Math Teachers at Play #105

24 February 2017
Welcome to the 105th edition of Math Teachers at Play (MTaP) Blog Carnival!  MTaP is a monthly blog carnival with a collection of tips, games, and activities for teachers of students of all ages.  If you haven't seen the carnival before, you can read the previous posts.  I also hosted the 82nd and 89th editions.

Math Teachers at Play Blog Carnival - ideas, games, and activities for all math teachers

First off, a few facts about the number 105.  105 is a triangular number, the double factorial of 7, and is the sum of the first five square pyramidal numbers.

Now, on to the posts for this month!

Why and How to Implement Discovery-Based Learning in Your Math Classroom
Amanda from Free to Discover believes strongly in allowing students to "play" with math ideas, but she knows that sometimes it can be intimidating to design an inquiry-based lesson.  Others may not see the value.  This post offers the WHY as well as the HOW to make it happen effectively - giving teachers and homeschool parents the confidence to try it out for their students.

Engineers use Manipulatives
Middle and high school students should also be encouraged to use math manipulatives when learning a new concept.  Crystal from Triumphant Learning explains more.

How I Teach Factoring Quadratics
In this post, I explain how I teach factoring to my students.

Fibonacci, Math Mondays, and Rabbit Trails
This blog post shares how Tracy's homeschool has started to non-traditionally play with math on Math Mondays.  They used a book as the spine and followed rabbit trails all week.  It was delightful.

High School Math Word Wall Ideas
Scaffolded Math teaches special education Algebra 2 to students who are not at all confident in their math abilities.  They do well when they have reference sheets and visuals that help them remember steps, graph shapes, and vocabulary.  She likes to make her classroom a colorful, happy place that her students look forward to coming to.  These ideas for a math word wall are sure to make your classroom a colorful, happy place too!

Confession: I Am Not Good At Math
We don't have to be "good at math" to enjoy learning something new.

A Different Approach to Warm-Ups
Julie from Secondary Math Solutions shares a great idea for warm-ups in your class.  Her students were taking their time before beginning their warm-ups.  She decided to work with them instead of against them.  Check out what's working for her!

Taking Time for Tessellations
Tessellations are one of the most engaging activities in math, and yet many explanations to create them are either too vague or overly complicated.  Teachers will enjoy the ready-to-use tips and be able to implement them in their classrooms.

Dear Community; Sincerely, Math Teacher
Just read it :)
A letter about what every math teacher wishes everyone knew.

Calculators are as Smart as the User
Tyra from Algebra and Beyond explains how she teaches calculator skills to her students.  She also uses reference sheets that help students remember the steps.

A Map of Mathematics
Pure mathematics, applied mathematics, and more - all summarized in one diagram!

Proof that Proofs Belong in Geometry
In this post, Math Giraffe explains the importance of proofs in high school Geometry.  This is worth a read, even if never plan to teach Geometry.

I Notice, I Wonder | Math as Art
Lacy at Play, Discover, Learn came to write this article because of the helpful video Denise Gaskins shared after she asked a question about she gets her children to see the math in their artwork.  They ended up having a lot of fun noticing and wondering about the artwork and it was a lot like Gattegno's pedagogy of observing and asking questions.

Transformations Logo Project
This project is a great option for a non-traditional assessment or a quick project in Geometry.


I hope you found something interesting to you!  If you're looking for more, you may be interested in the Carnival of Mathematics Blog Carnival!




Trig Ratios INB Pages

20 February 2017
At the recommendation of a colleague, I taught trig ratios a little bit differently this year.  I ended up spending a week on trig ratios.  The first day, I only introduced the ratios.  The second day, I actually had students set them up into an equation.  The third day, we did inverse trig ratios.  The last two days were spent on application and word problems.

It. Was. Awesome.

I’m so glad I tried it.  In the past, I’ve always done some kind of investigation about the tangent ratio, then did the other two ratios the next day.  It was okay, but the investigation didn’t really do much for my students and it all seemed like a waste of time.  Changing it up was just what I needed.

The first day, all I did was talk about the ratios.  We completed this page explaining what each ratio was and labeled a right triangle.

