How to make a Geoboard!

I was going through my workshop journal from a journaling workshop several years ago and I ran across the Geoboard page. This is a great idea, but I haven't used Geoboards in my classroom. This is very easy and the idea can be used elsewhere.

Materials needed:

• print a grid of desired measure onto cardstock (I was given 1 in. squares)
• push brads
• string

Decide first if you want this to be a removable tool from the journal or not. If you decide on removable, I would suggest making a pocket to store the Geoboard in.

Next, push the brads through each point of intersection or your desired scaling on the grid paper. Then glue a second piece of cardstock to the back to secure the brads.

I made a separate small pocket for the string.

My Geoboard in the picture is just a sample from a workshop. I have no experiences to reference for it, but I think it is a great idea.

 

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Geometry: Special Segment Construction with Paper Folding

Pg 5. Special Segment Construction

After the paper triangle folding lesson, I gave students this assignment. This turned out really well. Students cut out their own triangle and when they came across significant scenarios - same altitude, median, etc. we got to discuss this one on one.

 

Here's an example of an obtuse isosceles triangle I was assigned in a workshop.

 

Pg 6. Venn Diagrams of Triangle Relationships

I noticed that some of my students could use a visual diagram for equilateral and equiangular as a subcategory of isosceles and acute.

Pg 7. Intersection of Medians

Pg 8. Intersection of Altitudes

Pg 9. Intersection of Perpendicular Bisectors

Pg 10. Intersection of Angle Bisectors

Pg 11. Constructing Altitudes

 

Pg. 12 Midsegments

Steps:

1. Cut a triangle out.
2. Fold and pinch each side side in half to locate the midpoint.
3. Fold a vertex to the midpoint of the opposite side and crease the midsegment.
4. Using a straight edge either trace the fold or connect the midpoints using a straight line. There should be three midsegments.
5. (EXTENSION) Cut along the midsegments to divide the original triangle into four congruent triangles similar to the original.

OR

My first year, I had students cut out a triangle and then duplicate three more congruent triangles by tracing/copying the original.

I then had the students trace them on a piece of paper.

After tracing, students measured all of the segments and angles. We then compared the lengths using ratios. This showed an approximate scale factor of 2. We also compared and showed the angles of simlar figures to be congruent.

 

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Geometry: Applying Parallel Lines, Transversals, and Special Angle Pairs with a Mini Flip Book

Pg 4. Over the past three years, I have approached these theorems/postulates in different ways.

First attempt: Completed a worksheet and summarized our findings as seen below.

Second attempt:

We completed two flip books with sentence strips that the students had to match the if statement to the then statement and to the diagram.

Third attempt:

Within a large flip book project, we wrote the postulates/theorems out along with each converse.

For the large flip book project, students were to google an image that they could illustrate parallel lines and a transversal on.

INTERESTING: Students brought up the interesting difference between parallel in the real world versus the result of a two dimensional image. For example, one student wanted to use an image of railroad tracks knowing that they were parallel in the real world. However, another student pointed out that when viewed on a two dimensional service the tracks appeared to intersect at the perspective point. Is the picture a valid option? After this discussion, I had students justify their chosen image. How did the idea of parallel apply?

Next, they labeled the angles and identified the special angle relationships.

This had some interesting results. I had the students make up some algebra problems, solve and check them, and then exchange with a partner. Some of the results the students would makeup would have infinite solutions, no solution, and result in negative angle measures.

Here are the postulates/theorems and converses.

 

 

 

 

Out of all that I teach in Geometry, this is one of the hardest concepts to get my students to understand. Proving lines paralell or angles congruent. It took me two years to see the pattern. Maybe next year I will be able to present it better.

 

I gave students two angle puzzles to complete. We discussed every detail and justified each strategy used. Next, students were to create their own angle puzzles for homework. The next day, I mixed up each puzzle and passed them out to the class. Great idea, but kind of overwhelming. Students could critique and troubleshoot each others puzzles, but some would use incorrect properties and their answers wouldn't work out. This activity requires quite a bit of time and would probably do better if the students work with a partner.

 

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Geometry: Finding Distance, and Applying Coordinate Geometry to Quadrilaterals

Pg 10. Finding the Distance

 

 

This is a foldable that I wrote as a template.

Pg 11. Rectangle Analysis

FAVORITE: This is an individual project that we paced ourselves through as a class.

GEOGEBRA: We used Geogebra to graph a rectangle. This required students to be able to enter in two sets of parallel lines perpendicular to adjacent sides. Each student was required to create their own individual rectangle (no two projects were alike). This required some thinking and reworking. Once graphed, printed, and pasted, students had to justify that the shape is a rectangle. On page one, they listed the equations, intersections/ordered pairs, slopes, y-intercepts, and the parallel/perpendicular relationships.

We discussed the other critical attributes needed to justify the rectangle; they came up with midsegments and lengths of each side.

I tried my best to focus on notation, and I wish that we had written a final summary justifying the rectangle. Writing is an important component on math.

This kind of activity allows students to collaborate without copying another's work. They see multiple rectangles and help others troubleshoot.

 

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Geometry: Undefined Terms, Basic Definitions, and Intersections

Pg. 3. Undefined Terms (Point, Line, Plane):

OR (from year two, printable template)

This is a foldable template I pulled from a Dinah Zikes book.

Pg. 4. Ms. Haley's Example:

I worked a guided example which I had the students copy. Their assignment was to create their own diagram and complete a set of fill in the blank sentences.

NEW IDEA: In a recent workshop, the presenter gave a suggestion: The homework we send home should have students working what they learned in that day's lesson backwards or undoing the process. For example, I gave them a diagram that they identified points, lines, and planes. Then for homework I should provide them with the complete sentences and the student tries to create a diagram that satisfied the statements. I think this would have been a neat way to see the different diagrams and level of creative thinking that each student is working at.

 

Pg. 5. Basic Terms and Definitions: (Not a real big fan of this page... I'm looking to improve it.)

Improved look:

Pg. 6. Basic Intersections:

ORIGINAL

Above images were copied and pasted from CSCOPE curriculum.

Another look:

 

New and Improved look:

When I create a foldable, I am always thinking about how a student will see, study, and use it. Is the foldable defining a concept or to be used a review tool? This usually helps me determine the placement/order of vocabulary, definitions, and diagrams.

 

 

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