Tactile Tangrams - Guidebook

by Karen J. Poppe

APH Logo

Print Guidebook Catalog No. 8-08439-00
Tactile Tangrams Kit Catalog No. 1-08439-00
Braille Guidebook Catalog No. 6-08439-00

Project Staff

Karen J. Poppe
Tactile Graphics Project Leader/Author

Rosanne Hoffmann
Research Assistant

Andrew Dakin, Katherine Corcoran, Tom Poppe
Model/Pattern Makers

Bryan Rogers
Manufacturing Specialist

Bisig Impact Group
Guidebook Layout and Cover Art

Print Guidebook Catalog Number 8-08439-00

Copyright © 2012

American Printing House for the Blind, Inc.
1839 Frankfort Avenue
Mailing Address: P.O. Box 6085
Louisville, KY 40206-0085
Phone: 502-895-2405
Toll Free: 800-223-1839
Fax: 502-899-2274
Email: info@aph.org
Web site: www.aph.org
Shopping: http://shop.aph.org


In keeping with our philosophy to provide access to information for people who are blind or visually impaired, the American Printing House for the Blind provides an electronic version of this book for large print and braille readers.

Print Guidebook Catalog Number 8-08439-00

Copyright © 2012, American Printing House for the Blind, Inc.

All rights reserved. Printed in the United States of America.
This publication is protected by Copyright and permission should be obtained from the publisher prior to any reproduction, storage in a retrieval system, or transmission in any form or by any means electronic, mechanical, photocopying, recording, or otherwise, unless where noted on specific pages. For information regarding permission, write to American Printing House for the Blind, 1839 Frankfort Avenue, Louisville, KY 40206-0085.



Acknowledgements

The project leader would like to thank the following Teachers of the Visually Impaired who contributed their time, knowledge, and creativity to the field evaluation of Tactile Tangrams:

Special thanks, too, to the 66 students who were involved in the field testing of this product.




INTRODUCTION

Image of all seven tangram puzzle pieces in a square shape. Puzzle pieces are multi-colored.

The tangram puzzle is an ancient Chinese puzzle consisting of seven pieces in three different shapes: two large triangles, one medium triangle, two small triangles, a square, and a parallelogram. The materials and activities presented in Tactile Tangrams make this timeless and popular puzzle accessible to students and adults with visual impairments and blindness.

The use of tangram puzzles encourages the development and reinforcement of many educational and recreational skills including spatial reasoning, shape recognition, size comparison, pattern replication, and independent problem solving. Concepts such as congruence, symmetry, sides and angles, and fractions are also reinforced. Most notably, the use of tangram puzzles supports the following National Geometry Standards:

The following expanded skills, especially important for tactile and low vision readers, are also addressed:

Tactile Tangrams includes the following components:

The activities in this guidebook are presented in an order that first acquaints a student with the tangram puzzle pieces, focusing specifically on geometry concepts (e.g., sides, angles, symmetry, etc.) before puzzle solving is introduced. These activities can be de-emphasized or omitted for the student or adult who prefers to focus exclusively on the task of solving the tangram puzzles. In this case, skip to Activity 11 for puzzle solving instructions and game options.


Image of Activity 1 heading against Vase puzzle (Puzzle #23).

Activity 1:
Puzzle Piece Comparisons

Explore and discuss the unique shapes of the tangram puzzle pieces. Focus on the overall shape, the number of sides, and the angles of each piece.

Small Triangle

Image of small triangle puzzle piece.

Medium Triangle

Image of medium triangle puzzle piece.

Large Triangle

Image of large triangle puzzle piece.

Suggested Questions for Triangle Pieces

Square

Image of square puzzle piece

Parallelogram

Image of parallelogram puzzle piece.

