## Congruent Triangles Cut and Paste

I did a quick, fun activity with my Geometry kids the other day!  One of my friends, Secondary Math Shop knows I'm LOVING cut and paste activities right now.  She gave me her “Methods of Proving Triangles Congruent Cut and Match Group Activity” to try with my classes.

We had talked about SSS, SAS, and ASA the day before.  In class, we talked about SAA and HL and talked about why SSA and AAA don’t work.  Then, I split them into groups and gave them this activity.

The actual size of the pieces are bigger, but I copied them two pages to one page.  I didn’t want to use a ton of colored paper; the supply is getting low.  :)  I had my kids glue the pieces onto the large anchor chart type paper (I call them giant non-sticky notes, but I don’t know what they’re really called).  I had my kids mark the congruencies (vertical angles, shared sides, etc.) with a marker.

Once my kids got started, they were so funny.  I walked toward one group to see if they needed help and I was met with, “We get this Mrs. E.  We don’t need you.”  Well then!  I also overheard this conversation:
Student 1:  Hey, you glue these.
Student 2:  No, you do it.
Student 1:  I’ll be honest here, my strength is cutting.  I glue like a Kindergardener, but I cut like a beast.
Student 2:  But I like cutting…
Student 1:  Then it’s gonna look like \$h!7.  You ok with that?

I like the posters my kids made.  I didn’t give them much time for decoration, but I think they turned out nice.  My favorite part of this activity (besides the mathematical conversations) was the fact that there was a category for “More Than One Method”.  How have I not thought of this before?!  I actually changed their test so that a couple of the problems have more than more method and the students have to list each one.  Love it!

## Congruent Triangles - Extra Information Activity

I really like congruent triangles.  It is one of my favorite units in Geometry.  I have lots of activities for congruent triangles and the kids are finally starting to get used to proofs.

Throughout the unit, I constantly remind my students that they need three pieces of information to show that the triangles are congruent.  I really like using this little activity to reinforce that idea.  This activity is part of my free resource library.  You can get access here.

First print all of the little matching cards.  All of the pieces look like this.

When, I copied the matching cards, I used a different color for each “problem”.  That way, I didn’t have to number the bags or worry about pieces getting lost.  It took some organizing though.  Each problem has four pieces.  So, I made sure that one of the SSS problems was light blue for all of the pieces.  When matched, the pieces look like this:

All together, I have three sets of each problem.  That way, I don’t have to have a bag of each one for every student.  They just return the bags as needed.

When the student takes a bag, they sort through the pieces.  They decide which piece of information is not needed to prove the triangles are congruent by the given theorem or postulate.  Then, they record the information on their recording sheet.

This works really well for my students.  It’s like they are working on little mini-proofs.  If you try this, I hope it works well for you!

## Polynomial and Rational Inequalities Matching Cards

So, you know that I love matching cards.  I made these cards to help my students practice solving rational inequalities.  I wrote the cards out by hand, so I don’t have an electronic file to share.

The students had to match the problem, the solution in interval notation, and the solution on a number line.

I also wrote letters and numbers on the backs of the cards to make them quicker and easier for my students to check their work.

These are the problems that I used for the matching cards.

If you make your own, tell me how it goes!

You may also be interested in:

 Factoring with Symbols

 6 Reasons I Love Matching Cards

 Simplifying Rational Expression Matching Cards

## 7 Ideas for Using Task Cards in the Classroom

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I’ll be honest, the first time I saw task cards I thought they were only for elementary students.  They started popping up different places and I saw that some high school teachers were using them too.  So, I decided that I would try them.  I’m always up for trying something new.  As strange as it may sound, my students are much more willing to work on task cards, rather than a worksheet.  I think it is because they aren’t overwhelmed by a huge list of problems.

I decided that today I would share a list of ways I’ve used them in my classroom.  Hopefully, you can find some ideas that could be useful for you!

1.  Stations - Before class, tape task cards around the room.  Students get a recording sheet or use scratch paper and move around the room answering the questions.  Students can choose to work alone or with a partner.  My students really like stations because it gets them moving around.  My stations mazes are an adaptation of this idea.

2.  Seatwork - Spread task cards out on a table (or a desk, the floor...).  Students pick a card, work on it, then put it back and get a new one when they are finished.  After a certain amount of time, go over the answers as a class. This works very well for me when I use task cards with QR codes.  This way, the students can work at their own pace.

3.  Quiz, Quiz, Trade - This is a Kagan cooperative learning strategy.  Give each student a task card and they do the problem on their card.  Then, the students partner up.  Partner 1 asks the question on their card.  Partner 2 answers (they are allowed to say “I don’t know”).  Then, Partner 1 praises the correct answer or explains the problem.  Then the students reverse roles.  When both questions have been asked, the students trade cards, find new partners, and begin the process again.  This works best for me if I only have them do this for about 10-15 minutes (depending on the length of the problem).

4.  Bellwork - Have students work on 1 or 2 cards as their bellwork.

5.  Whiteboarding - Each student gets a whiteboard and a dry erase marker.  I love Quartet Dry Erase Markers for student use.  They have a fine tip and last a long time.  Project a task card and have the students work the problem on their whiteboard.  When they have finished the problem they hold up their board so that you can see their answer.  This works best for me if I do it for about 15 minutes.

6.  Jeopardy - Play Jeopardy.  Use task cards for the questions.

7.  Speed Mathing - This is like speed dating, but with math and school appropriate.  Arrange desks in two rows (like speed dating).  Each student receives a card, works the problem on the card and checks their answer.  Then, the students trade cards with their partner sitting across from them and work the problem on their new card.  They are now sitting across from the “expert” for that problem.  After a few minutes, the students receive their original cards again and one row moves one seat down.  This process continues until all of the cards are completed.

