The Distance Formula and Pythagorean's Theorem Foldable Practice Notes

  Here are foldable practice notes I created to continue to practice the concept of finding a missing side of a triangle or shape by using both the Distance Formula and Pythagorean's Theorem. After we practiced this multiple times using straightforward problems and word problems, I then allowed them to solve the problem using any method that worked. 

Distance Formula and Pythagorean's Theorem

Perimeter on the Coordinate Plane Using Distance Formula and Pythagorean's Theorem

Area Guided Notes

Here are some guided notes for you to use with your students. These are especially effective, alonh with further instruction and hands on learning, for students who struggle with area, are Special Education students with a math disability, are ESL learners or Regular Education students. I do a lot of paper folding with the students first, and I really try to get them to develop the formula first before I reinforce the formula with notes.

Area of a Triangle

Area of Rhombus, Kites, and Trapezoids

Compositions of Transformations Foldable

 Throughout my transformations unit, I found wonderful foldables and resources. However, what was missing were two skills that my students needed a lot of extra practice with. 

     My students in particular need sooo much help with Algebra skills. It seems they have forgotten them all by the time they get to Geometry. They cannot identify x=1 or y=3, much less a negative line of reflection or x=y. So, we practiced this skill in isolation. We then talked about Reflections, Rotations and so on. We continued practicing a ton after the notes too because students struggle with the spatial aspect of this unit. At the end of the unit, I used the composition notes to really go over how multiple transformations would look on the same graph.

Lines of Reflection Notes

Composition of Transformation Notes

Short. Simple. And best of all...already made for you!

Here is another link for a great practice project: Transformations on a Map

The "When I'm Done" Board

When you're done... You should always have something to do. 
Some of my students innately understand this, and they always have a word search around or a drawing pad. However, many of my students prefer to dull their minds with incessant texting, talking, or other distracting behaviors. Therefore, I created this board, which also encourages holiday decorating, reconnecting with one's childhood pastime of coloring, scaffolded instruction with both anchor projects, remediation (extra practice), and brain teasers for those who just want to try something frustrating;)

The brain teasers, extra practice, and anchor projects are all extra credit dependent on the length and difficulty of the task. The coloring sheets are just for fun, and they are the most popular. One of my students will take one of each of the coloring sheets home each weekend, and bring them back colored. It makes my room bright and cheery! I theme the coloring sheets for each season/holiday.

Sierpinski's Triangles

You have to love the Sierpinski triangle. We used it when talking about equilateral triangles, and then we tied in learning about similar triangles, dilations, ratios, repeating patterns, length (rulers), and more. Each student created their own triangle. Then we put them together to create a huge design on the bulletin board. 

Modifications: I had one student who could not create the design using a ruler, and he was really embarrassed. So I made a template triangle, and all he had to do was color it to show the different sized triangles. This is an extreme modification. Lesser modifications might include leaving out triangles that are drawn to the 1/4 of an inch for example. 

Challenge: Continue the pattern to the smallest triangles possible.

Transformations

This year I enjoyed teaching transformations so much! Not only did I find some awesome foldable notes from Mrs. Hester's Classroom and To the Square Inch Blog, but I also continued to assign my two favorite projects of the year. Both of the projects are similar, and I require students to complete both. I do modify the assignment though based on interest/artistic talent and ability. Effort is most definitely graded, but I do give leeway to those who are not as in love with art projects as I am:) 

Two reasons I complete the projects:
     #1 It is a two year class, and we all can use the break to do something less structured.
     #2 My students really struggle with spatial relations and the more we touch objects, move objects, and practice, the better they do.

Project One: Tessellation (Based on M.C. Escher's Art)

I share a Power Point presentation I made about M.C. Escher's Art and its influence on the math world. In addition, we talk about real life tessellations from wall paper to tiles on the floor. I always provide some of M.C. Escher's artwork for the students to color on the "When you're done board..."

Level 1: Students with the most ability are encouraged to rotate, reflect, and translate a figure to make a tessellation.

Level 2: Students are encouraged to make a unique design out of their index card...perhaps make it look like a fish, bird, wave, etc.

Level 3: Basic design, clean lines, fit the translated shape crisply together. Then outline and color in neatly.

Level 1: 1st Place Winner

Level 1: Simple but Nice:)

Level 1: Honorable Mention

Level 1: Honorable Mention

Level 2: 1st Place Design

Level 2: 1st Place Design (This is a student who dislikes Art)

Project Two: Kaleidoscope Name Reflection Design

I wished I had taken pictures of all of my best Name Reflection Projects, but I didn't. Here are the two that I have left. Again, there are levels of difficulty build into them. Students who needed challenged were asked to create three dimensional letters and appropriately rotate and reflect using any method they wanted (as long as it was accurate). Tracing was fine. Students less blessed with the gift of spacial relations could use a simple design and simply reflect the information. There are more modifications for this project too if needed. 

You can find the instructions to the project here:

Level 2: Initials Used; Great Result

Level 1: Basic Design for Student who lacks talent and motivation. Still a great product

House Blue Prints

House Blue Prints, for my blue collar hands-on crew that live for the practical applications of Geometry. The project is simple and used by many. I've seen many different versions. This time around I utilized the project as a disguise to get them to practice finding the area of shapes. I allowed them to determine the difficulty of the project, and I allowed them to include as much detail as they wanted. I just set basic criteria and allowed them to work. Here are some of the results. 

Secret Door Foldables!!

What to do at the end of a two year Geometry class, with a group full of seniors who have had senioritis since Christmas...

It is my every day dilemma that I sometimes overcome after stumbling upon genius on Pinterest or Youtube. In this case, it was the latter. BEHOLD, Geometry research projects made fun. A three to four day project incorporating hands-on learning, organization, research skills, math inquiry, and creativity in order to produce something purposeful but also self-paced.

I began by creating criteria for my students on what should be on the project. See the handout below.

Hidden Door Research Project Handout


Then I had students watch the Youtube video below in order to create the crazy cool foldables. Let me tell you...my students were complaining like crazy (because they have senioritis and do not want to complete much work, much less research), but they quickly changed their minds when they got to play with this mind teaser. They thought they were so cool, and quickly agreed to the rest of the project because of it! So watch this video, and use this project to either practice vocabulary, to complete a project, or just to amuse your students for an hour;)

Secret Door Foldable Video


Watch this video showing all of our work!!

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Photo Scavenger Hunt

April, April, April. What to do during that long drawn out month without any days off...when students have already checked out for the summer, and yet I still have an observation left. Oh and let's not forget the endless battle with student phones. Ugh! Well, the solution to all those problems is a nicely planned photo scavenger hunt!! 

1. Use this Power Point to introduce the project, set up guidelines, establish groups, and get the project rolling.

Introductory Power Point Presentation

2. Have students carry around these lists looking for their geometric photo op!

Scavenger Hunt List

We present in a couple of days. When they do, I will post some student work!

Here is a fantastic presentation that came in. I had to delete some hilarious student photos that the students added, but the students had a ton of fun with this as you can see, and they really let their personality show.