Suggested Questions for Square and Parallelogram


Puzzle Practice

  1. Using Puzzle Frame #1, have the student insert each puzzle piece into its corresponding puzzle frame. This is good practice for familiarizing the student with the concept of puzzles and how to insert the pieces within the raised frames.
    Image of Puzzle Frame #1 with tangram puzzle pieces inserted
  2. Using any of the Puzzle Solutions, have the student place each tangram puzzle piece within the corresponding outline shape.
    Tangram puzzle pieces are placed within the outline shapes of the Solutions Page for Puzzle #9 (chicken)

Image of Activity 2 heading against 'spinning top' puzzle (Puzzle #18).

Activity 2:
Types of Angles

Review types of angles using the seven tangram puzzle pieces.

Square

Image of square puzzle piece

Present the square tangram puzzle piece to the student and ask the following questions:

Triangles


Image of small triangle puzzle piece. Image of large triangle puzzle piece. Image of medium triangle puzzle piece.

Present all three sizes of triangle tangram puzzle pieces to the student and ask the following questions:

Parallelogram

Image parallelogram puzzle piece.

Present the parallelogram tangram puzzle piece to the student and ask the following questions:


Image of Activity 3 heading against 'table' puzzle (Puzzle #21).

Activity 3:
Flips, Turns, and Slides

Demonstrate three shape transformations using the tangram puzzle pieces.

.Important: Non-magnetic tangram puzzle pieces are required for this activity so that the color and texture stay the same when shapes are flipped. Two sets of tangram puzzle pieces are needed so that duplicate square and parallelogram shapes are available.

Example of Reflection

Present two identical tangram puzzle pieces in two different orientations shown below. Ask the student to move one shape so that it matches the other. What type of transformation is needed? In this example, one of the triangles must be flipped.
Two small triangles are flipped in opposite directions.

Example of Rotation

Present two identical tangram puzzle pieces in the two orientations shown below. Ask the student to move one shape so that it matches the other. What type of transformation is needed? In this example, one of the parallelograms must be rotated.
Two parallelograms are rotated in opposite directions

Example of Translation

Translation or sliding of a shape is frequently executed while solving a tangram puzzle. Practice sliding a tangram piece within a puzzle frame (with or without other tangram puzzle pieces in place). Can a prediction be made as to where the shape will fit? In this example, two possible locations for the square puzzle piece within the unsolved puzzle are illustrated by a sliding motion.
Image of Puzzle #6 is partly solved. A double arrow shows two possible positions for the square puzzle piece through a sliding motion.

Extended Activities


Image of Activity 4 heading against 'house' puzzle (Puzzle #13).

Activity 4:
Congruent Polygons

Construct congruent polygons using two sets of tangram puzzle pieces included in Tactile Tangrams.

Examples

Discuss why some polygons are similar, but not congruent. For example, these two squares have the same number of sides and their angles are the same size, but their sides are not the same length.
Image of two squares that are similar, but not congruent. One is a square built using two large triangle puzzle pieces placed together. The other square is formed with two small triangle puzzle pieces placed together.


Image of Activity 5 heading against 'swan' puzzle (Puzzle #20).

Activity 5:
Convex and Concave Puzzle Frames

Illustrate the differences between convex and concave polygons using the puzzle frames included in Tactile Tangrams.

Convex Polygon
All vertices of a convex polygon point outward and away from the interior of the shape. All interior angles of a convex polygon measure less than 180 degrees.

Concave Polygon
Some vertices of a concave polygon point inward, toward the interior of the shape. At least one interior angle measures greater than 180 degrees. At least one line exists between two points such that part of the line segment lies outside of the polygon.

Examples

Silhouette of Puzzle Frame #6 is shown as an example of a convex polygon.
CONVEX POLYGON
Silhouette of Puzzle Frame #10 is shown as an example of a concave polygon. Part of a line segment connecting two points within the shape lies outside the polygon.
CONCAVE POLYGON

Sort the puzzle frames into two groups representing "Convex" and "Concave" polygons. The puzzle trays can be grouped like so:

Convex Puzzle Frames

Silhouette of Puzzle Frame #6 as an example of a convex polygon.
#6
Silhouette of Puzzle Frame #11 as an example of a convex polygon.
#11
Silhouette of Puzzle Frame #13 as an example of a convex polygon.
#13
Silhouette of Puzzle Frame #15 as an example of a convex polygon.
#15
Silhouette of Puzzle Frame #16 as an example of a convex polygon.
#16

