a fact that Apple works through schools and can have field trips to local Apple stores to have your students be proffessionally trained on iPads, iPods, and apple computers.

Right-Brained Students

I have student taught in places where right-brained students were left in the dust.  I don't want your classroom to be this way.  Right brained students are math teacher's best friends always very helpful and if you tailor your lesson plans correctly, they will eat up everything you put in front of them.  Every teacher needs to teach from different perspectives and teaching both left-brained and right-brained students is easily accomplished.  Follow a couple of these steps and you will have no trouble handling all students.

• Captivate and Entice- right-brained students need to be lured in with attention getter's and interesting information.
• Complex Mathematical Concepts- where is this going, right brained students need to see a big picture and if they are going to use this information in the future they will master this information now.
• Hands-on- all students are hands on especially right brained students to help solidify information.
• Real-World-Examples- when are we going to need this, real world examples will help students use the mathematics in the real world.
• Mental Math- it is easier for right-brained students to visualize the problem not writing it down.  A favorite quote of mine is when a student came in for help after school and the student was struggling the teacher said, "Wait, anyone can do math on paper, try to visualize the problem in your head, then solve the problem." It worked.
• "See the Problem"- word problems can be straight up tricky.  Have the students visualize (the attack!)

Extra Super Bonus Post

Since today is 9/7/11 all odd, today my post goes out to Ron Gordon.  A California teacher spreading the word about numbers and not just numbers, but how math can be fun and exciting at the same time.  On his website he has created a contest and offering the date in dollars.  For most of the world an odd day happens only a few times in century, but now more than ever they are becoming especially rare.  The next true one will occur 9/11/13 (in two years). 

So if you are feeling odd today, just know you are not alone.  (Even though most people are odd all the time)  There are even events on Facebook dedicated to Odd Day. (Odd Day Event) "Grab your friends and family and hold a 'Parade of Odd Characters,' or any celebration you deem fit for this rare and wonderful holiday!"

Incorporating Physical Education

As a younger students have recess and middle school students might have P.E. for 30-45 minutes in a day, math class is an easy way to incorporate moving around and abilities you might not get to see in other classrooms.  There are many different ways to incorporate movement and higher-order thinking at the same time, not only does it help the student, but also helps student's brains get organized and have to think harder.  Some examples are located below: (this might be a little long)

• Dice Math:  form circle throw dice in middle-> have students do activities based on number they throw. (activities might include jumping up and down, other stuff)
• Pathways:  linear equations: move around class- information about Christopher Columbus, Oregon Trail, and seasonal migrations.
• Mid-class Stretch:  arm stretches, shake hand, reach for sky, walk around.
• Music:  math problems- math musical chairs.
• Area:  calculating the area of mypyramid.gov
• Paper:  basketball, volleyball, golf, soccer.
• Paper Plate Math:  target toss math, numbers on paper plates.
• People Graph:  circle, hyperbola, parabola, ellipse
• Touch:  touch numbers on the board for answer, race.
• Activities:  different shapes mean different activities.
• Balance:  have students balance or on their tip-toes to answer problems.

Incorporating History

"Where does this math come from?", "Who uses this math?", and "Who came up with this stupid stuff?" are all questions students ask and most of these questions are valid questions.  I know my math teachers in high school never told me where this hunk of information came from.  But, sometimes the information can be quite interesting and math has had a role in shaping our history and where we are today.  Sounds like a cliche, and it is.  Not only can math be fun and interesting, but the background about mathematics is easy to teach and helps ground students and have a deeper connection with mathematics.

• Archimedes
• When Syracuse finally fell to the Romans, Archimedes was preoccupied with a mathematics problem that he was drawing in the sand.  The Roman General told his soldiers that he should be spared.  Archimedes refused to follow a soldier until he finished the problem that he was working on, then the soldier drew his sword and killed him.
• Well known for his estimate on Pi.
• Set fire to a Roman ship using mirrors.
• Negative Numbers
• European mathematicians argued that negative numbers would represent quantities less than 0, which if less than nothing doesn't exist.

I have a lot more on the history of mathematics, please don't hesitate to ask, and happy teaching!!

S2D2 Graphic Organizer

Graphic Organizers are all the rage now.  My favorite graphic organizer in the math classroom is S2D2 graphic organizers, which the letters don't go exactly in order, but what the heck.  S: for spell the word. D: define the word.  D: draw the word.  And finally, S: use the word in a sentence.  Below is featured a template and below that is an example one featuring parallel lines.  These examples are a roughly done, I'm hoping that you tailor yours to your classroom.

Template

Example Template

Interactive Websites

There are many websites out there that you view to get a different manipulative or even a different way to teach a particular concept and it turns out to be a bad website that offers no advantages to your students.  There is the main one that everyone knows about, which is Illuminations which is based off NCTM and their standards, which is a good way to find lesson plans that are "ready to go."  Through Utah State University there is the National Library of Virtual manipulative's, located at NLVM it is a great way for students to see algebra and understand geometry to a further degree.

Smart Board Mathematics

Smart boards are the teachers best friend.  Teachers best friends use to be PowerPoint's, but how boring can those be? SNORE!  Listed below is a website that has many different games and templates for teachers to use in mathematics, most of which are more elementary concepts such as adding, multiplication, subtraction, and numbers.  But, the one I want to focus on is sequences.  In algebra you start to touch upon series and sequences, a good introduction is a useful smart board application where as the teacher you can move the student to count by 2's, 5's, 100's, and even negative numbers.  You get a glimpse of sequences in elementary school and here is a good introduction to build upon the student's prior knowledge.  The link to the main website is The Teacher's Guide and the link directly to sequences is Sequences .