Triangle Similarity

17 April 2017
After I taught similar polygons, triangle similarity came next!  I’m sharing the interactive notebook pages that I used for the second half of this unit.

The first day, I only taught my students SSS and SAS Similarity.  I used a foldable that only had SSS and SAS.  I really wanted my students to get used to finding the corresponding sides.  I knew AA would be easy for them, so by teaching it the second day, I was essentially giving my students a review day, with one small new thing tacked on.  I’ve found that with some topics, this is especially effective.  

SSS and SAS Similarity Foldable for Geometry - Triangle Similarity

The next day, we completed a foldable and practice page with all three triangle similarity shortcuts.  When I told them about AA, they thought it was easy after learning the other two rules.
AA, SSS, and SAS Similarity Foldable for Geometry - Triangle Similarity
Then, we completed a foldable about similar right triangles.  I liked that this foldable had the theorems typed out on the front.

Similar Right Triangles Foldable

I split this lesson over two days.  My students completed a practice page with their partners the day after the foldable.

Similar Right Triangles Practice Page
The last lesson in this unit was proportions in triangles.  The flaps has the theorems written out, but there are examples under the flaps.

Proportions in Triangles Foldable

Similar Polygons

14 April 2017
Triangle Similarity isn’t my favorite unit in geometry.  I have done things in the past to make it more interesting (for me at least!).  For a few years, I used the Flip Family activity.  However, this year I just tried to make foldables that were more interesting.

First, I made a page about scale drawings.  I think next year, I will start with a day of review of ratios and proportions.  My students did ok without it, but I think I need a review day next year.

Scale Drawings INB Page for Geometry Interactive Notebooks

Then, we completed a flip book about similar polygons.  The similar figures examples worked very well for my students.  I had my students highlight the corresponding sides of the polygons in different colors so that they could see which sides matched.  It helped my lower level students.

Similar Polygons Flipbook for Geometry

Similar Polygons Flipbook for Geometry

Then, we completed an additional page of similar figures word problems.  I’m trying to get my students more comfortable with word problems and pulling out the important information.  

Similar Figures Word Problems Practice for Geometry INB

Similar Figures Word Problems Practice for Geometry INB

Then, my students did a number line activity to practice.  When I copy the background on colored paper, they look go nice hanging on the wall!  I had my students work with partners to complete it. 

Similar Figures Cut and Paste Activity for Geometry
After that, we talked about proving triangles similar.  You can find that post here.

Quadrilaterals INB Pages - Part 1

25 March 2017
I’m getting behind on posting my INB pages!  When I taught Quadrilaterals, I tried to include lots of extra practice pages.  I’ve been including more practice pages this semester.  

This page was a review of the properties of parallelograms.  I also included the theorem with multiple parallel lines.

properties of parallelograms interactive notebook page

Next, came the lesson about proving quadrilaterals are parallelograms.  I was very surprised about how quickly my students caught on during this lesson.

proving quadrilaterals are parallelograms interactive notebook page

Then, I taught about rhombuses, rectangles, and squares.  I used this foldable and practice sheet.  Inside each flap there is the definition, the properties, and two examples.

rhombus, rectangle, and square foldable for geometry interactive notebooks

rhombus, rectangle, and square practice sheet for geometry interactive notebooks

I included always, sometimes, never statements on the practice sheet.  I don’t require my on-level students to do this type of questions on their own, but we do talk about them together.  When I taught honors, I had several of these on their test.

I have several more pages from this unit that I will be sharing soon!

Exponents INB Pages

18 March 2017
I just finished my exponents unit in Algebra 1.  It was interesting to me that some students that struggle seemed to really excel in this unit.  This is really the first unit that didn’t depend heavily on their ability to solve equations - maybe that was part of it.

To begin, I made this page to remind students of the information they learned in pre-algebra.  This page reviewed the expanding process.  Also, it reminded them of the zero exponent rule and the negative exponent rule.

exponents interactive notebook page

Then, we completed this domino activity by Math Dyal.  

exponents activity for interactive notebooks

The next day, we talked about the multiplication properties of exponents.  We completed this foldable and practice sheet.  I’ve started adding practice sheets to a lot of my lessons.  I usually have my students do a few at a time with a partner.  I hate letting them start their homework during class (only like half of them do!) and I can get more kids to practice this way.

multiplication properties of exponents foldable for algebra

multiplication properties of exponents foldable and practice for algebra

Then, we talked about the division properties of exponents.  We completed this foldable.  There were tons of examples inside the foldable, so I did not include a practice sheet for this lesson.

division property of exponents for algebra

I gave them a sheet with all of the exponent rules summarized on it.  I had them try to fill it in themselves before I showed them the completed sheet.  

exponent rules for algebra

The last page we completed was from Scaffolded Math and Science.  It is just a worksheet, but I copied it at 80% so that it would fit in their notebooks.  Students found the area of familiar shapes and used the exponent rules.  Looking back, I would have completed this before the division properties.  She has a few other pages like this and I need them all!!

multiplying exponents area activity

During class, we also played speed mathing, did a coloring sheet, and did a couple worksheets.  I think I want to include another activity or two in their notebooks for this unit next year.  