Silhouette of Puzzle Frame #17 as an example of a convex polygon.
#17
Silhouette of Puzzle Frame #19 as an example of a convex polygon.
#19
Silhouette of Puzzle Frame #25 as an example of a convex polygon.
#25
Silhouette of Puzzle Frame #26 as an example of a convex polygon.
#26

Concave Puzzle Frames

Silhouette of Puzzle Frame #5 as an example of a concave polygon.
#5
Silhouette of Puzzle Frame #7 as an example of a concave polygon.
#7
Silhouette of Puzzle Frame #8 as an example of a concave polygon.
#8
Silhouette of Puzzle Frame #9 as an example of a concave polygon.
#9
Silhouette of Puzzle Frame #10 as an example of a concave polygon.
#10

Silhouette of Puzzle Frame #12 as an example of a concave polygon.
#12
Silhouette of Puzzle Frame #14 as an example of a concave polygon.
#14
Silhouette of Puzzle Frame #18 as an example of a concave polygon.
#18
Silhouette of Puzzle Frame #20 as an example of a concave polygon.
#20
Silhouette of Puzzle Frame #21 as an example of a concave polygon.
#21

Silhouette of Puzzle Frame #22 as an example of a concave polygon.
#22
Silhouette of Puzzle Frame #23 as an example of a concave polygon.
#23
Silhouette of Puzzle Frame #24 as an example of a concave polygon.
#24

Temporary line segments can be drawn on the puzzle frames using Wikki Stix® or strips of APH's Graphic Art Tape to illustrate why a certain shape is a concave polygon.
Temporary line segments are drawn with strips of Graphic Art Tape on Puzzle Frame #12 to demonstrate why it is a concave polygon.


Image of Activity 6 heading against 'rectangle' puzzle (Puzzle #17).

Activity 6:
Making Convex and Concave
Polygons

Construct a variety of convex and concave polygons using the tangram puzzle pieces. Alter the number and type of pieces used.

.Note: Review the definitions of convex and concave polygons in Activity 5.

Examples


Image of Activity 7 heading against 'house with chimney' puzzle (Puzzle #14).

Activity 7:
Concept of Symmetry

Introduce the concept of symmetry using the seven tangram puzzle pieces. Explore each shape separately and determine if it has lines of symmetry and, if so, how many lines of symmetry are present.

Symmetrical Shape
A shape is symmetrical if at least one fold line allows the shape to fold over on itself allowing the two halves to match up exactly. Some shapes have more than one line of symmetry. The fold lines are called "lines of symmetry."

Triangles

One line of symmetry is drawn on the medium triangle puzzle piece. One line of symmetry is drawn on the large triangle puzzle piece. One line of symmetry is drawn on the small triangle puzzle piece.

Square

Four lines of symmetry are drawn on the square puzzle piece.

Parallelogram

Demonstrate and identify the lines of symmetry of the tangram puzzle pieces in the following ways:

  1. Provide paper cut-outs of the tangram puzzle pieces and fold the cut-out shapes along the line(s) of symmetry.
  2. Using Puzzle Frame #1 from Tactile Tangrams, draw temporary lines of symmetry by directly applying Wikki Stix® or strips of APH's Graphic Art Tape to the puzzle frame shapes.
    All lines of symmetry are drawn on the frame shapes displayed on Puzzle Frame #1. Dotted lines indicate where temporary lines of symmetry can be drawn with Wikki Stix or Graphic Art Tape.
  3. For low vision students, trace the tangram puzzle pieces onto a dry-erase surface (e.g., APH's ALL-IN-ONE Board) and draw dashed lines of symmetry (using a marker of a different color) on the outline shapes.
    Tracings of the large triangle, square, and small triangle puzzle pieces are shown on the dry-erase surface of the ALL-IN-ONE Board. Dashed lines of symmetry are drawn on each shape.