Task cards are great and keep my kids engaged.  If you haven't tried them, I highly recommend it!  If you don't have time to make your own, I have several sets in my Teachers Pay Teachers store.  You could also must write problems on notecards.

## Using Color with a Purpose

I’ve used highlighters and markers during my lessons for awhile now.  This year, I started the year telling my students that we were going to use color with a purpose.  While I don’t use this technique every day, it is VERY helpful when teaching some lessons.

At the beginning of my lesson, I tell my students that whenever I write in black, that’s the signal they should be writing in pencil.  If I’m using a color, then they should be too.  I let them pick their colors - they like having choices.  Here is a list of five examples of when I use color with a purpose.

1.  Conditional Statements  -  When I teach conditional statements, I have the students mark the hypothesis (“P”) with one color and the conclusion (“Q”) with another color.  When they write the converse, I make then use the colors to show that the P and the Q switched places.

2.  Parallel Lines  -  When I first introduce the vocabulary of alternate interior angles, same side interior angles, etc. I like to have students color code the types of angles.  I think that the angles stand out to the students a little bit more.  Using Color with a Purpose can really help students if they need to use a diagram for multiple problems.  They can mark the diagram in a different color for each problem.

3.  Composition of Functions  -  My students always seem to have trouble visualizing composition of functions.  By writing each function in a different color, my students can clearly see what is happening.

4.  Multiplying Matrices  -  I don’t know how else I would teach this lesson if I couldn’t color code the different parts of the matrix.  My very first year, I did not use color and my kids were lost.  Now, I use color every time I multiply matrices by hand, and I haven’t had any students have trouble.  This one was a life saver for me and my students.

5.  Angles in Circles  -  It can be very difficult for students to see the different relationships between the angles in a circle.  By highlighting angles, all of the distracting segments are removed and students can identify the types of angles easier.

Now that I’ve used Color with a Purpose, I won’t go back.  I have an odd collection of colored pens and pencils, markers and highlighters in a giant tub in my room.  Kids know that they are free to borrow them at any time.  Any homeless pens, markers, or pencils are just added to the tub.  I collected so many homeless ones last year that I didn’t even have to buy any at the beginning of the school year.

## Equations of Parallel and Perpendicular Lines Inquiry Activity

In Geometry Honors we do coordinate geometry throughout the school year.  Since we’re working on parallel lines, I also teach equations of parallel and perpendicular lines.  I totally changed the way I taught this lesson this year and it went great!  Since it went so well, I want to share what I did with you.

While I normally use guided notes, foldables, or flip books as notes for my students, it is important to me that my students learn how to take notes if they aren’t given a guide.  I explained to my students that their teachers may not always give them a powerpoint or a guide to take notes.  So, I made them take notes on a blank sheet of paper.  We reviewed the slope formula, the slope-intercept form of a line, and the point-slope form of a line.  I made up examples as I went along.  As we talked, I had students do a thumbs up or a thumbs down to show me what they remembered from Algebra 1.  This is what their notes looked like:

Then, I used these notes as an inquiry activity.  I passed them out to my students and told them to use the notes that they just took to help them.  I walked around while they were working with their partners, but I didn't even need to answer questions.  The way the activity is presented, all of my students were able to work through it without me at all.  I was so surprised!  One of my students even said, "Can we do notes like this every day?"  Um, sure!  Honey, if you will do work without complaint, we absolutely can.  I said, "We'll just have to see..."  This is a free download from TPT.  Get it.  I hope you love it too!

It was a block day, so I had a 75 minute class period.  Once they were finished with the notes, they worked on my Equations of Parallel and Perpendicular Lines Chain Activity.

I didn’t feel like using lots of colored paper, so I copied the two pages next to each other on the copier using the “2 Pages -> 1 Page” setting.  I don’t know what it’s called, but the copier at my school has this setting.  Once I copied them, on the colored paper, I cut them in half (so each page was the size of a half sheet of paper).

Then the kids worked the problems.  The problems and the answers fit together like dominoes into a chain.

My students did so well with this lesson that I just wanted to share.

My Geometry Honors students have been cutting and gluing so much lately.  I think I’m going through a crafty phase in my teaching.  :)  I thought my Algebra 2 Honors kids might like to get in on the craftiness.

I typically derive the quadratic formula by hand for my students on the board while they follow along.  This year, I typed up each step in the proof and had my students derive it themselves.  It worked so well and they enjoyed doing it.  You can download the file that I used.

When we were finished, I showed them a couple of videos to help them memorize the quadratic formula.

This was my student's favorite.

Overall, it was a fun day in Algebra 2 Honors.

## Complex Numbers and Story Time

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A couple of times per year I like to have old fashioned “story time” with my students.  In Geometry, I like to read Sir Cumference and the Isle of Immeter (Math Adventures) by Cindy Neuschwander.  I let the kids sit on the floor, use voices for the characters, and we basically take a little break.  In Algebra 2, I read John and Betty’s Journey into Complex Numbers by Matt Bower.

When I first saw the story, I wanted to buy the book, but I couldn’t find the book anywhere online.  From what I can tell, it is only available on slide share.  So, I re-typed the story and made my own book.  If you know where I can buy a for-real printed copy, please let me know!

Basically, the story is about John and Betty and it is told in the old fashioned “Dick and Jane” style.  John and Betty have some cookies that they want to share and by doing so, investigate the sets of numbers.  Then, they wonder about imaginary numbers.

It’s a super cute little story that is memorable for my students.  You should check it out!