Get Out The Scissors and Glue - It's Cut and Paste Time!

There are so many skills that we strive to master as children from writing, coloring and of course using scissors. As we move through school cut and paste activities are highlighted and incorporated often because they achieve so many goals and can be used so many ways. Some of these uses can be to match two related things (i.e. the number one with the word one) or to combine various parts of things to make a whole (i.e. the parts of a snowman or a turkey). Doing such things really help students to "see" the connections.

As we move up through the school years, however, this method of teaching and enrichment really starts to fall by the wayside. We get so busy trying to prepare students for the next grade, the next test or for college that we forget that we can use other techniques besides just "stand and deliver", homework, tests and quizzes. Additionally, at the secondary level these methods are not usually highlighted, taught or to be honest, encouraged. As my years as a teacher have gone on and my students have changed so much, however, I have started to seek out new methods to make connections and help students to see how the math topics we discuss interact with each other.

Congruent Triangles

The first time I did a cut-and-paste activity I was sure that it was doomed to failure. I mean, these are high school students after all, and cutting and pasting is
an elementary task. But everything else I had tried to get my students to see the methods of proving triangles congruent were not working so I needed to try something else. I laid in bed that night brainstorming (that is, after all, where teachers do their best thinking!) and racking my brain about what I could do. I came up with a task where my students were given a set of triangles that were marked with one (or more) method(s) of proving triangles congruent and they had to sort them. I decided to go beyond sorting on a piece of paper, however, and made them actually cut them out and paste them into their categories. The students LOVED it and more FINALLY got the methods and what they look like! I was floored that something so "elementary" worked so well! 

Algebraic Proofs

Similar Triangles

I went on the create similar activities on proving triangles similar that not only had students cutting, pasting and identifying the similarity methods but also had them practicing the angle sum theorem and setting-up and solving proportions.  As we started a unit on logic and proof I devised a way to make algebraic proofs a little more interesting and again help to engage them As need arises, I'll create them on other topics as well - which is currently segment and angle addition proofs!

Domain and Range

It was with little surprise to myself then, that when my Algebra students started struggling with domain and range that I turned to my favorite website to find some resources to help them and I found the best cut-and-paste activity on domain and range. It gives students graphs, mappings and tables and asks them cut out the domain-and-range cards and paste them on to the corresponding graph/table/mapping cards!  The activity came as a part of bundle made by ScaffoldedMathandScience. It was amazing how many students not only finally "got it" but the great conversations and collaboration that occurred.


I have since picked up cut-and-paste activities by the fantastic Lindsay Perro including some on Writing Equations and Point-Slope/Slope-Intercept forms. I have also picked some up by the amazing activities from All Things Algebra on Linear Inequalities and 4 The Love Of Math on Order of Operations.  I shopped at MissMathDork  for help on Translating and Matching One - Step Equations and Factoring when a > 1.

 I love cut-and-paste activities and have many more on my wish list for future visits. I encourage you to reconsider using some traditionally elementary techniques in your secondary math classroom. You might just be surprised at the results! What are your favorite "elementary techniques" that you adapted to the secondary level?

The Delicate Balancing Act - Parent and Teacher, part two

As a parent we are faced with many challenges as our children grow. The first days they come home we have to figure out their many cues and what different cries mean. We have to figure out how change a diaper without getting peed on (especially if you have a boy or two) and how to burp a child without getting spit-up on. We have to figure out how we balance being a parent, a spouse, housework and for most of us, working a job too! We spend time wondering if we are doing it right, wrong or like most of us, somewhere in-between. Then that magical day comes and we send our first child off to kindergarten and a whole new balancing act begins.

My husband and I had this joyous experience a few months ago when our oldest who will forever be "our baby" boarded the bus that would take her off to kindergarten. I had written in a previous post about my trepidation about doing so and for the most part, that trepidation was unfounded. Her teacher is awesome, she has made friends and genuinely loves going to school.

So while my original reasons for worry were most unfounded, I have found things to worry about that never occurred to me! First, my daughter is smart. Not Sheldon Cooper smart, but smart enough to be reading at an almost second grade level in Kindergarten. This has resulted in her doing first grade ELA in Kindergarten at a time when most of her classmates are still on sight words. This led to issues the first few weeks because she couldn't understand why she was in a reading group with only one other girl while everyone else had reading groups of 5 - 7 students. She felt singled out and got sad. After we explained that she was being challenged and was doing well, she calmed down and felt better about it.

Until they started doing math that is...now being the daughter of a math teacher and an engineer with teachers and engineers as grandparents she is inundated with math in one form or another on a pretty consistent basis. She and her brother will "help" me check papers, "assist" me creating activities, "build" with daddy and so on. As a result, she is also advanced in math. This lead to a great deal of frustration on her part because everything was so easy for her. And her frustration lead to her acting out in class in the form of "helping" her friends do their work which really translates into giving them the answers. Cue another discussion about the difference between helping someone and doing it for them.

