Help Students Visualize Overlapping Triangles

15 September 2017
When teaching triangle congruence, overlapping triangles appear at some point.  I always teach students to draw the triangles separately before making any conclusions.  This activity/demonstration helps students create overlapping triangles and separate them to see the triangles individually.

This is an activity to help students visualize overlapping triangles. It is perfect for a congruent triangles unit!

First, fold one corner of a piece of paper to form a triangle.  Trace the triangle on the piece of paper.

Investigating Overlapping Triangles - this is a great hands-on activity to do before congruent triangles proofs

Cut along the traced edges and cut along the fold.  How do you know that the two triangles are congruent?

Investigating Overlapping Triangles - this is a great hands-on activity to do before congruent triangles proofs

Label the angles of the triangle.  Have students write a congruence statement.

Investigating Overlapping Triangles - this is a great hands-on activity to do before congruent triangles proofs
Use the two triangles to create different shapes.  Have some of the shapes use overlapping triangles.  

Investigating Overlapping Triangles - this is a great hands-on activity to do before congruent triangles proofs

See how many other shapes students can find with their congruent triangles.

Investigating Overlapping Triangles - this is a great hands-on activity to do before congruent triangles proofs

This is a great activity to do before starting congruent triangles proofs!
a congruent triangles activity to help students visualize overlapping triangles - great for high school geometry students beginning triangle congruence proofs

How to Create a Seating Chart

19 August 2017
This post contains affiliate links.  If you make a purchase through the link, I earn a very small commission that keeps this blog running.

Teachers, do you struggle with ideas for making a seating chart?  This simple teacher hack is so easy to use in any classroom!

I always have my students sit in assigned seats.  Anytime I’ve ventured out of assigned seats, I have regretted it.  With assigned seats comes seating charts.  One thing that’s a MUST for me is that I have the seating chart up as students come into class.  Getting high school students to move seats once they’ve already settled in is near impossible.  I’ve tried making seating charts several different ways over the years, but they have all had their flaws.  

When I first started teaching, I had little cards with my students names on them that I put on their desks.  Yeah, you can imagine how that worked out between classes in a high school.  I was running around like a crazy person trying to get the next class period’s cards laid out.  Dumb idea.  Don't do this.

I’ve also tried making a powerpoint of my seating chart and projecting it for students to see on the board.  That’s fine, but that’s also how I display student’s bell work.  So, this didn’t work well either.

The software that our attendance is on has a seating chart feature.  You can arrange the seats and then print it.  It always turned out formatted funky and my students had a hard time reading it.  Yuck.

I finally settled on printing copies of a blank seating chart and handwriting my student’s names on it.  I would tape it to the board in a prominent location and my students would see it as they came in.  This worked beautifully most of the time.  However, sometimes I would write a student’s name twice and forget another student.  Occasionally, I would spell a student’s name wrong and then feel bad later.  

And then I discovered the best idea ever!  A teacher-friend shared it with me, and it’s too good for me to keep it to myself!

At the beginning of the year, I print one blank seating chart for each class period.  I also write all of my student’s names on Post-It page markers.  I know it’s a huge pain if you have a lot of students, but it’s totally worth it.

Do you see where I’m going with this?

I put the little page marker on each student’s assigned seat and slide it into a sheet protector.  Hang it on the board for students to see as they come into class.  If you ever want to move seats, you just have to move the little Post-Its.  BEAUTIFUL!

Teachers, do you struggle with ideas for making a seating chart?  This simple teacher hack is so easy to use in any classroom!

Have you ever used this method for creating a seating chart?  

8 Ideas for Sub Plans in Secondary Math

07 August 2017
Need FREE emergency sub plans for middle school or high school?  These substitute teacher ideas would be great in any secondary math class.
This post contains affiliate links.  If you make a purchase through the link, I earn a very small commission that keeps this blog running.

