IV GEOMETRY
1 Similar Shapes 2 Symmetry and Origami 3 Cutting and Overlapping 4 Figure Puzzles
GEOMETRY
A
B
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1. Similar Shapes B
Find the Similar Shapes
If two shapes canAoverlap completely, they are the same shape.
A A
C A
B AB A
B B
C C
A and C overlap completely. A and C are the same shape. When A and B are placed on top of each other, they do not overlap completely. A and B are not the same shape.
Exercise
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C AC the same shape as the given shape in the box. Find and circle A
Creative and Critical Thinking Skills 1A Elementary
Find the Cut-out Shape The shape that is cut out should fill the cut form completely.
The shape that is cut out is the same as the shape that is formed on the cut paper.
Exercise Circle all the shapes that are made when the shapes are cut out.
Geometry
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Type Study
Find the Similar Shape Draw the same shape as the one on the left on the given dot board.
Geoboard The Geoboard shown on the right is an interesting tool to use for studying Geometry. It is a grid made with sticks nailed into a wooden or plastic board. Rubber bands are used to make shapes by hooking the bands around the sticks. Dot boards and grids are used in the same way with paper and pencil.
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Creative and Critical Thinking Skills 1A Elementary
Problem solving
1
Draw the same shape as the one on the left on the given grid.
Tip Look at where the lines meet and place points on the grid to connect them.
2
Circle the two shapes that are the same.
Tip Compare the placement of the circles.
Geometry
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Type Study
Find the Cut-out Shape The blanket with a hole needs to be patched. Find the best piece to patch the hole.
A
B
C
D
Developing Shape Recognition The development of shape recognition in children occurs in the following stages. • Before the age of four: shapes with a similar form like below cannot be differentiated.
• After the age of four: when comparing two or more shapes, children will gradually focus on the differences. Common distinctions in shapes include the number of sides, the number of corners, lines of symmetry, length of sides, size of angles, and parallel and perpendicular sides.
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Creative and Critical Thinking Skills 1A Elementary
Problem solving
1
Find the part that is cut out from the picture on the left.
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Tip Draw the missing portions in the hole.
2
Look at the shape seen in the magnifying glass and find the original shape.
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Tip Two lines cross at a point and one of the lines meets another line below the point.
Geometry
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2. Symmetry and Origami Symmetrical Shapes With some watercolours, is used to paint a shape on one side of a piece of paper. When the paper is folded in half, both halves will have the same drawing. Fold
Unfold
Unfolded paper
The dotted line* divides the paper into equal halves. *called the line of symmetry
Exercise Draw the shape made when a paper with a watercolour drawing is folded
Cut in half and then unfolded.
Unfold
â‘´ Unfolded paper
â‘ľ
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Creative and Critical Thinking Skills 1A Elementary
Unfold
Fold
Unfolded paper
Fold and Cut Origami The shapes on two sides of a fold are the same when the piece of paper is folded, cut along the line, and unfolded. Cut
Unfold
Unfolded paper
Exercise Which shape will be made when the origami paper is folded in half and
cut along the line as shown below?
A
B
C
D
Geometry
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Type Study
Symmetrical Shapes Circle all the shapes that, when folded along the dotted lines, the two equal halves will fit exactly.
Decalcomania Paintings that are created by painting something on one side of a paper and folding it in half to stamp the other side are called decalcomanias. Oscar Dominguez painted decalcomanias. They were first used on ceramics or glass crafts. Now they are used in art and psychotherapy as well as to teach symmetry in mathematics.
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Decalcomania
Creative and Critical Thinking Skills 1A Elementary
Used as a tool in psychotherapy
Problem solving
1
Complete each shape below with the dotted line as the line of symmetry.
2
Draw a line so that the two equal halves of each picture fit exactly when folded along the line.
Geometry
107
Type Study
Fold and Cut Origami The following diagram shows the unfolded shapes after the piece of paper is folded in half and the drawn shapes cut out. Circle the correct shapes.
Spatial Awareness and Cutting Origami Spatial awareness is the process of turning, flipping, and moving plane figures and the ability to imagine three dimensional figures. Spatial awareness is developed with experience, which can be gained by participating in activities such as paper folding, stacking bricks, assembling blocks, etc. Imagination can especially be developed in cutting origami as the students must first imagine a shape and then confirm what they had imagined by actually cutting and unfolding.
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Creative and Critical Thinking Skills 1A Elementary
Problem solving
1
Match the correct shapes to how they would look like when unfolded.
Tip Draw the same shape to the left of the folded papers.
2
A piece of paper was folded, cut, and then unfolded to make the shape on the right. On the folded paper to the left, draw the shape that was cut out.
Tip The unfolded figure has the same shape on the left and right sides of the folding line.
Geometry
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3. Cutting and Overlapping Cutting Shapes If a shape is cut along the lines as shown, it is divided into different pieces.
When the cut pieces are put together correctly, the original shape can be formed again.
