# 1 Description

```1 Description
Pattern blocks are a type of mathematical manipulatives, developed in the sixties by the
Elementary Science Studies[1]. They allow children to see how shapes can be
decomposed into other shapes and introduces them to tiling. The standard pattern blocks
are divided into two different sets. In the first set, the shapes can all be built out of the
green equilateral triangle. This set contains:
Equilateral triangle (Green)
Regular rhombus (Blue)
Trapezoid (Red)
Hexagon (Yellow)
The second set contains shapes that can't be built of
the green triangle, but can still be used in tiling patterns
Square (Orange)
Small rhombus (Beige)
Pattern blocks form the basis of a number of mathematical activities in schools.
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Polygons and Problem Solving
Patterns and Tiling (Tessellations) 1
Perimeter
Area
Fractions
Symmetry and Motion Geometry
Pattern Blocks are also available as a virtual manipulative on the web or as learning
objects. They provide further enrichment for a student who is struggling with some of
the abstract concepts in maths and make it more concrete.
2 Purpose
A mathematical manipulative is an object which is designed so that the student can learn
some mathematical concept by manipulating it. The use of manipulatives provides a way
for children to learn concepts in developmentally appropriate, hands-on ways.
Mathematical manipulatives are used in the first step of teaching mathematical concepts,
1
A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also
speak of tessellations of the parts of the plane or of other surfaces.
that of concrete representation. The second and third step are representational and
abstract, respectively.
2.1 TEACHER:
Pattern Blocks by themselves have no inherent meaning. It is important for teachers to
make this meaning explicit and help students build connections between the concrete
materials and the abstract symbols that they represent. This holds true for both concrete
and virtual Pattern Blocks, but virtual Pattern Blocks often have this type of structure built
in. For example, many virtual pattern block activities give students hints and feedback,
something that the more traditional concrete pattern blocks cannot do without teacher
assistance.
Students report that virtual pattern blocks are easy to use and as engaging as concrete
ones. Although virtual pattern blocks provide some support for individual student use, as
with physical pattern blocks, students benefit from teacher guidance to help them use the
manipulative correctly and connect to the underlying math. Most virtual pattern blocks
include activities and suggestions for teachers (and often parents), as well as ideas for
student discussions and sharing. The use of virtual pattern blocks extends the classroom
back into the home and parents become involved in their children’s learning.
Pattern blocks lend themselves to several types of group learning. Think –pair share, in
groups where the students can discover their own information while sharing and
reflecting their own discoveries with each other or the teacher. Pattern blocks help
identify students who are struggling as the teacher is able to visually identify the student.
2.2 STUDENTS:
Pattern blocks help students make concrete, abstract mathematical constructs. There are
five specific areas that students can use pattern blocks to concretize their learning.
• Polygons – This allows students to fill up pre-defined shapes with pattern blocks.
The by walking around the class, they realize that there is more than one solution
to the problem. This trial and error manipulation process introduces the idea that
there may not be one correct solution but many valid solutions.
• Patterns – allow students to create a pattern and then by using flips, slide and
turns propagate that initial pattern into a larger tiling. By using pattern blocks flips,
slides and turns are kinaesthetically learnt and understood.
• Perimeter – as the length of a side of a pattern block is defined as one unit in
length, the student is able to lay pattern blocks along the perimeter of a shape and
then count up the number of blocks. This process then linked with the lengths of
edges of the shape allows student to make a physical connection between the
pattern block and the dimensions of a shape.
• Area – is another concept that lends itself well to making a physical link to the
abstract. Each block has an area of one unit and therefore covering a shape with
pattern block then allows a student to make the connection between the
dimension and the area.
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Symmetry – this is a more advanced use of pattern blocks to relate such concepts
as rotation, line and motional symmetry.
3 Sample Activities
Activity 1:- Calculating Perimeter (Think – Pair – Share)
Let the one edge of a green triangle be one unit of length.
Which pattern block has the
smallest perimeter?
Which pattern block has the
largest perimeter?
Calculate the perimeter of
each pattern block. Use the
edge of the green triangle as
one unit of length.
Green Triangle
Blue Rhombus
Red Trapezoid
Orange Square
Beige Rhombus
Yellow Hexagon
More Discoveries: •
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Explain to another group member how to calculate the perimeter of any of these
polygons
Find out the meaning of a regular polygon?
Which of the figures above are regular polygons?
Activity 2:- Flips and Turns (Think – Pair – Share)
Cover this design
Complete the design above
as a robot. Colour or even
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Make it again so it is standing on its head.
Make it again so that it is lying on its side
Show your partner how it looks when it is flipped upside down
Show your partner how it looks when it is turned on its side
Make a rocket. Flip it. Turn it
Activity 3:- Equivalent Fractions2
Teacher Notes
One of the areas most frustrating for teachers and students alike is the study of fractions,
specifically operations with fractions. Year after year, students learn and forget how to
add, subtract, multiply and divide with fractions. The main reason students have difficulties
with fractions is that they seem to want to memorize formulas or algorithms instead of
understanding them.
Exercise:
Have students work in pairs with the blocks. Have the students discover the relationships
between these 4 blocks:
● How many green blocks are equivalent to a blue block, or a red block, or a yellow
block?
● how many red blocks are equivalent to a yellow block?
● how many blue blocks are equivalent to a yellow block?
● How many green blocks are equivalent to a yellow block?
Teacher Instructions
Have the students cover the form with red blocks.
What fraction of the whole does 1 red block
represent?
Write this fraction down on the overhead, the
blackboard or chart paper for future reference.
Clear the outline. Have them cover the outline with blue
blocks. What fraction of the whole does 1 blue block
represent?
2 blue blocks?
3 blue blocks?
Write these fractions down.
Clear the outline.
Have the students cover the outline with green blocks.
What fraction of the whole does 1 green block
represent?
2 green blocks?
3 green blocks?
4 green blocks?
5 green blocks?
6 green blocks?
Write these fractions down.
2
Time
5 min
(1/2)
(1/3)
(2/3)
(3/3)
(1/6)
(2/6)
(3/6)
(4/6)
(5/6)
(6/6)
Modified by me to fit standard pattern blocks Understanding Fractions (Grades 5 to 8); Diane Hanson, Regina Catholic Schools
Which of these fractions is the same as 1/2? Ask
students to show and explain this using their blocks.
Which of these fractions is the same as 1/3? 2/3? Ask
students to show and explain this using their blocks.
Have students list all fractions smaller (but greater than
0) than 1/2.
Have students list all fractions greater (but smaller than
1) than 1/2
Have students list from smallest to greatest all the
fractions which can be represented by the blocks (up to
1).
4 Black Line Masters
Activity 3:- Equivalent Fractions
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