Algebra Skills in the Geometry Classroom

There was a time when Geometry was seen as the stand alone class in the math family tree.  When I was in high school, you could take Geometry in 10th grade or 11th, before or after Algebra II.  Basically you took it where ever and whenever it best fit in to your schedule.  Geometry at time was all about shapes, angles and proofs.  There was little to no Algebra used and the little that you did need, you could sort of fake it.  Not anymore.  Now Geometry is Algebra based.  With the advent of constantly changing standards and continually changing standardized testing each  math class is now a continuation of the previous one, often relying heavily on mastery of the previous one to be successful in the next.

Multi-Step Riddle

When I start a new school year in Geometry I spend the first day or two reviewing how to set-up and solve linear equations.  Why you may ask?  Simple.  Every new concept that we do from solving for parts of segments and angles all the way through surface area and volume, can and will, involve finding the value of a missing variable.  This is done more often than not through a linear equation, usually in one variable to the first power.  In regards to solving equations, we even use them as the basis for our proof structure.  When I begin to introduce how to write a proof, I don't start with Geometric proofs, I start with Algebraic.  I ask my students to solve multi-step linear equations and to tell me what they did in each step.  This not only gets them used to the structure, but also reinforces why they do what they do when solving a linear equation.

Coor Dist/Mdpt Task Cards

As we move further on into the school year even more concepts from Algebra begin to pop up.  One of the most prevalent is the use of the Cartesian Coordinate Plane.  We first encounter it when we are finding the length (distance) of a segment.  We graph the two endpoints and use the Distance and Midpoint formulas to find how long the segment is and where the halfway point is.  Since this is more of a review, then a new concept however, I teach it using Task Cards for the students to practice versus spending a day on it like it is a new lesson.  We continue using the coordinate plane and Algebraic Concepts when we graph triangles and quadrilaterals and use the distance, midpoint and slope formulas to classify our shapes.  The last time that we explicitly use the coordinate plane is in our unit on Transformations when we graph our figures and reflect, translate, rotate and dilate them using coordinates.  

Trans Unit Review

The other major Algebraic concept that use consistently is square roots and radicals.  We first encounter them when we solve the distance formula but at point it is a pretty basic use.  Once, however, we hit our unit on Right Triangles and Trigonometry, squares roots stick with us for the rest of the school year.  We use them to solve our right triangles and to find missing pieces of quadrilaterals.  We also use them when finding the tangent, radii and diameter lines for circles and the surface area and volume of three dimensional figures.  

Spec. Right Triangles Bundle

For these reasons, and so many more, I stress mastery of concepts, not just retention of them for a test in my Algebra class.  I am honest with my students and I tell them that this ideas will not "go away" once Algebra is done.  They will use them again in Algebra II and then will take Algebra I and II skills with them as they move into Geometry.  Additionally, we talk extensively about which of these skills will be useful in the workforce and why.  I try to be as transparent as possible with my students and normally it works in my favor.  What Algebra skills have you seen move beyond Algebra?

Riddle Worksheets, Mazes and Coloring Sheets: Making Practice Fun(ny)!

Not everything in life is fun, I get that. Sometimes you just have to push through and get it done, I understand that too. When you are competing, however, in a world of technology, bright colors and immediate gratification you have to get creative to hook your students in. As a result I went on a quest to find ways to get my students to practice the math that I was teaching and make it somewhat "fun" for them too.

My first stop was my own years in school from which I vaguely remembered getting the Pizzazz worksheets. They had this funny little pun or joke that you solved as a reward of sorts by finishing the problems. In my quest, however, I discovered that a) they were out of print and b) the ones that I could find were at a much

Geometry Riddles

Algebra Riddles

lower level than I could really use for a high school geometry class. That idea, however, lit a spark and made me wonder, could I create such a thing? I discovered that the answer was yes I could in fact do so and my Riddle Worksheets were born! Thus far I have created 22 "non-seasonal" worksheets for Geometry (available individually or in a money-saving bundle) as well as multiple versions of the most popular topics with a Halloween, Thanksgiving and Christmas theme. I have also created ten for Algebra (also available individually or in a money saving bundle) on some of the more popular topics. I have more planned for both areas, when the creativity bug strikes me again! Each worksheet features about 15 problems that required the students to solve the problem, locate their answer in the answer box and then solve the pun. Mystudents usually groan, a lot (!), when they solve the pun but they get excited when I hand them out and enjoy doing them! The practice that students get and the collaboration they do is so rewarding!

4 The Love Of Math

Alas through, teachers cannot live by riddles alone, nor do I really want to! This lead to my second stop, which was a search on TeachersPayTeachers for fun algebra or geometry worksheets and I discovered Mazes! These worksheets are beyond phenomenal! They require students to start by solving a problem and give them two answer solutions. Whichever answer they get, leads them to the next problem to solve. The students repeat this process until they gotten all the way to the end of the maze! I love these for so many
reasons! 1) They are self-checking. If students don't get one of the two answers provided they know that they did something wrong. 2) They identify the most commonly made errors since the "wrong path" is created by making the most common mistakes and leads to great classroom discussion. 3) The students have fun! Students need to realize that math is enjoyable and these mazes help to make that happen. My favorites so far are by:   4 The Love Of Math, Teaching High School Math and All Things Algebra

Mrs. E Teaches Math

Another type of maze that I happened upon are created by Mrs E Teaches Math and are a "get up and move" type of station maze. In these problems the students start by solving a problem. Depending on the answer they get, they move to a specific station. If a student makes a mistake, they are sent back to a station that they already completed and have to back track to figure out where they made their mistake! She has a variety of these mazes as well as chain activities and sum 'em activities. I love everything in her store and she has a great blog too!

