Venn Diagrams: Quadrilaterals and other Polygons

These activities are AWESOME! I love the discussions that come up, the type of thinking that occurs, and the multiple possibilities there are.

These materials were provided through a workshop. I have yet to use them in my classroom, but I have no doubt these would be an excellent addition to the unit of quadrilaterals.

You start with four different Venn Diagrams.

 

 

 

You have a selection of set titles and shapes.

Here are some examples of the use of these materials.

(Don't forget about the universal set on the outside of the circles.)

 

 

Some suggested strategies/conversations:

• Have a student demonstrate their Venn Diagram.
• Have students justify their decisions.
• Start with with set titles and categorize shapes.
• Start with categorized shapes and determine the set title.
• Ask students where they started and how they categorized the shapes.

 

Posted with Blogsy

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.

 

Posted with Blogsy

Geometry: Parallel Lines, Transversals, and Special Angle Pairs

It has taken me about three years to grasp the point of this unit. The angle relationships are later used in Unit 6 Quadrilaterals and Unit 7 Properties of Two Dimensional Figures.

Pg 1.

Pg 2. Transversals and Special Angle Pairs

OR

Diagram of Lines and Transversals

 

Pg 3. Special Angle Pairs

OR

 

 

 

 

 

I have noticed in the past that students sometimes struggle with all the numbers assigned to the angles. A fellow teacher at a math and science symposium shared this star-dot labeling she has used in the past. She said that this is to be used once an exploratory is complete where a student builds an understanding of congruent and supplementary angles. This allows the students to quickly relate two symbols with location instead of dealing with the numbers.

 

Posted with Blogsy

Geometry: Transformations on the Coordinate Plane

Pg 12. Transformations

 

I pulled the information from the given website and typed this assignment.

Pg 13. Translations

Pg 14. Reflections

 

Pg 15. Rotational Symmetry

Pg 16. Rotations

During my third year, I implemented a new strategy for transformations.

Materials needed:

• paper coordinate grid
• coordinate grid on a transparency
• push pin
• piece of cardboard

Plot the original image on the paper grid.

 

Layer materials:

1. cardboard
2. paper
3. transparency

Using a dry erase marker, copy/trace the original image; then using the transparency, complete a selected transformation. For translations, slide the transparency. For reflections, flip the transparency about the line of reflection. For rotations, turn the transparency in the desired direction and degree. Use the push pin to poke holes through the transparency, paper, and cardboard to mark the resulting image coordinates. Remove the transparency, and replicate the pre-image.

Pg 17. Dilations

Pg 18. Transformations Booklet

OBJECTIVE: This is another one of those 'create your own' projects. Students are given a grid and asked to plot a triangle of their own. I always use points that create a scalene triangle that does not have horizontal or vertical sides. I love watching students throughout this project because they see other's results and begin to connect patterns.

One year, I completed each section after each lesson and practice for the four transformations. The next year, we completed the entire booklet after all four lessons and practices were done. I'm not sure which had a better result. I think that the sequence depends on the level the students are performing at.

We then wrote a translation statement and completed a table using notation. I think students graphed first and then we completed the table. Graphing is easier for students because it it visual and kinesthetic.

We completed dilations after reflections and rotations.

I do remember stating at the beginning, that if you feel daring, then plot across the axes; however, if you are not sure, then keep it in a single quadrant.

 

Posted with Blogsy