Translating from Words to Math

This year, we worked on translating from words to math at differing levels. We began with the basics earlier in the year.

Writing Variables and Expressions

 

 

 

 

 

 

Then we defined and compared expressions to equations on a journal page.

Next, we practiced writing equations with basic terminology.

Writing Equations

 

 

Then we added some more operation and words to our arsenal of writing algebraically.

Translating from Words to Math

(This page brought in square, square root, cube, absolute value, and multiple steps.)

 

 

 

 

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Geometry: Quadrilaterals

This is one of my favorite units out of geometry now, but it wasn't the first time I taught. My secret... I will reveal in a later post. ;)

Pg 1. Unit 6 Quadrilateral

Pg 2. Map of Quadrilaterals

This is my original organization and understanding of quadrilaterals. Some students like the Venn Diagram feel of this graphic organizer. This notes page does not include the trapezium and also leads to the misconception that legs of trapezoids always extend outwardly. I added that small trapezoid image to remind me about that misconception (and that trapezoids should also be seen 'upside down').

Pg 3. Properties of Quadrilaterals

This page is used to define and list the attributes of quadrilaterals. This foldable is a collaboration of my second year project from my students.

 

There has been some controversy over whether or not the complex are actual polygons or not. Some of my resources are

• http://www.mathsisfun.com/geometry/polygons.html
• http://www.math.com/school/subject3/lessons/S3U2L1GL.html
  
• http://mathworld.wolfram.com/Polygon.html
  
• http://www.mathopenref.com/polygon.html

I always try to use multiple resources along with different curriculums and textbooks. When get to a gray area, I let my students know, provide them with the references, and tell them to keep an open mind because math is up for interpretation. (And I am not always right. :))

Pg 4. Flow Chart of Quadrilaterals

This page was a result of a tutoring session with a student at Sylvan. This student wanted to look at my class journal to compare my information to the information from her teacher. After viewing my Map of Quadrilaterals page, she disagreed with my graphic organizer and drew up the following flowchart on a scratch sheet of paper. My students really like the flow and relationships that this graphic organizer gives. I used this graphic organizer to visually notate the critical attributes of each quadrilateral. As we went shape by shape, I encouraged students to reference our previous notes page.

 

During my second year of teaching, I had students write a paper analyzing the relationships of quadrilaterals or depicting the relationships through fiction. My favorite result was the student that wrote about the rhombus and the rectangle that stayed out late one night, and nine months later, there was a square.

Pg 5. Properties of Trapezoids

This is an important page as far as properties go. I didn't know how to go about this journal page, so I went with my go to half page fold. I need to find another foldable or way to help organize and emphasize each property. Suggestions?

 

 

NEW: I viewed these in an amazing geometry workshop and I can't wait to try them out next year.

Who am I? Puzzles:

Read the lines one at a time to students. One teacher suggested giving students whiteboards to draw their guesses as each line is given. If a student makes a guess, then they are required justify their guess using attributes and definitions.

 

 

 

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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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