Trig Ratios Interactive Notebook Page for Geometry

Then, I had students glue in this triangle that we labeled.  I had them find the missing side and write the ratios for each angle.  I showed them the relationship between tanA & tanB, cosA & sinB, and sinA & cosB.  Then, we made a “magic book” were students had to write six ratios (three for each angle) for each triangle.  

Trig Ratios Interactive Notebook Page for Geometry

The next day, we actually used the ratios to solve problems.  I used my trig ratios foldable.  I also helped them trouble shoot potential problems on the calculator.

Sine, Cosine, Tangent Foldable for Geometry Interactive Notebooks - Trig Ratios

On the third day, we solved for angles using the inverse trig ratios.  I used by inverse trig ratios foldable.  By this time, most of my kids were pros.

Sine, Cosine, Tangent Foldable for Geometry Interactive Notebooks - Inverse Trig Ratios

On the fourth day, I used these interactive notebook pages by Secondary Math Shop.  They explained the angles of elevation and depression and then had two practice problems each.  
PSA: Whenever you teach this, always remind students where a shadow is.  So many of them want to make the shadow the hypotenuse.  I try to help them fix the problem themselves by asking, “If you want to see your shadow, where do you look?”

Angles of Depression and Elevation Interactive Notebook Pages

Angles of Depression and Elevation Interactive Notebook Pages


The next day, we reviewed angles of depression and elevation using a stations maze.  My students did SO WELL on this.  Several of them have said it was their favorite thing so far this year!

Equations of Lines INB Pages

15 February 2017
I loved teaching Equations of Lines in Algebra 1 this year!  I have a million interactive notebook pages that I used in this unit, and today I’m going to share a few.

First, this page for writing equations in standard form was boring, but effective.  After the four examples, my students got it and we were able to move on.

Writing Equations of Lines in Standard Form Interactive Notebook Page

Then, we moved on to the point-slope form of a line.  I showed students how the point-slope form of a line is derived from the slope formula. I had students write this in their notebooks.  Most of mine color-coded theirs.

Point-Slope Form of a Line Interactive Notebook Page

I made a practice page with the steps to writing equations from two points.  

Writing Equations from Two Points Interactive Notebook Page

This next page was PURE GOLD.  I have no idea where I got this worksheet.  If you know where it’s from, let me know so that I can link it.  Each of the four problems gives different information.  I think I want to do the same worksheet next year, but expand it to include eight examples.  I’ll do one page with them, and they can repeat the same thing with different numbers.

Linear Equations Interactive Notebook Page

Graphing Horizontal and Vertical Lines

08 February 2017
In the past, I’ve always noticed that my Geometry and Algebra 2 students have HUGELY struggled with graphing horizontal and vertical lines.  I was determined to nail it in Algebra 1 this year, so that it wouldn’t be a problem for them in the future.

First, I put the graphs of several horizontal lines on the board.  I asked them “What would slope dude say?”  He would say “This is zero fun”, so I had my students write the equations of the lines in slope intercept form using zero slope.  This was pretty easy for them to grasp and they saw the patten quickly.  

Then, I put the graphs of some vertical lines on the board.  They were totally stumped.  They knew the slope was undefined, but they had no idea how to write that in an equation.  I drew several points on one line and asked them, “What does x equal here?”  “What about here?”  “What about here?”  Then, I wrote the equation of that one line.  After that, they quickly were able to write the equations of the rest of the lines.

After all of that discussion, I finally had my students take out their notebooks to take their notes.  I taught them the HOY VUX acronym and gave them the pink flap book.  Under each flap, they wrote what the letter stood for.  

HOY VUX Flapbook - Graphing Horizontal and Vertical Lines Interactive Notebook Idea for Algebra 1

Then, we folded a mini-book by Sarah from Math = Love (this whole lesson was heavily influenced by her).  Each page of the book has students graph a horizontal or vertical line.  Yes, it totally drives me nuts that I glued the flapbook in crooked.  I was in a hurry!

Graphing Horizontal and Vertical Lines Interactive Notebook Idea for Algebra 1


This lesson was short, and seemed simple when you look at their notebook.  However, they remember it!  We are finishing systems of equations now, and my students have not been struggling with horizontal and vertical lines at all.  This lesson is definitely a keeper.

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