5-B-1 Reflection of Images

Transformations are something that I think most students will enjoy.  Visual learners are especially going to enjoy this activity.  This is a good introduction or review to reflection. I don’t think this will be too difficult for them to do.  Part C would give them the most challenge, but it’s not impossible for them.  After the students finish their work, they can fold the coordinate graph along the x- and y- axis to check their work.  The 2 images should line up with each other with the same side lengths and with observation realize that angle measures remain the same too.  Students should be able to recognize that the when reflected across the x-axis the figure will seem upside down from the original.  When reflected across the y- axis, the figure will seem flipped either left or right from the original.

To extend this activity, have the students write out the coordinate pairs and compare the original points with the reflected points.  When reflected across the y- axis, the y coordinate value stays the same but the x coordinate value changes to the opposite number.  When reflected across the x- axis, the x coordinate value stays the same but the y coordinate value changes to the opposite number.

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Geometry 4-A-1 Categorizing Two Dimensional Figures

I would present triangles to the students after talking about the definition of a polygon.  I would first have them define the different types of triangles in their own words.  This would let me know their prior knowledge of triangles.

Triangle: A polygon with 3 sides.

Triangles (classified by sides)

Equilateral Triangle:  A triangle with 3 congruent sides.

Isosceles Triangle:  A triangle with 2 congruent sides.

Scalene Triangle:  A triangle with no congruent sides.

Triangles (classified by angles)

Right triangle:  A triangle with one angle equal to 90°.

Acute triangle:  A triangle where all angles are less than 90°.

Obtuse triangle:  A triangle where one angle is greater than 90°.

I would first have them explore the characteristics of each triangle.  Some questions:

  • Is it possible to have 2 right angles in a right triangle? Why or why not?
  • Explain if all angles have to be less than 90° in an acute triangle, why or why not.  Illustrate your observations.
  • Can you draw an obtuse triangle that have 2 angles greater than 90°?  Explain your answer.
  • Is it possible for an isosceles triangle to be equilateral, or an equilateral triangle to be isosceles?  Why or why not?
  • What can we determine about the angles of an equilateral, isosceles, and scalene triangle?  Illustrate your findings.  Why is this important to know?

I would then have the students compare the triangles, look for similarities and differences among them.  We would look at a variety of triangles and have them experiment with classifying them.  My objective would be for the student to obtain the knowledge that every triangle can be classified by its angles and by its sides. They could explain their knowledge by drawing a diagram to illustrate all possible ways a triangle can be categorized by its sides and angles.  At the end, revisit their first definitions and change what they have discovered.  A journal entry would also be a nice way to collaborate all the ideas they have developed in their discoveries.

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Geometry 3-C-2: Logic and Reasoning

The most valuable information I got out of this module have been the activities associated with Bloom’s Taxonomy.  When I was teaching I taught more at the Knowledge, Understand, and Apply levels.  The top three areas, Analysis, Synthesis, and Evaluation, did not appear too often.  We would orally discuss higher-level questions as a class, but rarely did they show up on assignments or tests.

We, as teachers, need to be more aware of the logical and lateral skills being taught.  With Common Core becoming implemented in the majority of the states, teachers need to think of more questions at the higher-levels so the students can develop the critical thinking skills necessary to move onto the next level of understanding.  On my journey back to the classroom, this really opens my eyes to how I need to approach and change my teaching methods.  To do this I will incorporate higher-level questioning from Bloom’s Taxonomy in my lesson planning.  It will be a conscious effort to include questions as part of assignments, journal writing, experimentation, cooperative learning projects, and assessments.

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Geometry 3-B-2 Solving Lateral Thinking Problems

Eggs in a Basket

There are six eggs in the basket. Six people each take one of the eggs. How can it be that one egg is left in the basket?

I have to admit that this puzzle stumped me.  I thought about all ways that the six people could take an egg.  Was it possible for 2 people to take the same egg?  Maybe someone put their egg back and another person took it?  So, my first possible solution was that someone took an egg but did not keep the egg; they put it back in the basket.  I finally decided that everyone kept their egg, so the last person would have to take the basket with the last egg still in it.

Manhole Covers

Why is it better to have round manhole covers than square ones?

I think ultimately this question is classified as an evaluation question.  You can reach the evaluation level with guided questions that would also follow through as questions at the analysis and synthesis level.

On the “Analysis” level, you can think of the characteristics of a square vs. a circle.  What is different about the 2 shapes?

On the ‘Synthesis” level, you can discuss the different ways for the manhole to line up with the opening.  How can the shape be repositioned in the opening?  Construct a new design to make a manhole, compare and contrast the new design with the square and the circle.

On the “Evaluation” level, you can access the safety of the design. Why is it safe or not safe to have a circle vs. a square manhole?  Why is it not good to turn it certain ways? You could look at your new designs that were developed at the “Synthesis” level and check for safety too.  Another safety feature is moving the manhole cover. Is it easier to move a circular manhole cover or a square one, why? What are other safety features to consider when developing a manhole cover?  To able to avoid an injury is crucial.  With today’s company’s being safety conscious, questions at the “Evaluation” level are very important.

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2-B-4: Building a Personal Glossary

Congruence  – comparing any 2 objects and know they are the same size or shape.

I developed this entirely solely on prior knowledge.  I just thought of what it means to be congruent.  You have:

Congruent Segments

Congruent Angles

Congruent Circles

Congruent Triangles

Formal Definition of Congruence:   being isometric — roughly, the same size and shape (Wikipedia)

Two-Dimensional:  An object having 2 dimensions, the object will have a perimeter and area.  The object can be drawn on a flat surface or plane.

This definition is based on my prior knowledge.  Example of two-dimentional figures.

Formal definition of Two-Dimensional Shapes:  A shape that only has two dimensions (such as width and height) and no thickness.(mathisfun.com)

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Introducing me……

My name is Julie. I graduated from the University of Iowa in Math, then I went to Indiana University to get my teaching certification. I am in the process of renewing my teaching license in Indiana. I taught for 5 years at Bloomington High School South in Bloomington, Indiana. I taught pre-algebra, algebra, and geometry over the course of that time. I resigned 10 years ago to take care of my three kids. My oldest is 10 and my youngest are 7 year old twins. I have been married to my very supportive husband for 18 years. I like to be with my family, be outdoors, read, and cart my kids to their after school activies. I was born and raised in Iowa (GO HAWKS!). I have lived in Texas, Indiana, Illinois, Nebraska, and now presently living in the state of Illinois for the second time.

My 2 learning goals are: 1.to understand and be able to bring writing and/or journaling into the classroom and, 2. get motivated and excited about going back to the classroom. I have been gone for a while, so I’m a little nervous about the jump back into my former profession. I’m hoping to get ideas and confidence into my teaching style.

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