On the flipside, while my daughter is advanced on an academic scale she is exactly where she needs to be on a maturity scale. She has difficulty keeping her hands to herself, gets cases of the giggles, forgets to use her inside voice and is the most adorable, wonderful little girl that I love more than any other. She is strong-willed and while that will serve her well someday, it does earn her strikes in school for wanting to do things her own way. She is a unique little girl with a well developed imagination who will be a handful as a teenager. I still haven't figured out how to teach her to temper her impulse to act on the things that cross her mind. I know as a teacher that this can lead to big(ger) problems the older she gets. But, she is five and that ability comes with time. So in the meantime, I'll keep doing the delicate balancing act and hope that it serves all of us well! How do you handle the balancing act?

Reviewing Beyond A(nother) Worksheet

After all the days of teaching a unit, doing practice work, quizzes and other formative assessments I find that I need to change it up a little bit for the review before an assessment. I have explored many different methods and want to share a few of my favorites with you. The results will of vary depending on the make-up of your class and how well they can keep the noise level down when being up and moving around!

My first favorite is to use station activities. Station activities can be designed in multiple ways. I have done some stations where students complete task cards at each station that focus on different skills or concepts for the unit. For example, I just finished a unit in Algebra on functions. My students had a station activity where each of the five stations focused on major skills - 1) finding the domain and range from a table/graph/mapping and identify whether it not it was a function, 2) evaluating functions, 3) writing a function rule from a table, 4) find the domain and range from a graph, and 5) applying functions to create distance time graphs. I found that this worked well because they were focusing in on one concept at a time and I could quickly identify if there were gaps or holes in their knowledge.

I have also done station activities where different stations actually have them completing tasks. I did one where one station has them going online (usually using i-pads) to look up a topic, one station had them constructing something out of pipe cleaners, another had them doing a matching activity, and two were problem solving. This type usually works better in a more visual class like Geometry. Regardless of the type that you use, make sure that you have a timer displayed and that students know the direction of rotation. Also, make sure to build in rotation time when you are planning out the lesson.

My second favorite form of review is to use a review game such as BINGO or Jeopardy. I especially like using BINGO in a unit that is identification heavy be it from vocabulary or diagrams. My students enjoy it because they get to a) compete, b) win prizes and c) be noisy! When setting up a BINGO game make sure that you either laminate your cards so that can be reused or have the students create their cards themselves. While I don't use Jeopardy as often, the times that I have I found that my students really enjoy it. The only drawback that I have yet to overcome is how to have students "buzz" in.

It was from this drawback and I discovered my favorite review game of all time to play in the classroom...KAHOOT! :) I love this game. My students love this game! It is a win-win situation all around. The game is free and if you search on the website there are ready made "Kahoots" already created that you can download and edit to suit your needs. The two essential requirements are a board to broadcast on and devices (i-pads, computers, phones) that can connect to the internet. It is an online game. Whenever I mention Kahoot my students get excited. They enjoy it so much that they ask if we can play. A really wonderful feature of Kahoot is that you can download the results and save them so that you can use it as a form of assessment or a record of their knowledge gained. Are there still units that I use a paper and pencil review on? Of course there because a review game or station activity won't fit every unit. But they are not always my go-to anymore. I still always create on though in case the technology goes down and so that absent students can still have a review to use to prepare for the assessment. How do you review?

Dear Santa...Nerd Libs Link-up with Mel and Gerdy

Mel and Gerdy

Some spectacular people named Mel and Gerdy have started a Saturday Linky Party called "Saturday Nerd Libs".  I am new to all of this but when I saw that this week's is a letter to Santa, well I just had to join in the fun! :)

Jump over to their blog (Mel and Gerdy) and join in on the fun!

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! :)   

It's not a "sin" to do Trigonometry, It's a "Sine" of new content!

One of the biggest jokes in my class when I teach the Right Triangles and Trigonometry unit in my Geometry class is how to pronounce "sin".  I inevitable end up telling my students (jokingly of course) when they pronounce it as "sin" and not "sine" that it is not a sin to do Geometry.  Most of them giggle and then we discuss how to properly pronounce Geometric terms. 

One of the biggest problems I find in my Geometry class is a students inability to define the terms.  I cannot begin to count the number of times that I found it necessary in past years to redefine terms that we have already covered multiple times (think alternate interior angles versus consecutive interior angles).  Since vocabulary is so important in both general content and problem solving as well as on state testing I decided to talk the issue head on.

So in that spirit I want to share with you my top four ways to reinforce Geometrical vocabulary and to help students to retain it beyond a single unit.

Geometry B Bundle

Geometry A Bundle

1)  Illustrate, illustrate, illustrate!   I have embarked on a quest to illustrate our terms whenever possible.  I created sets of posters for every unit that we will study throughout the entire course.  Each poster is 8.5 by 11 and includes the definition, a labeled illustration and and pertinent facts.  I print them on card stock, laminate and hang them around the round grouped by unit.  I leave them up the entire trimester and refer to them constantly.  (I have them in my TeachersPayTeachers store in money saving bundles).