Systems of Linear Equations Word Problems INB Page

14 March 2017
I made my students do TONS of word problems when we studied systems of equations.  They were fine at solving the systems, but they struggled with setting them up from the word problem.  So, we had one entire class day where I went through a million word problems and just set them up.  After that day, my students improved so much!  

I used this hamburger book one day to help my students set up different systems of equations.  I copied it on legal paper to give my students more room to work.

Systems of Equations Word Problems Interactive Notebook Page for Algebra 1

Systems of Equations Word Problems Interactive Notebook Page for Algebra 1

Angles in Polygons INB Pages

03 March 2017
I feel like I’ve been so focused on Algebra 1 lately that Geometry has been on the back burner!  I have so many Geometry INB pages to share.

I used three pages for my Angles in Polygons lesson.  I don’t typically use that many pages for a lesson, but it happened.  I prefer to do a two-page spread for each lesson.  That’s my fav.

First, I gave my students a table with polygons and spaces for the number of sides, number of internal triangles, and the angle sum.  This is a pretty common page (I think everyone has some version of this!), but you can find mine here.  By the time we got to the hexagon, my students were tired of it and had figured out the pattern.  Every year my kids have thought this was lame.  Either my delivery with this part of the lesson is incredibly boring (quite possible!) or I need to come up with something a little different.

Angles in Polygons Interactive Notebook Investigation Activity for Geometry

Then, we completed this foldable for all of the different formulas for the interior and exterior angles.  We had talked about them on the previous page, but this foldable just put it all together more neatly.  There were also practice problems inside.  I wrote a few notes at the top of the page too.  See the whiteout smudge?  I was asking a student nicely (ahem, stern teacher voice) to stop talking while I was talking, and I started writing what I was saying to the kid.  Everyone thought that was funny…  Me, not so much.

angles in polygons foldable for geometry interactive notebooks

Lastly, I gave my students this sheet of practice problems.  I gave them a few minutes to work with their partners and told them to skip around.  Then, I interrupted them (for time sake) and we went over it as a class.

 *free*  angles in polygons practice page for geometry interactive notebooks

Slope-Intercept Form of a Line INB Pages

26 February 2017
I know I’ve said it before, but I loved teaching linear equations in Algebra 1.  When I first started teaching, I said I never wanted to teach Algebra 1 or Geometry.  I thought they would be boing and I would hate it.  I was totally wrong.  I love Geometry and I’m loving Algebra 1 now too!  I just didn’t know…

Anyway, I used several pages when I taught slope intercept form of a line in Algebra 1.  I’m only sharing some of them, because some of them were total flops and some were direct copies from others.  

I liked this page about linear vs. non-linear equations.  It worked well and my students liked drawing the “crazy” graphs on the left.  I told them they were graphs they would learn more about in Algebra 2.

Linear vs. Non-Linear Graphs Interactive Notebook Page for Algebra 1

The slope intercept form puzzle was a fun review.  If you look closely, you can tell that I cut straight lines instead of cutting around the indents in the puzzle.  You can’t even tell when it’s glued down and it saved a lot of time.  I made my students write what Slope Dude would say on every problem.  It’s becoming forever engrained in their minds.  Success.

Slope-Intercept Form of a Line Practice - interactive notebook puzzle

The hamburger book for interpreting linear graphs was more effective than I thought it would be.  I thought it was decent (but boring) when I made it.  However, my students referenced it many times throughout the unit and whole studying.  They also remembered the problems and mentioned them later.  After the lesson, I used my Interpreting Slope and Intercepts Stations Maze.

Interpreting Linear Graphs Interactive Notebook Page for Algebra 1

Interpreting Linear Graphs Interactive Notebook Page for Algebra 1

As a review, I used my Graphing Linear Equations Cut and Paste Worksheet.  I copied it at 80% to make sure it would fit in their notebooks.  Again, you’ll notice I’m still writing what Slope Dude would say on each graph.

Graphing Linear Equations Cut and Paste Review Worksheet

I’m totally loving Algebra 1 and looking forward to using some of these same activities and lessons again next year.

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

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