At some point, all teachers have to miss school.  Between illness, field trips, coaching responsibilities, and life everyone misses a day at some point…. and it’s a huge pain.

teacher sick day

I try to keep continuity while I’m gone, and have students work on something that we have been doing in class.  However, that’s not always possible.  If you get sick in the middle of the night or something happens on the way to work, you may not get a chance to organize sub plans.  My school requires that we keep emergency sub plans in a binder, just in case.  They have to be educational, at least sort of related to the content area in which we teach, and keep student occupied and out of trouble.  Yeah, in math, that’s not always easy!

These 8 ideas can be used in almost any level high school math class.  Some would work better for older students or younger students, but all could be modified to suit your needs in a pinch.

Need FREE emergency sub plans for middle school or high school?  These substitute teacher ideas would be great in any secondary math class.

This statistics lesson is accessible for any high school student.  Also, let’s be real, EVERYONE needs this lesson.  Have you watched the news?  It is an online lesson, but if you’re not 1:1 the sub could click through the screens on the projector and students could write their answers on notebook paper.

This lessons teaches students about different number bases and the history behind them.  It’s interesting and different, which your students just may love.

You can’t go anywhere right now without seeing emojis.  They’ve pretty much taken over.  These logic puzzles are a combination of the logic puzzles you see plastered on social media and the emoji craze.  Between the 32 task cards and the extra worksheet, I’ll be able to split it into two days worth of sub plans.

This is a fun activity if you have access to some blocks or math cubes.  Students will build their own figures and draw them with a partner.  There is also a stations maze to wrap everything up.

The birthday problem is a common example used in statistics, but it’s fun to do with any math class! This video would probably be better for older or honors students, but it really is fun. 

Between the seven stations, the extra editable stations, the worksheet AND the extension activities, this could easily be used as more than one day of sub plans.  JACKPOT!  I love that kindness and growth mindset are included, because my students ALWAYS need reminders about both of those!

I’ll be honest, I did this lesson myself.  It was actually really interesting.  This is a lesson that I think students would be interested in, and it’s pretty accessible to any high school student.  

I’m not going to lie; I love this.  It’s an article that was posted in The Atlantic and is wonderful at explaining that being good at math is the product of hard work - not good genes.  I plan to have my students read this and write a paragraph or two about whether they agree or disagree.  Yay for writing in math!

Side Note:  Many of these require students to watch a video for a few minutes.  In this case, I've found that students tend to stay on task better if they share devices with a partner and each use one earbud.  In my experience, having a partner tends to keep them on the correct website a little more.  (It's at least worth a try!)  Also, I like to keep a few extra pairs of these cheap earbuds on hand for the forgetful kids.

Have you used any of these on a sub day?  How did it turn out?

Interactive Notebook Tips: Teaching a Lesson

25 July 2017
Teachers that are new to interactive notebooks often ask me how I run a typical class period and how I teach a lesson.

In this post, I’m going to outline exactly what I do with my classes and how I do it.  For reference, my classes are 48 minutes long and I have a document camera.  I do not have a smart board or any thing like that.

This post explains how to teach a lesson using interactive notebooks. It explains how to structure middle school and high school class periods.


My students are supposed to start their warmup as soon as they walk into class.  I don’t do anything fancy.  I typically project a couple problems that review what we did the day before or a spiral review topic.  I usually just zoom in on a couple of problems on a worksheet and project them on the board.  My students have a sheet that they do all of their warmups on and turn it in at the end of the week.  I cut them off when I’m ready to move on, regardless if they are finished yet.  Then, I write the solutions on the board and answer any questions.

Checking Homework

Next, I have students check their homework.  I project the solutions on the board and have students check their own homework.  They are supposed to write the correct answer of anything they missed.  I walk around with a clipboard and check to make sure they did it.  If they gave the majority of the problems a good effort, they get full credit.  If they only did half of it, they get half credit.  Yeah, some kids cheat on this method.  I don’t stress about it, because I can TOTALLY tell when it comes to test time.  I usually just put a note in the grade book that little Johnny has been cheating on his homework and don’t worry about it.

The Lesson

For the sake of explaining, I’m going to pretend I’m teaching my Algebra 1 classes about adding and subtracting polynomials. For this lesson, I would use my adding and subtracting polynomials flip book.