Exercise Find the pieces that are made when the piece of paper is cut along the
lines as shown.
D
B A
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Creative and Critical Thinking Skills 1A Elementary
C
Overlapping Shapes When shapes drawn on transparencies are overlapped, the shapes in the same location overlap to look like one shape and shapes in different locations look like separate shapes.
Exercise Draw the shape that will be formed when the two transparencies are
overlapped.
Geometry
111
Type Study
Cutting Shapes Circle the pieces that are needed to make the shape on the right.
12-piece Puzzle Each person should have three pieces of origami paper of the same colour. Cut each piece of paper into four pieces to make a total of 12 pieces. Mix the 12 pieces and exchange with a partner to play the 12-piece puzzle game. Students will cut, move and match shapes to build their geometric sense while having fun and creating their own puzzles. When piecing the puzzle together, it is actually easier with more complex pieces. Piecing together simpler shapes like triangles or quadrilaterals is more difficult. Have students cut simple shapes and move, rotate and flip to piece together each puzzle.
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Creative and Critical Thinking Skills 1A Elementary
Problem solving
1
The shape on the left is cut into pieces shown on the right. Draw the lines where the shape was cut and circle the pieces that are made.
Tip First, find the pieces on the right that can be used to make the shape on the left.
Geometry
113
Type Study
Overlapping Shapes The following two shapes are drawn on transparencies. Which shape is made when the two transparencies overlap?
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Names of Figures If the exact name of a figure or shape is unknown, use a common name instead. For example, a square may be called a “box”. If students know the actual names and characteristics and can use the language naturally, then have them use the vocabulary that they know.
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Creative and Critical Thinking Skills 1A Elementary
Problem solving
1
Find the two transparencies that overlap to make the pattern in the box.
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Tip Think about the transparencies on top of a blank paper.
2
Draw the shape that results when the two transparencies below are overlapped.
Tip Coloured portions are still coloured when the transparencies are overlapped.
Geometry
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4. Figure Puzzles Pattern Blocks The following six blocks are pattern blocks.
Fun figures can be made using pattern blocks.
Sailboat
House House
Exercise Use the given pattern blocks to colour each figure.
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Creative and Critical Thinking Skills 1A Elementary
Sailboat
Tangram A square cut into seven pieces as shown below, is called a tangram.
Fun figures can be made using tangrams.
Crow
Cat
Exercise Two triangles are used to make a bigger triangle and a square. Draw a
line to show how they areCrow pieced together.
Cat
Geometry
117
Type Study
Pattern Blocks Choose one of the following pattern blocks to fill the rest of the figure.
Pattern Blocks Pattern blocks were developed in the 1960s by the Elementary Science Studies. Pattern blocks are widely used in activities at schools. These manipulatives can be used to study shapes, learn about patterns, and play strategy games.
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Creative and Critical Thinking Skills 1A Elementary
Problem solving
1
Use two different pattern blocks from the box below to make the shape on the right.
Tip First, find the biggest pattern block to fill the given shape.
2
The rabbit shape on the right is made using six pattern blocks. Circle two shapes from the pattern blocks in the box that must be used.
Tip Look at the rabbit’s ears and tail.
Geometry
119
Type Study
Tangram Use the coloured tangrams to form the shapes on the right.
Tangram Tangram is a dissection puzzle that originated in China. It was widely used and is still a popular puzzle. The seven pieces are used to form specific shapes without overlapping.
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Creative and Critical Thinking Skills 1A Elementary
Problem solving
1
All seven tangram pieces are used to make a dolphin. Number the pieces used.
Tip Think about how the pieces change when they are rotated or flipped.
2
All seven tangram pieces are used to make a tiger. Draw lines and number the pieces 2, 3 and 6 to show how the remaining shape is made.
Tip First, find where the largest piece, â‘Ľ, is used.
Geometry
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Boost Your Creativity
01
Find and colour the shapes that are similar to the two shapes given in the box.
Find similar shapes by comparing the lengths, widths, and angles.
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Creative and Critical Thinking Skills 1A Elementary
02
Julie took six pattern blocks and placed them on top of each other. Write the order (1, 2, 3, 4, 5, 6) of the pattern blocks arranged from bottom to top.
Geometry
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Challenge Yourself
01
Two shapes are drawn on transparencies as shown in the box. Find the shape that cannot be made by turning and overlapping the given transparencies.
A
B
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F
A different shape is formed when the transparencies are turned and overlapped!
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Creative and Critical Thinking Skills 1A Elementary
02
This is a bird that Carl and his friends made using the pattern blocks shown in the box. Who is lying?
I used I14 I used used blocks. 14 blocks. 14 blocks.
Carl
I can make it IIusing can it can make make it 5 blocks. using 5 blocks. using 5 blocks.
Sue
Wow! I used Wow! II used Wow! used 6 blocks to 66 blocks to blocks to make it. make make it. it.
Mary
Geometry
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