All Things Algebra

As I was searching on TPT for fun worksheets I also came upon my third stop which is some great coloring worksheets and honestly, who doesn't love to color??? :) These worksheets ask students to solve a problem and then color in an area a specific color if their answer falls between a certain range of values. These are fantastic for so many reasons! 1) They get students practicing and working out the problems with a goal in mind. 2) Students have to be able to place their answer in a range of values which is great for ordering numbers. 3) Students love to color. They may complain, but they really do love it! Some of my favorites so far are made by: Lindsay Perro, All Things Algebra , Activities by Jill, and 4 The Love Of Math .

I encourage you to check out some of the great resources I've highlighted here and go searching for your own. Not only will your students thank you, but you'll thank yourself too! :)   

Celebrating the Holidays in Secondary Math Land

It is often difficult at the secondary level, especially in a math class, to find ways to incorporate the holidays.  We can't study the history of them like you can in the social studies curriculum or read stories about them like you can in the ELA curriculum.  The link that would allow us to illustrate them like you can in Art or easily do skits like you can in Theater doesn't readily exist either.  So after much thought, I decided to create holiday versions of my riddle worksheets.

Doing so allows me to a) bring a little of the holidays in, b) review or practice needed skills and c) allow the students to have a little bit of fun.  This of course, also lead to some difficulty as not all Geometry classes are at the same point at the same time.  So I picked some generic topics and focused on the three major holidays of Halloween, Thanksgiving and Christmas.  

Since it is only a week until Thanksgiving, I thought I would share a few of the riddles I created with you - just in case you are in the same spot as I am! :)

I have riddles that cover the Basic Concepts topics of Angles of Triangles, The Segment and Angle Addition Postulates and Angles Formed by Parallel Lines

Angles of Triangles

Angles Formed by Parallel Lines

Segment and Angle Addition

I have riddles that cover the Right Triangle concepts of The Pythagorean Theorem, Special Right Triangles, Simplifying Square Roots and Trigonometry.

Pythagorean Theorem

Simplifying Square Roots

Simplifying Square Roots

Sin - Cos - Tan

  Finally, I have riddles on the Quadrilateral Topics of Properties of Special Quadrilaterals and Interior/Exterior Angles of Polygons.

Interior/Exterior Angles of Polygons

Properties of Special Quadrilaterals

I hope you can find something to add a little Thanksgiving to your Spectacular World of Secondary Math!

Happy Thanksgiving!

How To Assess Student Comphrehension and Have Fun at the Same Time!

As a secondary math teacher I am always on a quest to find ways to not only assess my students' knowledge but to also engage them as I do it.  I have researched various techniques looking for ones that encourage collaboration, assess knowledge and allow students to communicate mathematically.  The incorporation of these activities helps me to shift my room from the more traditional teacher center to one that is more student centered.

Right Triangles Vocabulary Matching

The first technique that I use addresses the variety of new vocabulary that arrives in Geometry and helps students to connect the pieces that go along with those terms including the definition, diagrams and ways to label the diagrams.  I have created a series of vocabulary matching activities for various units including triangles and congruency, right triangles and trigonometry, quadrilaterals, beginning concepts and circles.  Each activity includes a set of teacher instructions, a student answer sheet, cards for the term, definition, diagram and label (when applicable).  The activities encourage students to work collaboratively and are also great for use in station activities!

Beginning Concepts Bingo

The second technique, Bingo Games, also address not only vocabulary but also the ability to hear a definition or description out loud and make the connection to the terms/concepts.  These are also great fun!  I have made them for various units including triangles and congruency, right triangles and trigonometry, quadrilaterals, beginning concepts and circles.  Each Bingo game includes two sets of 32 cards - one with the term and one with diagrams, two different teacher call sheets and the cover squares as well.

Task Card Bundle

The third technique that I use is task cards.  Task cards allow students to focus in on just one problem at a time and can be written at different questioning levels which allows for differentiation and for students to work at their level of understanding.  They also allow you to identify where students may be having difficulty without the students feeling overwhelmed.  I currently have five sets of tasks cards that can be purchased individually or in a money saving bundle.  I have many more sets planned!  

Geometry Riddle Bundle

The last technique that I use is riddle worksheets.  Riddle worksheets are worksheets that have the students working through a puzzle as they solve problems.  Riddle worksheets are usually 15 - 18 questions where each answer corresponds to a letter in the answer to the riddle.  I love them so much that I currently have 22 riddle worksheets covering the major topics in Geometry and 7 for Algebra!  The Geometry riddle worksheets can be purchased individually in a money saving bundle. 

I am investigating new techniques as well including formative assessment, group projects and station activities!  I will share them with you a future post so stay tuned!