I pass out the foldable for the day and show them how to fold it (if necessary).  This is exactly what I would say:
“Ok, you have two pages for your flip book.  Look at the page that says SUBTRACTING POLYNOMIALS on the bottom.  Put it on your desk like this.”
Then, I would set it under the document camera so that the SUBTRACTING POLYNOMIALS tab is at the bottom.
“Now, set ADDING POLYNOMIALS on top of it so that they are layered.  Then, fold it over.”
I would model exactly what I am saying under the document camera.
“I’m going to pass around staplers.  They will start at the front of the room.  Please staple like this.”
I model correct stapling.
“Don’t bang on them like an idiot.  It breaks them.  You know how to staple.  When they get to the back of the room, please pass them over to my desk.”
Then, I glue the foldable into my notebook and my students do the same.  This whole process takes about 2-3 minutes, at the longest.  After about October, my students can figure all of it out themselves unless it’s a new kind of foldable.  They can usually put it into their notebooks as I pass things out.
Once I glue my flip book in my notebook, I start teaching!  I fill in everything with my students.  I have one notebook per class period and I write along with them.
First, I would open the vocabulary tab.  I would talk through the new vocabulary words and do the examples with them.
Then, we would move on to the adding polynomials tab.  I would show them the first two examples, then they would work with a partner for the remaining examples.  When they were done, I would put the answers up.
Last, I would do the subtracting polynomials tab the same way I did the previous tab.  


When we are finished with the lesson, I typically let my students start their homework or we do a short activity.

Honestly, the way I present lessons isn’t much different than when I didn’t use interactive notebooks.  The big change was in what my students were doing.  Before interactive notebooks, my students just dutifully filled in their guided notes….and lost them in their backpacks…  Now, they are manipulating the pieces of the foldable, color-coding, and chunking ideas while I’m teaching.  Everything is glued in their notebooks so that it isn’t lost.  That’s the big change!

Any more questions?  Leave them below so I can help you get started!

Visualizing Intersecting Planes

19 July 2017
Students have such a hard time visualizing intersecting planes.  It helps so much if they have something concrete to hold.

Are you teaching high school geometry?  This hands on activity helps students visualize intersecting planes.  It is perfect after teaching about points, lines, and planes.

I have a giant piece of foam board that I cut in half, and then cut slits in.  A saw works nicely for this :)  

Use foam board to demonstrate intersecting planes in geometry

Check out how awesome this looks once the foam board is stuck together.

Use foam board to demonstrate intersecting planes in geometry

I use my giant foam board to introduce the lesson and talk through the main points.  Once I’m ready to have students start taking notes and dive into specifics, I pass out two notecards to each student.  I have them tear notches into the notecards to show intersecting planes.

Using notecards to model intersecting lines and planes in geometry

Then, I have students stick their pencil through the notecard to show a line intersecting the plane.

Using notecards to model intersecting lines and planes in geometry

After that, I have students put the two planes together and use their pencil as a line.

Using notecards to model intersecting lines and planes in geometry

This works so well to have students visualize things.  Their homework typically involves true and false questions for this lesson, so I have them get out their notecards if they get stuck!

Surface Area and Volume INB Pages

08 July 2017
I wanted to share my interactive notebook pages for my surface area and volume unit!  I like the pages that I used, but I think I will include a few more “drill and kill” pages next year.  Instead of teaching all of the surface area formulas and then all of the volume formulas, I taught all about prisms and then all about pyramids.

