WORD BANK FOR GEOMETRY SURVEY - Tidewater Team for...

11th Annual W&M Mathematics Education Day February 26, 2008

WORD BANK FOR GEOMETRY SURVEY

length perimeter three-dimensional

two-dimensional 2-D 3-D spatial

line segments milk size tans

Tangram similarities vertical

horizontal diagonal parallel

perpendicular rotation reflection

translation line of symmetry tessellation or transformation

plane region triangles line angle

four quadrilateral end points

closed polygon width outside

inside around eight three

degrees 180 ° 360° two

congruent Isosceles right triangles similar

equal area classified

Created by: Mary Collins, Sandy Manning, Erica Sheehan


Fill in the blanks with terms from the word bank provided. 1. A _________________________ has an unlimited number of points and continuously

extends from one direction to the other.

2. Lines have only one dimension, ________________________.

3. Part of a line, marked by _____________________ ___________________, is called a

__________________________ _____________________________.

4. A closed figure made with line segments is called a________________________.

5. The combination of two line segments at a common point is called an

_________________.

6. Draw a 90° angle and label the angle. _______________________

7. Two dimensional shapes have ___________________and __________________.

8. A _______________ is a flat surface that extends on and on in all directions.

9. Draw 4 points and connect them with line segments.

10. This shape is called a _______________ _____________________

11. Another name for the shape in question #9 is _____________________________,

because it has _______________ edges or sides.

12. Lines that are drawn from the top to the bottom of the plane are called

____________________ lines.

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13. ______________________________lines are drawn from one side of the plane to the

other and are ____________________________to the edges.

13. ______________________________lines can be connected from a square’s top right

point and the bottom left point in the interior region.

14. Three- sided polygons are called _____________________________.

15. A polygon can be called a _____________________ __________________, because it

has boundaries and doesn’t continue on forever and forever in all directions.

16. _______________ _____________________ shapes are used to draw

__________________ ___________________________ forms.

17. The sum of a polygon’s _________________ ________________________ is called

the _____________________________ of that shape.

18. In a glass, if you add milk to milk, and add milk again, then you will have a glass

of_____________.

19. For perimeter, the unit being added is length, therefore the total sum of these units will

have a value of _________________________.

20. With polygons, there are ________ regions: __________________________________.

21. The perimeter of a polygon is the region __________________________ of the shape.

22. A fence around a pool is an example of _______________________________.

23. How many sides does an octagon have? ___________________________.

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24. On a separate page, draw each of the basic geometric shapes you’ve studied in math and

label its parts: length, width, height, and diagonals.

25. _____________________are the unit measurements of angels.

26. The sum of the angles of a triangle are __________________.

27. The sum of the angles of a square are ___________________.

28. __________ ______________ ____________ triangles can be combined to make a

square.

29. Congruence means that two shapes are _____________ in size to each other.

30 The region inside of a polygon is called its ___________________.

31 Polygons have groups of shapes that are ______________________________. They are

______________________, or grouped according to their _______________, even

though their _____________ vary.

32. ____________ are Chinese puzzle pieces that can be used to form a square and many

other shapes.

33. A popular math puzzle that has 7 individual pieces which can be used to explore the

geometric properties of shapes is called a ______________________.

34. The line where a figure is reflecting an indentical, but flipped figure is called the

______________ of ________________.

35. The movement of a shape around one fixed point is called _______________________.

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36. Sliding a shape from one position in a plane to another position in the same plane is

called _________________________.

37. Repeating and changing shapes in a way that creates a geometric pattern is called

____________________________ or ____________________________.

38. Polyhedrons are ________ versions of __________ geometric shapes.

39. ___________________awareness is the ability to predict and plan a project using

symbols to represent areas, or spaces within the plan.

40. The sum of the angles of any polygon is at least ________.

REMARKS / COMMENTS:



FINDING THE SUM OF INTERIOR ANGLES

Shape # of sides (n)

# of angles

# of diagonals

# of triangles

Sum of Angles

How did I find the

sum

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Dodecagon

Icosagon

n-gon



PARTS TO WHOLE AND WHOLE TO PARTS EXPLORATION A FRACTION EXPERIENCE WITH THE TANGRAM

“WATER GARDEN” copyright Sandy Manning 2007 Using the tans of the Tangram, experiment with the questions below: Create a table to show drawings of the process you are using to answer these challenges.

1. If _____________ is 1 unit, which shape would be equal to ½ a unit?

2. If _____________ is ½ unit, which shape is equal to 1 unit?

3. How many other combinations can you make of this relationship, using different

tans?_____________

4. If _____________ is ¼ unit, which shape is equal to 1 unit?

5. If _____________ is one unit, which shape is equal to 3 units?_______________

6 units?________________

6. Make a shape 2 ½ ( the chosen unit). 2.5 X the unit. Draw the new shape:

7. Make a shape 4 ( the chosen unit). 4 x the unit. Draw your unit and the finished figure.

8. What kind of shape did you make? Can you make more than 1? More than 3?

9. Continue with explorations of your own. Describe what discoveries you have made in

written form.

