Finding the Distance Revamped!

"Finding the Distance" foldable was requested in the form of a pdf.

Finding the Distance

I have typed it up and uploaded it as a word document (editable) and as a pdf. An answer key has been uploaded also. As always, printing can be tricky. I print "two sided along the short edge". After printed, you'll notice a dotted line along one short edge. Cut along the dotted line so that the foldable will fold up nicely.

First unfold reveals methods for distance off a slanted line along with using method 1. 

Second unfold reveals the use of method 2. 

The order of the methods did not hold a significance initially. I now teach the use of the Pythagorean Theorem first to bridge a connection the the distance formula.

Geometry: Pythagorean Theorem

Pg 6. Right Triangle Basics (Optional - Used this my second year, but not my third.)

 

Pg 7. Pythagorean Theorem

LEFT: We took a square piece of paper and folded it until the entire square is made up of small right triangles. We then selected a right triangle and the three surrounding squares to demonstrate the Pythagorean Theorem.

RIGHT: Another time, we selected, drew, and then cut out the diagram to demonstrate the Pythagorean Theorem.

I have seen other diagrams using all the pieces to make a square, but I have yet to understand them or see the purpose. Any suggestions for enlightening resources?

Pg 8. Pythagorean Theorem and It's Converse

This next year, I will use Anglegs and worksheet to introduce and classify triangles.

My students came with excellent prior knowledge of the Pythagorean Theorem.

Pg 9. Multistep Pythagorean Theorem

 

 

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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: Midpoint Formula and Distance Formula

Pg 5. Discovering Midpoint Formula

 

Pg 6. Midpoint Formula

 

Pg 7. Midpoint Formula: Working It Backwards

 

Pg 8. Where does the Distance Formula Come From?

 

Pg 9. Distance Formula

 

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Geometry: Euclidean and Non-Euclidean Geometry

For my third year, I began with an in depth discussion over the types of Geometry. We had a few debates and lots of illustrations and demonstrations. I couldn't believe how engaging these discussions were and how useful an old basketball could be!

Then we dove into the foundations of Euclidean geometry. Next year, I plan on teaching constructions as a continually developing concept through each unit. I love the vocabulary development that results from these experiences. Constructions became a hands-on collaborative activity for my classes.

I will try to post my Geometry Journal ideas and experiences in the chronological order that I use. I will be sharing differing foldables and information from about three different journals-year two experience, year three experience, and the 'creating an idea' journal.

Pg. 1. Foundations of Geometry: (This is the Unit 1 I have been creating for next year. Information has been pulled from the CSCOPE curriculum mostly. Some have been pulled from older journals.)

Unit Pocket (yes, it is backwards)

Pg. 2. Geometry - "To measure the earth" (These are foldables-mainly half folds, that are glued on a sheet of construction paper folded in half. I use the half fold book alot.)

 

 

My students came up with the real world example for the Non-Euclidean Geometry, and we celebrated with Pringles the next day!

Pg. 3. Structure of Euclidean Geometry

OR (the original from year two)

pg 1

pg 2

 

 

 

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