First, I started with this messy looking page about the parts of a prism.  I realized at the last minute that my students needed a refresher about parts of solids.  This page only had parts of prisms.  I also had a derivation of the formulas at the bottom of the page.  I cut and pasted the diagrams from my student’s textbook.  

parts of prisms interactive notebook page

Next, we did a flip book with the vocabulary formally introduced and practice problems.  I taught the cylinder as a special case of the prism.  I did not give students a separate formula.  Many of them figured it out, but they didn’t have to use it.

surface area and volume of prisms and cylinders flipbook for geometry interactive notebooks

Next, I did this page about composite volume.  The first problem has students add the volumes and the second problem has students subtract the volumes.

composite volume practice page for geometry interactive notebooks

I did another messy looking page to describe the parts of pyramids.  

parts of pyramids interactive notebook page

Another flip book with the vocabulary and practice problems came next.  Again, I taught the cone as a special case of the pyramid.  

surface area and volume of pyramids and cones flipbook for geometry interactive notebooks

Lastly, I taught the surface area and volume of spheres.

surface area and volume of spheres flipbook for geometry interactive notebooks

Area and Perimeter INB Pages

03 July 2017
I started my area unit with a short review of simplifying radicals and special right triangles.  It’s ALWAYS needed.

The first lesson was about the area of parallelograms and triangles.  They learn these formulas in pre-algebra, but I think they needed a little review and I include special right triangles.  I also have students highlight the perpendicular parts, so that they can find the base and the height easier.  Highlighting helps my struggling kids.

area of parallelograms and triangles foldable for geometry interactive notebooks

area of parallelograms and triangles foldable for geometry interactive notebooks

The next day, we talked about the area of rhombuses, kites, and trapezoids.  The examples in the flip book include special right triangles and the Pythagorean Theorem.

area of rhombuses, kites, and trapezoids flipbook for geometry interactive notebooks

I also have a foldable that students can use to help organize the area formulas.  I made it optional for students to complete this foldable.  I also included notes about regular polygons.  I just had them take notes in their notebook for those pages.  No pictures, sorry.  :(

Then, we moved on to circles.  The first day, we talked about circumference and arc length.  I have a post about how I explain the difference between arc length and arc measure.

circumference and arc length foldable for geometry interactive notebook

The next day, we talked about the area of a circle and the area of a sector.  I didn’t do segment area with my kids this year.  They struggled with the area of a sector and I didn’t want to create a disaster.  I was allowed to leave out a few little topics this year because our math standards were being revised this school year.

area of a circle and sector area foldable for geometry interactive notebooks

The last lesson of the unit was perimeter and area of similar figures.  I broke it down as simple as possible.  On the flaps of the foldable were the different types of problems.  Inside each flap there are two practice problems.

perimeter and area of similar figures foldable for geometry interactive notebooks

Quadrilaterals INB Pages - Part 2

29 June 2017
I shared the first part of my quadrilaterals unit a couple of months ago.  I didn’t share all of the pages though!

I still need to make decent pages for kites and trapezoids.  I had my students just take notes in their notebooks.  I want to make something better for next year.  I had my students do LOTS of practice with the different properties of special quadrilaterals.

First, I had my students fill in this family tree for quadrilaterals.  I had another separate family tree page for special parallelograms, but I forgot to take a picture of it!  This family tree is part of my Special Quadrilaterals Always, Sometimes, Never Card Sort.  

On the next page, I had my students do the card sort in their notebooks.  

Then, I gave my students this sheet for them to check off the properties in columns.  It’s part of my Special Quadrilaterals Properties Cut Out Activity.  

On the last page for this unit, I used quadrilaterals task cards as review problems.  I had students glue the task cards in their notebooks and write the answer off to the side.  I shrunk the task cards when I copied them, so they would fit into their notebooks nicely.

These pages were a good review and wrap up of the rest of the unit.  Kids have so much trouble keeping the properties straight, that I try to do as many activities as possible!

6 High School Teacher Must Haves - Guest Post

26 June 2017
Today, my friend Shana will be sharing her 6 MUST HAVES for new (and old!) high school teachers.  Shana is my friend and the mastermind behind Scaffolded Math and Science.  Her passion is helping math phobic kids find success.  Check out her budget-friendly tips!

This post contains a Amazon Affiliate links.  This does not effect you in any way.  However, if you make a purchase through this link, I receive a very small commission that keeps this blog running.

