October 26, 2007

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Lesson Plans and Creative Activities for Geometry Classroom

- Mathematics > General
- Mathematics > Geometry

- Grade 9
- Grade 10
- Grade 11
- Grade 12

Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length).

Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

distinguish between attributes that define a two-dimensional or three-dimensional figure and attributes that do not define the shape;

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This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of 2009-07-25.

Content Accuracy: 3

Appropriate Pedagogy: 3

This is something between a lesson plan and an exercise. It is a tough problem requiring insight, and the problem is fully worked out in the text.

Regis Smith

April 17, 2011

I only see one major problem with the "CircumCircle" lesson-- the triangle side lengths are mislabeled. I think Johnny Texas' review is a bit harsh and misleading, especially since his (Texas') third paragraph includes a mathematical error-- moving point A along the circumference of the circle does not change the measure of angle A, as long as angle A cuts out the same arc BC.

I think the "CircumCircle" lesson is a fine example of a special case of a well-known result. It shows students they do not have to automatically apply memorized formulas to every scenario. The typesetting could be improved, but that's just presentation.

Johnny Texas

April 28, 2010

This rating and comment only applies to the resource labeled "CircumCircle." Your problem (while interesting) is not solvable by your own presented solution.

First the triangle you present does not exist (the one you have for this very problem on your website

Furthermore the interior angle is twice the measure of its corresponding exterior angle as long as the angles measure the same arc of the circle AND share the diameter and the corresponding radius as one of their sides. What you have presented is completely illogical and frankly impossible because you could rotate point A around the circle and create many different angles which must equal the same angle when doubled according to your answer.

Please Please do not use this to teach math to students as you will just give them a greater hardship than they may begin with!

Table of Contents

- Point P Where You Like
- Snake Eyes
- Security Cameras
- A Cute Triangle
- Square Peg, Round Peg
- The Truncated Square
- The Right Plot
- Two Triangles
- The Goat Problem
- The Square Problem
- Pie Free Circles
- Pie Free Circles
- Circum Circle
- Pick a Shape
- Paper Crease
- Intro to coordinate geometry
- Proving vertical angles conjecture
- Pythagorean theorem and the distance formula
- Finding the area of a trapezoid
- Geometry Analysis
- Interactive Math Websites

Lesson Plans and Creative Activities for Geometry Classroom

An interesting property about area and an arbitrary point on a triangles interior is explored in this activity

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An interesting problem that has students find the area of a particular section of a circle that resembles the pupil of a snake eye. The result is rather surprising, because the area does not involve pi.

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Students use the relationship between central angles and inscribed angles in a circle to solve a problem involving the installation of security cameras in an art gallery.

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A clever puzzle which has students investigate the least number of smaller acute angled triangles you can dissect a triangle into.

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This activity has students investigate which fits better, a square peg in a round hole or a round peg in a square hole.

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Students use the Pythagorean theorem to solve a tricky puzzle involving a square with four isosceles triangles cut from the corners.

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A math problem involving the area of an irregular quadrilateral and the Pythagorean Theorem

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Students look at two triangles and must prove whether one line is longer than another. The results are surprising, and there are many different ways to prove the answer to be true.

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This problem has students investigate the area of a pasture in which a goat would be able to graze.

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A great problem that combines practice in graphing linear functions with a challenging problem involving the area of a square.

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A problem involving the area of a crescent. Many students are surprised to discover that their answers do not involve pi.

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A problem involving the area of a crescent. Many students are surprised to discover that their answers do not involve pi.

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A nice problem that encourages students to think backwards. Instead of inscribing a triangle in a circle, the triangle is given, and the student must discover the diameter of the circle.

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Students investigate Picks Theorem, involving the area of an irregular polygon on a lattice point grid. This problem has students look for patterns, try to establish a formula, and test the formula with a more difficult case. The area of a lattice point Pterodactyl.

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A fun geometry problem that takes a little creativity to visualize. Students investigate the length of a crease that is formed when you fold a piece of paper corner to corner.

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Intro lesson and worksheet to coordinate geometry

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Students will use both inductive and deductive reasoning to prove the vertical angles conjecture

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Students use the pythagorean theorem in order to derive the distance formula. Includes pythagorean theorem practice problems

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Students cut a parallellogram and then tape it to form a trapezoid. They then answer a series of questions which enable them to discover the area of a trapezoid.

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Template for Analysis of Mathematics Programs/Series
Mathematics Core Curriculum
Mathematics Toolkit
Curriculum Guidance Materials & Resources
Template for Analysis of Mathematics Programs/Series

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This resource is a list sorted by subject and individual lessons that include web pages for students to obtain extra practice.

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