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.

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!


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.  

Functions, Tables, and Graphs INB Pages

I used these interactive notebook pages during my functions unit in Algebra 1.  It built on my student's previous knowledge, which I loved!

There are three main parts on the notebook page.

three views of a function foldable  {function rule, table, and graph} for algebra 1 interactive notebooks

First, I reminded students of the definition of the words "discrete" and "continuous".  They learned these words in Pre-Algebra and in science class.  However, I wanted to make sure they were in their notes.  Then, we completed a foldable relating an equation, table, and a graph.  I also had students label key features of a graph.

After we completed the different parts of the notes page, I had students practice with a partner on a practice page.  I copied the page at 80% so it would fit in their notebook.  I could have left it full sized and used it as homework though.

three views of a function practice page  {function rule, table, and graph} for algebra 1 interactive notebooks

This is what the pages look like as a "spread".  I like to plan pages as a two page spread, like a newspaper.  :)  To keep my students interested, I copied everything on different colors and I let them choose what colors they wanted.  Honestly, I dropped a stack of colored paper on the way to the copier, so I made it work ;)

three views of a function foldable  {function rule, table, and graph} for algebra 1 interactive notebooks

You can find the foldable and practice page here.

Arc Length vs. Arc Measure

18 June 2017
Students always seem to get confused about the difference between the length of an arc and the measure of an arc.  When I teach this concept, I try to relate it to sports.  The vast majority of the kids in my class have run around the track at some point.  So I start asking them questions. :)

If you have to run one lap around the track which lane do you want to run in?
The inside one!

Why?
It's shorter!

Why?
The circle is smaller.

Interesting...  You have still run one lap though.  All the way around the circle would be 360 degrees.  So, it should be the same distance.  If you run the outside lane, that's the same distance as the inside lane.
[At this point, controlled chaos ensues.  Most of the athletes become indignant.]

Then, I tell them that the measure of an arc is the degree measure.  The length of the arc is the actual distance you would have to run.  Most of them get it by this point.

arc length and arc measure cheat sheet for interactive notebooks - free download

I made a handy little "cheat sheet" for students to glue in their notebooks.

Coordinate Quadrilaterals INB Pages

14 June 2017
Instead of teaching coordinate quadrilaterals throughout the quadrilaterals unit, like I normally do, I taught it all together.  It worked.  I don’t know if it was better or worse than doing it throughout.  

The first day, I only taught about proving a quadrilateral is a parallelogram.  Before I started the lesson, I gave all of my students a sticky note and had them find the formulas for midpoint, slope, and distance and write them down.  They stuck it on their desk and referred to it during the lesson.

I felt super fancy with the foldable I used for this lesson… partly because I used an “I can…” statement on the foldable, and partly because I used a shutter fold, but kept one flap up.  I also feel like the way I have a flap for each formula takes any guess work out for the students.  Under each flap, we worked the example, using that method.  So, when my students had their homework they could mimic the work under the flap.

coordinate geometry with parallelograms - foldable

On the facing page, I gave students a scrap of graph paper.  I gave them the four points in the margin and had them draw the graph.  The worked with their partners to prove it was a parallelogram using all three methods.  I honestly didn’t have to use the graph, but I think it helps them visualize things better.

interactive notebook page idea for parallelograms on the coordinate plane

The second day, I taught students how to determine the type of quadrilateral, using coordinate geometry.  Some of these problems take up so much room (if you want things to be organized), so I used a giant hamburger book.  There were three problems in this book.  It took almost the whole class period to work the three problems - that could be because my students worked slow.

interactive notebook page idea for quadrilaterals on the coordinate plane - free download

interactive notebook page idea for quadrilaterals on the coordinate plane - free download

The third day, I had my students do a stations maze to practice their coordinate geometry.  They worked on it the whole class period.


I haven’t decided if I will teach it all together again next year, or if I will do a little at a time throughout the unit.  Good thing I have time to decide!

Systems of Equations INB Pages

07 June 2017
This year, I taught systems of equations right after Christmas break.  My students STRUGGLED.  I think I need to do a two day review of graphing equations before jumping in next year.

First, we talked about what a "system" of equations actually is.  We also talked about the three types of solutions they could have and what they looked like graphically.  At the bottom of the page, I included a magic book that substitute points into a system to determine if they were a solution.  The file was corrupted, so I will get to remake that for next year.  Yay.

Systems of Equations INB Page

Next, we solved systems of equations by graphing.  I gave the students a step by step list for their notebooks that had one example included.  Next year, I think I will include a "drill and kill" practice sheet on the facing page.

Solving Systems of Equations by Graphing Interactive Notebook Page

The next day, we solved systems of equations by substitution.  I used the same step by step list with one example format as the previous day.  This one worked well and I liked the way I highlighted what we were substituting into each equation.

Solving Systems of Equations by Substitution Interactive Notebook Page

On the next page, I had a practice sheet.  Each time I substituted into an equation, I highlighted the substitution.  Showing that helped my visual students SO MUCH.  I also started throwing in word problems.  They hated me a little for that. :)

I spent the next day reviewing and showing them what the special cases looked like algebraically.  No cool foldable for this page.

Solving Systems of Equations {special cases} Interactive Notebook Page

I continued following the same format for solving systems of equations by elimination.  I had a step by step list with one example for their notebooks.  This time, I highlighted the "stacked" variables.  I was trying to make them notice that they needed to make sure they were combining the same variables.

Solving Systems of Equations by Elimination Interactive Notebook Page

The example page came next.  I continued highlighted the "stacked" variables.  Also, more word problems :)

Solving Systems of Equations by Elimination Interactive Notebook Page

We had several days of review and when I was sure that my students had it down, I pulled out the big guns...MORE WORD PROBLEMS.  I used legal paper to make a giant hamburger book.  It gave us plenty of room to work all of the problems.  My students whined loudly that they were going to die.  No word problem related deaths... yet.


Intro to Systems and Solving by Graphing INB Page
Solving Systems by Substitution and Elimination INB Page
Substitution and Elimination Practice Pages

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