Triangles and Congruency

2)  Practice leads to retention!   I start every unit by asking my students to complete a vocabulary assignment (I usually give it to them as their assignment to complete after finishing the prior unit assessment).  Each vocabulary assignment includes a few pages where students give the definition, an illustration if necessary and any prior knowledge they might have.  I also include a crossword puzzle and a word search.  The students enjoy usually enjoy doing these assignments since it helps to give them a preview of what the unit will be covering. We refer back to these vocabulary lists as the unit goes on and students refine their definitions as the unit progresses. 

Congruency Vocabulary Activity

Early Concepts Bingo

3)  Play games or do activities!  Whenever possible I do vocabulary activities or play vocabulary games with my students.  I created some cut, paste and match activities for my students that require them to match the term, definition, a diagram and a label.  The students LOVE doing these.  It helps to tie all of the pieces together for them!  Additionally, we play vocabulary bingo games too.  I play one of two ways.  I either give them cards that are the terms or cards that are a diagram of the term.  Depending on what I gave them as a card, I will either read the term, read the definition or a project a diagram of the term.  We also play Kahoot (this does require you to have access to either I-Pads or smartphones and a projector or smart-board with internet access) which is the best online game to play I have seen in many years of teaching. 

4)  Get the students talking about the vocabulary and using it correctly!  I'm pretty sure that at times my students are either rolling their eyes when I'm not looking or thinking I'm slightly strange but I do not let them get away with skipping over the vocabulary during classroom discussions.  I ask them questions like "why can you do that" or "what geometry concept is being illustrated/applied" leading them back to the vocabulary all the time.  "Tell me why" is so commonly said in my classroom that after a couple of weeks I find students saying "wait, let me tell you why" or asking each other why!  I love it when it works!

Whatever works the best for you, embrace it!  The more you can get the students to understand the why, the what and the how behind what they are doing, the better they get at it!  In my opinion, students need to use mathematical vocabulary to truly retain the material. 

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!

Triangles, Congruency and Proofs Oh My!

There are few words that a teacher can utter in a Geometry class that inspire fear students at just the mention of the word.  The big ones are of course, test, quiz, exam and maybe "you have to write a paper".  In my class, however, these words compete with one more - proofs.  Literally, as soon as I mention the word I get
hit with a tidal wave of sound and complaints that all have one common theme - they hate proofs even though they have never written one yet. 

So this year, I set out on a mission to teach my students how to write proofs without the fear. I planned out what I thought was the best way to introduce them and how I thought I could transition them to writing Geometric proofs.  My game plan started out with a discussion on logic and how to try to communicate what you thought to be true with a logically sound argument.  Given that they are high school students I knew that I need to started it out a little fun so I shared with them my favorite logic, but not logic, but logic movie clip! The Battle of Wits from the Princess Bride.  The students had a blast watching it and it spawned an awesome discussion on logic, arguments, and how to support your point.

Cut, Match and Paste

From there my game plan moved us on to the most non-threatening version of proofs that I could think of - Algebraic Proofs!  By the time students reach Geometry they have taken (at least in my district) two years of Algebra and therefore can solve pretty well a multi-step linear equation.  After teaching Algebraic Proofs I have my students do a cut, match and paste group activity.  I have designed the activity to be easily differentiated depending on student level and needs.  Different levels include asking students to fill-in missing pieces, cut apart scrambled proofs and reassemble them or to write the entire proof from scratch provided only the given and the prove statement. With my class, the majority did the cut and paste aspect as I am trying to focus on hands-on activities this year.  This really helped to focus the students how to support each statement with a reason.

Cut, Match and Paste

The next step in my game plan revolved around Methods of Proving Triangles Congruent.  These types of proofs have a "formula" to them more than any other type of Geometric Proof and therefore are the easiest starting place.  I spent a couple of days teaching the students about the five main methods (SSS, SAS, ASA, AAS and HL) and what they look like.  Once I felt that they had a foundational knowledge, I again put them in groups and had them do a second cut, paste and match activity on those methods.  The students are given the five main headings plus "more than one method" and 24 sets of triangles.  They need to identify the methods being used, plus draw conclusions about vertical angles and shared sides to deduce other methods as well. The discussion that the groups had during this activity was wonderful, full of mathematical facts and had all of the students engaged and learning! 

Missing Reasons

I felt that my students were close to being able to write proofs and feel confident about it, but I wanted to take one more lesser step along the way so I gave them a set of proofs that had all of the statements, but were missing the reasons.  I prepared two versions of this activity.  The first has all of the reasons (plus a couple of extra) in a box at the bottom of each proof.  This is designed to help the students who need to see the possibilities.  I also created a version without the "reason box" for those more advanced students.  My students really enjoyed doing this and I found that some students choose to do the activity without the reason box!

Proof Practice

The last step on our journey through proofs was to write the entire thing without anything besides the given, diagram and prove statement.  I was much less nervous about doing this than I had been in past years because I felt that my students were really prepared and had the foundational knowledge to be successful!  The best part, when I handed it out, the only complaints I got were the normal
"I don't want homework" versus the "I hate proofs, proofs are hard, this stinks".  When I graded it, the majority of the proofs were correct and well written!  I count this as win! :) 

Our next step...Geometric Proofs on Segments and Angle Addition.  Hopefully, this journey will help that task to be much less painful than previous years!