6 high school teacher must haves

I am very excited to be writing this post today as a guest on Mrs. E Teaches Math! Mrs. E's blog is one I have followed for many years, so this is a great honor. There are so many things I'd love to buy for my classroom, but then I'd be broke! In this post I narrowed it down to the 6 things I can't live without. If you or someone close to you just landed their first high school teaching job, congratulations! After so many years of preparation, this is a very exciting time. We have all seen the memes about how much money teachers spend on their classrooms, but it doesn't have to be that way. Here are 6 things that would mean a lot to a new high school teacher.

6 high school teacher must haves

1: A Mouse 
This one might seem silly, but it makes a world of difference. Chances are, you'll be issued a laptop of some kind. When I taught in Boston, we were given Apple computers that ran Windows because of some law suit about one or the other monopolizing education. It was so weird. It was also really awkward! Even more awkward with any laptop maneuvering the touchpad mouse while trying to work at the necessary light speed in order to get everything done. Having an external mouse cuts down on a whole lot of unnecessary frustration.

2: Magnets 
I'm not talking any old magnets here. I'm talking those mega magnets tough enough to hold half a ream of paper onto that 1992 magnetic whiteboard. These strong disc magnets are super cheap on Ebay and are so versatile in the classroom. They allow for student work to be displayed, which makes student engagement go way up. Magnets are also awesome for displaying a whole host of other things, like scavenger hunts, anchor charts and group directions.

6 high school teacher must haves

3: Panel Board 
This might also be called "tile board" at Home Depot. It's an 8-foot by 4-foot slab of shiny white board that, after being cut into sections, works great as personal student white boards. Whenever I need a quick filler activity or if my students are just not focused, personal white boards are a lifesaver. The ones sold at teacher stores are SO expensive. Panel board is almost as good and a whole lot cheaper. If you have no way of transporting the big sheet and/or can't cut it at home, Home Depot will cut it for you. I chickened out and only asked for mine to be cut into 8 sections, which were a little big but did work great for group work presentations. I am sure by asking nicely you can get more sections cut  Though a whole lot cheaper, panel board is not as durable as the personal whiteboards you can buy at a teacher store. A good workaround is a layer of dry erase paint at the end of the 2nd or 3rd year. This post from Alex at Middle School Math Math Man shows how dry erase paint can be used to make a dry erase table.

6 high school teacher must haves

The paint can also be used to spruce up personal whiteboards. Also, some teachers like to edge the cut sections with something like electrical or washi tape.

6 high school teacher must haves
4: Quartet Dry Erase Markers 
Everyone raves about Expo markers. I've found that the smaller Quartet markers, like the one in the photo, work awesome on personal whiteboards. They seem less scratchy, which helps the boards hold up, and the ink seems to last longer. This past year I laughed when I overheard a teacher's, "Whoa, what is this?" after being impressed with a Quartet marker. Usually the school will provide some dry erase markers, but never enough for all year.

6 high school teacher must haves

5: Flair Pens 
This one is such a teacher stereotype, but no doubt deserves its place in this top 6. For a long time I resisted the flair pen with an, "Ugh, like I'd fall for that trend!" Boy was I wrong. What makes them so great, and what I hadn't ever understood, is that the color is super bold yet, by sheer magic, doesn't bleed though the paper to the other side. They are the perfect grading pens. I can check all the correct answers I want on one side of a kid's paper and nothing goes through to the back. Awesome and mysterious!

6 high school teacher must haves

6: Document Camera 
This one is the most expensive on the list and may not be a must for some, but I love my document camera for so many reasons. When a student is out and will miss notes, I can give the class notes under the document camera so that the student can have the filled-in sheet the next day. My document camera lets students share their work and for us to discuss it as a class. When my graphing calculator software is acting up, which is usually, I can put a graphing calculator under the document camera and continue with the lesson.

What must-haves would you suggest to a new high school teacher?

  Scaffolded Math and Science
Shana McKay has been a Massachusetts public school math teacher since 2004. Teaching math to kids who are afraid of math is her passion, and every one of her lessons and activities is especially designed for students who struggle with self-confidence. She blogs at Scaffolded Math and Science.  

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