Image of Activity 8 heading against 'trapezoid' puzzle (Puzzle #26).

Activity 8:
Symmetrical Puzzle Frames

Identify lines of symmetry using the puzzle frames included in Tactile Tangrams. Which puzzle frames have one line of symmetry? Two? More than two? None? Draw the lines of symmetry on the puzzle frames by applying Wikki Stix® or strips of APH's Graphic Art Tape.
A vertical line of symmetry is drawn on Puzzle Frame #25 (the triangle) using a strip of Graphic Art Tape.

One Line of Symmetry

A vertical line of symmetry is drawn on Puzzle Frame #5 (the arrow).
#5
A vertical line of symmetry is drawn on Puzzle Frame #6 (the barn).
#6
A vertical line of symmerty is drawn on Puzzle Frame #8 (the bowl)
#8


A vertical line of symmetry is drawn on Puzzle Frame #10 (the rocket or fish).
#10
A vertical line of symmetry is drawn on Puzzle Frame #12 (the hourglass)
#12
A vertical line of symmetry is drawn on Puzzle Frame #13 (the house)
#13


A vertical line of symmetry is drawn on Puzzle Frame #18 (the spinning top).
#18
A vertical line of symmetry is drawn on Puzzle Frame #21 (the table)
#21
A vertical line of symmetry is drawn on Puzzle Frame #22 (the tree)
#22


A vertical line of symmetry is drawn on Puzzle Frame #23 (the vase).
#23
A vertical line of symmetry is drawn on Puzzle Frame #24 (the well).
#24
A vertical line of symmetry is drawn on Puzzle Frame 25 (the triangle).
#25

A vertical line of symmetry is drawn on Puzzle Frame 26 (the trapezoid).
#26


Two Lines of Symmetry

Two lines of symmetry (one vertical and one horizontal) are drawn on Puzzle Frame #11 (the hexagon).
#11
Two lines of symmetry (one vertical and one horizontal) are drawn on Puzzle Frame #17 (the rectangle).
#17


More Than Two Lines of Symmetry

Four lines of symmetry (one vertical, one horizontal, and two diagonal) are drawn on Puzzle Frame #19 (the square). #19


No Line of Symmetry

Puzzle Frame #7 (the boat) doesn't have a line of symmetry.
#7
Puzzle Frame #9 (the chicken) doesn't have a line of symmetry.
#9
Puzzle Frame #14 (the house with a chimney) doesn't have a line of symmetry.
#14



Puzzle Frame #15 (a six-sided irregular polygon) doesn't have a line of symmetry.
#15
Puzzle Frame #16 (the ramp) doesn't have a line of symmetry.
#16
Puzzle Frame #20 (the swan) doesn't have a line of symmetry.
#20



Image of Activity 9 heading against 'bowl' puzzle (Puzzle #8).

Activity 9:
Making Symmetrical Shapes

Build shapes using various combinations and numbers of tangram puzzle pieces. For each constructed shape, indicate the location of each line of symmetry.

Example 1

Using only (1) medium triangle, (2) small triangles, and (1) parallelogram, build a variety of shapes and indicate for each the line(s) of symmetry (if any).

Rectangle

Parallelogram

Trapezoid

Hexagon

Pentagon

Example 2

Using only (1) medium triangle, (2) small triangles, and (1) large triangle, build a variety of shapes and indicate for each the line(s) of symmetry.

Rectangle

Square

Discussion


Image of Activity 10 heading against 'barn' puzzle (Puzzle #6).

Activity 10:
Area and Perimeter

Find the area and perimeter of each puzzle piece and combinations of puzzle pieces included in Tactile Tangrams.

Area
The size of the region enclosed by the figure, usually expressed in terms of some square unit.