10. Share your findings with another classmate. Do you both have some that are similar?

Are there discoveries unique to your explorations?

Created by: Sandy Manning


CONSTRUCTING YOUR OWN TANGRAMS

Materials: A rectangular piece of paper suitable for folding, scissors, ruler

Activities

A complete set of tangrams consists of seven pieces:

a small square two small congruent triangles

two large congruent triangles a medium-size triangle

a parallelogram

You can make your own set of tangrams from a single piece of paper. Just follow these simple steps:

1. Fold a rectangular piece of paper so that a square is formed. Cut off the extra flap.

Reproduced by: Mary Collins, Sandy Manning, Erica Sheehan with permission from Drexel University, copyright 2008, by The Math Forum @ Drexel

(http://mathforum.org/). All rights reserved.


2. Cut the square into two triangles.

3. Take one triangle and fold it in half. Cut the triangle along the fold

into two smaller triangles.

4. Take the other triangle and crease it in the middle. Fold the corner of the triangle opposite the crease and cut.

Reproduced by: Mary Collins, Sandy Manning, Erica Sheehan with permission from Drexel University, copyright 2008, by The Math Forum @

Drexel (http://mathforum.org/). All rights reserved.


5. Fold the trapezoid in half and fold again. Cut along both folds.

6. Fold the remaining small trapezoid and cut it in two.

Reproduced by: Mary Collins, Sandy Manning, Erica Sheehan with permission from Drexel University, copyright 2008, by The Math Forum @

Drexel (http://mathforum.org/). All rights reserved.


References: Crowley, Mary L., “The van Hiele Model of the Development of Geometric Thought.”

In Learning and Teaching Geometry, K-12, 1987 Yearbook of the National Council of Teachers of Mathematics, edited by Mary Montgomery Lindquist,

pp. 1-16. Reston, VA: National Council of Teachers of Mathematics, 1987. Griffin, Coralie. “The van Hiele Model of Geometric Thought.” 10th Annual

Mathematics Education Day, The College of William and Mary, Oct. 24, 2006. Locher, J.L., ed. The World of M.C. Escher. Harry N. Abrams, Inc. NewYork, 1971. Mason, Marguerite. “The van Hiele Levels of Geometric Understanding” [Electronic

Version], Geometry: Exploration and Applications, Boston: McDougal Littell,1998, p.4-8. Retrieved Sept. 29, 2005 from

http://www.mcdougallittel.com/state/tx/corr/levels National Council of Teachers of Mathematics, “Exploring Shapes with Tangrams.”

In Navigating Through Geometry in Grades 6-8. Reston, VA: NCTM, 2004:

pp 61-62. Thatcher, Debra H., “The Tangram Conundrum.” Mathematics Teaching in the

Middle School. 6(March 2001). 394-99. Tompert, Ann. Grandfather Tang’s Story. New York: Crown Publishers, 1990.

Informative Websites:

http://www.nctm.org: The National Council of Teachers of Mathematics, Inc.

http://www.nlvm: The National Library of Virtual Manipulatives-an awesome site. http://www.tangrams.ca/index.htm : software downloads, tangram history.

http://www.ex.ac.uk/cimt/puzzles/tangrams/tangint.htm : examples of tangrams. http://mathforum.org/trscavo/tangrams/ : steps to creating a tangram.

http://www.smm.org/sln/tf/t/tans/tans.html : samples for puzzles and directions http://www.kidscom.com/games/tangram/game4/tangram04.html : games to play http://www.mathsyear2000.org/games/index.shtml : another tangram game site

http://www.funorama.com/tangram.html : a printable tangram pattern. http://pbskids.org/sagwa/games/tangrams/magistrate/ : presents an on-line game.

http://www.ac.wwu.edu/~mnaylor/tangrams/tangrams.jpg : tangram puzzle shapes. http://www.edex.com.au/pdf/tn060566.pdf : lessons/activities related to tangrams. http://www.joethedragon.co.uk/maths/tangrams.html : large collection of puzzles

http://www.cs.uu.nl/~markov/kids/tangram/ : free tangram software http://CTEresource.org: creator of Scientific Calculator Lessons for VDOE, 2005.

http://doe.virginia.gov: location of the SOLs for the State of Virginia, and more. http://catalog.teachingsupplystore.com/index.php?cPath=196_223&sort=2a&filter_id:

a catalogue of tangram-related items to buy

http://www.teachersnetwork.org/readysettech/tangram.htm: a Non-Profit resource of lesson plans and networking opportunities with other teachers.

Videos made with tangrams:

http://www.tygh.co.uk/tan/football.html: a football video, illustrated by tangrams.

http://www.tygh.co.uk/tan/tan.htm: the original tangram video.

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