This learning video deals with a question of geometrical probability. A key …

This learning video deals with a question of geometrical probability. A key idea presented is the fact that a linear equation in three dimensions produces a plane. The video focuses on random triangles that are defined by their three respective angles. These angles are chosen randomly subject to a constraint that they must sum to 180 degrees. An example of the types of in-class activities for between segments of the video is: Ask six students for numbers and make those numbers the coordinates x,y of three points. Then have the class try to figure out how to decide if the triangle with those corners is acute or obtuse.

The purpose of this task is to help students understand what is …

The purpose of this task is to help students understand what is meant by a base and its corresponding height in a triangle and to be able to correctly identify all three base-height pairs.

This activity gives students practice naming and using shape and color attributes …

This activity gives students practice naming and using shape and color attributes to create patterned sequences. The first challenge asks students to use attribute differences to extend a sequence. A second, more open-ended challenge asks students to maximize the length of their sequences under a further constraint. An interactive applet is provided as an alternative to physical manipulatives. The Teachers' Notes page includes suggestions for implementation and discussion questions.

This activity gives students a chance to relate some common three-dimensional solids …

This activity gives students a chance to relate some common three-dimensional solids to their polygonal faces. The object is to put solids in a sequence in which adjacent solids have a polygonal face in common. Ideas for implementation, extension, hints and support are included along with printable cards of the polyhedra.

This task shows that the three perpendicular bisectors of the sides of …

This task shows that the three perpendicular bisectors of the sides of a triangle all meet in a point, using the characterization of the perpendicular bisector of a line segment as the set of points equidistant from the two ends of the segment. The point so constructed is called the circumcenter of the triangle.

This activity allows students to explore reflective symmetry. They are asked to …

This activity allows students to explore reflective symmetry. They are asked to color a given arrangement of triangles in symmetric patterns using specific numbers of colors. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and printable sheets

This activity asks students to recognize differences in shapes and sort them. …

This activity asks students to recognize differences in shapes and sort them. They are given a set of 15 shape cards that they can sort by the criteria of color, size and shape. Ideas for implementation, extension and support are included along with a printable sheet of the cards.

This article helps educators answer questions about geometric thinking and the activities …

This article helps educators answer questions about geometric thinking and the activities that develop it. It outlines the 3 levels of thinking about shape and space and the 5 phases of activities known as the van Hiele model. The tangram puzzle provides a vehicle for describing these phases and the types of thinking students achieve in each one. The article concludes with a suggestion about followup activity.

This problem helps develop an understanding of the relationship between the part …

This problem helps develop an understanding of the relationship between the part and the whole. Given a square figure divided into smaller triangles, students are asked to use the pattern to divide the square into two halves, three thirds, six sixths, and nine ninths. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and a printable (pdf) worksheet of of the problem.

This task shows how to inscribe a circle in a triangle using …

This task shows how to inscribe a circle in a triangle using angle bisectors. A companion task, ``Inscribing a circle in a triangle II'' stresses the auxiliary remarkable fact that comes out of this task, namely that the three angle bisectors of triangle ABC all meet in the point O.

This problem introduces the circumcenter of a triangle and shows how it …

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter.

This task focuses on a remarkable fact which comes out of the …

This task focuses on a remarkable fact which comes out of the construction of the inscribed circle in a triangle: the angle bisectors of the three angles of triangle ABC all meet in a point.

This activity allows students to investigate line symmetry and reflections. Using a …

This activity allows students to investigate line symmetry and reflections. Using a mirror, students locate the lines of symmetry. in a square and then proceed to find other shapes by reflecting parts of the square. Ideas for implementation, extension and support are included along with a printable worksheet of squares (.doc)

This task is intended for instruction, providing the students with a chance …

This task is intended for instruction, providing the students with a chance to experiment with physical models of triangles, gaining spatial intuition by executing reflections.

In this activity students apply their knowledge of triangle properties. It asks …

In this activity students apply their knowledge of triangle properties. It asks students to sort three types of triangles based on angle and side comparisons, while ignoring the size and orientation differences. Students can work online with an interactive Flash applet, or on a printed sheet (included). The Teachers' Notes page includes suggestions for implementation, discussion questions, and ideas for extension.

This lesson is focused toward 2nd Grade Math - Shapes - using …

This lesson is focused toward 2nd Grade Math - Shapes - using iPad App Keynote. It includes triangles, quadrilaterals, pentagons, hexagons, and cubes. Time frame - 2 hours - can be expanded or reduced, taught and explored over 4 or 5 short lessonsFormat - Planned for face to face - adaptable to virtual environment - Math Talk would need to be face to face or a syncronous lessoniPad App Needed: Keynote

Students have been exposed to triangles often throughout the previous years of …

Students have been exposed to triangles often throughout the previous years of mathematics. Use these Venn diagrams to have students construct these triangles--if it is possible.

This brief article describes some of the mathematics of Pythagoras and his …

This brief article describes some of the mathematics of Pythagoras and his society. It relates what they believed to be the natural significance of numbers and the well-known Pythagorean Theorem. A link to a printable page is included.

This activity gives students an opportunity to use and develop their visualizing …

This activity gives students an opportunity to use and develop their visualizing skills in conjunction with the knowledge of fractions. Students are given one large rectangle that is divided into ten smaller quadrilaterals and triangles in which they have to find what fractional part is represented by each of the ten numbered shapes. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support.

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