Using a sheet of the provided tactile/print graph paper, determine the exact area of each individual puzzle piece by 1) counting the number of whole and half squares of each piece positioned on the grid, and 2) using logical reasoning based on the relationships between the tangram pieces. For example, if the large triangle has an area of four square inches and the medium triangle is half its size, then the area of the medium triangle is two square inches. If the small triangle is half the size of the medium triangle, then the area of the small triangle is one square inch. Since both the square and the parallelogram can be constructed using two small triangles, the area of each is two square inches.

The area of the whole tangram = 16 square inches
Image of all tangram puzzle pieces in the form of a square placed on grid sheet.

Extended Activity

Build polygons with specific areas.

Perimeter
The perimeter of a polygon is the sum of the length of all of its sides.

Using an inch ruler, find the perimeter of each tangram puzzle piece to the nearest 1/8 of an inch. An equation can be written for each:

Large Triangle
P = 4 + 2 7/8 + 2 7/8 = 9 3/4
Image of large triangle puzzle piece.

Square
P = 1 3/8 + 1 3/8 + 1 3/8 + 1 3/8 = 5 1/2
Image of square puzzle piece.

Small Triangle
P = 1 3/8 + 1 3/8 + 2 = 4 3/4
Image of small triangle puzzle piece.

Medium Triangle
P = 2 7/8 + 2 + 2 = 6 7/8
Image of medium triangle puzzle piece.

Parallelogram
P = 2 + 1 3/8 + 2 + 1 3/8 = 6 3/4
Image of parallelogram puzzle piece.


Image of Activity 11 heading against 'hexagon' puzzle (Puzzle #11).

Activity 11:
Solving Tangram Puzzles

Tactile Tangrams includes 26 unique puzzles. Each puzzle is presented as an outline raised frame or "silhouette" into which the tangram puzzle pieces can be arranged. The puzzle frames are labeled numerically in print and braille in the upper right corner of the frame and have corresponding three-hole punched Solution Pages located in the storage binder.

Puzzles Frames 1-4

Puzzle Frames 1-4 are intended to serve as easier puzzles for younger students to solve as they become acquainted with how the puzzle pieces fit within the puzzle frames. Each of these initial puzzle frames requires a different number of tangram puzzle pieces. For Puzzle Frames 2-4, multiple sets of tangram puzzle pieces are necessary to fill in all of the individual outline shapes.

Puzzle Frame 1: One puzzle piece per outline shape.
Image of Puzzle Frame #1 with tangram puzzle pieces inserted.

Puzzle Frame 2: Two puzzle pieces per outline shape.
Image of Puzzle Frame #2 with tangram puzzle pieces (various types and colors) inserted.

Puzzle Frame 3: Three puzzle pieces per outline shape.
Image of Puzzle Frame #3 with tangram puzzle pieces (various types and colors) inserted.

Puzzle Frame 4: Four puzzle pieces per outline shape.
Image of Puzzle Frame #4 with tangram puzzle pieces (various types and colors) inserted.

Puzzles Frames 5-26

Puzzle Frames 5-26 are typical tangram puzzles that are solved using the following rules:

Types of Puzzle Pieces

Tangram puzzle pieces are made of three different kinds of material and can be selected based upon the intended mounting surface, student's preference, and/or color choice.

Solution Pages

The Solution Pages present a dissected view of each whole image within the set of puzzle frames. The intended position of each of the puzzle pieces within the whole image or "silhouette" is illustrated. The dissected view is slightly oversized compared to the puzzle frame image to allow each puzzle piece to fit within its corresponding outline, leaving other division lines visually and tactually exposed.
Solution Page for Puzzle #7 (sailboat) is shown with four puzzle pieces inserted within the appropriate outline shapes.

.Note: Sometimes the student might discover solutions to a puzzle that are different from the one presented in the kit. For example, here are two other possible solutions for Puzzle #16.

Solution page for Puzzle #16. Possible solution for Puzzle #16.
Possible solution for Puzzle #16.

Variations


Image of Activity 12 heading against 'square' puzzle (Puzzle #19).

Activity 12:
Creating Tangram Puzzles

Create new tangram puzzles and challenge friends and family members to solve them. Use the following methods to make additional tangram puzzles: