Trish Boschetti – Cluster Coordinator Phase 1 – Maths for Learning Inclusion Tangram Information A tangram is an ancient Chinese puzzle consisting of a square cut into five triangles, a square and a parallelogram which can be reassembled into an amazing number of different figures. Each shape in a tangram is called a tan and must be used to solve the puzzle. The tangram shapes must lay flat and not overlap any of the other pieces in the puzzle. Tangrams & Problem Solving A manipulative is any object that aids in students visualising mathematical processes. They are invaluable in the classroom because students retain information gained from hands-on-experiences better that information they gain from memorisation. Learning with their hands as well as their minds enhances the learning experience as students explore an abstract concept using a concrete element. Tangrams excite natural curiosity and motivate students to take responsibility for their own learning. Students will become flexible thinkers with a knowledge of mathematics that can be applied to a wide variety of situations and learn to become problem solvers. Adding to Classroom Practice The use of a manipulative such as a tangram creates an extra educational opportunity for all students. This extra dimension facilitates the achievement of more positive educational outcomes for all students as ‘ah ha’ moments can turn negative feelings into positives. Students are able to enjoy mathematics because of its challenging ‘puzzling’ nature. Co-operative skills are also developed as students are able to brainstorm possible solutions with a partner or within a small group and also have productive discussions with an educator. The use of teamwork and verbal sharing adds another dimension to mathematical experience. Tangrams are a valuable tool for students to explore spatial concepts. Learning experiences can be followed by individual reflection or whole class reflection. The combination of practical experience, discussion, questioning and reflection is as asset to all mathematical classrooms. T T a a n n g g r r a a m m s s
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A tangram is an ancient Chinese puzzle consisting of a square cut into five triangles, a square and a parallelogram which can be reassembled into an amazing number of different figures. Each shape in a tangram is called a tan and must be used to solve the puzzle. The tangram shapes must lay flat and not overlap any of the other pieces in the puzzle. Tangrams & Problem Solving
A manipulative is any object that aids in students visualising mathematical processes. They are invaluable in the classroom because students retain information gained from hands-on-experiences better that information they gain from memorisation. Learning with their hands as well as their minds enhances the learning experience as students explore an abstract concept using a concrete element. Tangrams excite natural curiosity and motivate students to take responsibility for their own learning. Students will become flexible thinkers with a knowledge of mathematics that can be applied to a wide variety of situations and learn to become problem solvers.
Adding to Classroom Practice The use of a manipulative such as a tangram creates an extra educational opportunity for all students. This extra dimension facilitates the achievement of more positive educational outcomes for all students as ‘ah ha’ moments can turn negative feelings into positives. Students are able to enjoy mathematics because of its challenging ‘puzzling’ nature. Co-operative skills are also developed as students are able to brainstorm possible solutions with a partner or within a small group and also have productive discussions with an educator. The use of teamwork and verbal sharing adds another dimension to mathematical experience. Tangrams are a valuable tool for students to explore spatial concepts. Learning experiences can be followed by individual reflection or whole class reflection. The combination of practical experience, discussion, questioning and reflection is as asset to all mathematical classrooms.
Allow students time to explore and familiarise themselves with the tangram pieces
Square
Look at the square which is a regular quadrilateral. How many lines of symmetry does it have? Are the opposite sides parallel? How many degrees in all four angles? Are the diagonals equal and bisecting each other at right angles?
Triangle
What type of triangle is it? Are the triangles all the same size?
Parallelogram
Define parallelogram. Does it have lines of symmetry?
Language
Explore mathematical terms such as flip, slide, turn. Ask students to describe how they move the shapes.
Numbers and Letters
Create all of the alphabet letters and the numerals 0-9. Trace an outline of them on a poster or photograph your own alphabet and number chart. Have students create their initials with tangram shapes and display.
Make a Square
Use the 7 tans to make a square.
Congruent and Similar Shapes
Challenge students to use some of their shapes to create a shape congruent to their parallelogram.
Symmetry
Have students create some simple pictures and label them with a dotted line to represent the axis of symmetry. Find all of the axes of symmetry in different shapes.
Angles
Estimate and measure the angles in the various tangram shapes.
Area
Order the pieces from smallest to largest. If the small triangle is a ‘unit’ then how many units are in the square, a parallelogram, the medium triangle and the large triangle?
Fractions
Assemble the pieces to make a square. Which part of the square is made up of: Large right triangles, square, small right angles, medium right angle, parallelogram. Find the fraction of the square that each piece takes up. Convert the fraction into a decimal and/or a percentage.
Toolkits
Once a tangram is made it can be stored in a sandwich bag inside individual toolkits. Consider placing magnetic strips on the back of pieces or purchasing magnetic tangrams so students can use them on small and large whiteboards. Give students a photocopy of various tangram pictures. As they create each picture have them record on the sheet.
Students can solve a tangram each day of the week and record the results in their maths book or a maths journal. Start your lessons off with a competition to see who can create the tangram of the day first. Give students a photocopy of various tangram pictures. As they create each picture have them record on the sheet. This can also be a timed exercise with students trying to beat previous scores.
Tangram Challenge
Individual students can create tangram puzzles to be solved by the class.
Classroom Book
Create a classroom book of tangram puzzles and keep adding to it.
Classroom Quilt
Create a classroom quilt of all the tangrams produced.
Interactives
There are loads of interactive tangram sites. Great for using on the interactive whiteboard or for having students explore on the computer individually.
Power Points
Students can create their own tangram using Microsoft Power Point.
Checkerboard
Make your tangram into a 4 x 4 checkerboard. What can be created?
Stories
Illustrate a story using tangram pictures. Check your library for tangram picture books.
Posters
Have students create posters on some particular theme eg zoo, circus, theatre, sport, animals.
Reduce and Enlarge
Use grids to enlarge and reduce the size of the pieces.
Crayon Art
Create a piece of artwork that records the shapes of tangram creations. Have students carefully hold each piece in place and use crayon to colour across the edges onto the paper. When the pieces are removed the resulting tangram outlines will be displayed.
IInntteerraaccttiivvee TTaannggrraamm WWeebbssiitteess http://www.apples4theteacher.com/tangrams.html Children develop thinking and reasoning skills through the use of the tangram.