Explorations with Pattern Blocks
A. Comparing and contrasting the pieces
Have one student in a group choose one pattern block piece to serve
as the Target piece. Each of the other children describes how their
piece is like the Target piece and how it is different. Use their descriptions
as a starting point for the introduction of appropriate vocabulary --
names of the figures, vertices, etc.
Create puzzles whose clues lead to a specific piece, such as the following:
I am thinking of a piece
with more than three sides.
The opposite sides of this piece are parallel.
Opposite angles of this piece are congruent.
There are no right angles.
What piece am I?
B. Finding relationships
among the pieces
Give students some free time to explore and find relationships among
the pieces. These relationships will be used many times in future activities.
C. Problem solving with the blocks
Have students build a figure that you specify (such as a hexagon or
something more elaborate) in as many different ways as possible. What
determines when two figures are different? What is the minimum number
or maximum number of pieces it takes to build the design? Have students
record their results and then display them in an organized fashion --
using a chart or bar graph for example.
Have one student build a figure out of sight of a second student. Then
have the student provide oral directions so that the second student
builds an exact duplicate copy. Use an answering machine analogy when
describing the activity to solve the issue of questions being asked
and answers being given. Depending on the students, place some restrictions
on the number of pieces that can be used in building the design.
In journals, draw a sketch
of a figure using pattern blocks. On another page, write a set of directions
so that someone in your class can build your figure. Have students read
written directions and then check their answers with the "student
generator" of the picture.
Read A Secret Birthday Message. Have students write a set of
directions to their favorite place in school. Be sure to set a specified
II. Number Ideas
A. Multiplication Ideas
Build several copies of a figure. Have the students write sentences
dealing with the number of figures, the number of pieces in each figure,
and the total number of pieces. (For instance, 4 turtles made with 7
pieces each use a total of 28 pieces.) Record the data in a table to
help generate the multiplication table.
B. Values for the pieces and creating number sentences
Use only the yellow, green, blue, and red pieces. Assign a value to
one of these pieces and determine the appropriate values for the other
pieces. Then build a figure with a specified value in as many different
ways as possible. Write the number sentences associated with your figures.
(Later, extend this to problems done without pattern blocks. Have different
groups try to represent different numbers in different ways. Use both
familiar numbers and numbers that will be challenging for your students.)
Build a figure and call it a cake. Assign a total value to your cake.
What should you charge for each piece, where the pieces are the different
pattern blocks that build the cake? (You can choose to have the value
of each piece be an integer or a fraction depending on your choice of
the total value of the cake.)
C. Fraction representation
Use only the yellow, green, blue, and red pieces. Assign the value of
1 to the yellow hexagon. Identify the values of the other pieces.
Adjust the value of 1 -- that is, redefine which piece is equivalent
to 1. Find the values of the other pieces.
D. Problem solving with
Build figures with specified proportions for each color. For instance,
build a hexagon which is 1/2 red, 1/3 blue, and 1/6 green. Make up your
own such problem.
E. Fraction operations
Use only the yellow, green, blue, and red pieces. Determine the arrangement
of pieces that represents 1. Use the pieces to develop ideas related
to equivalence and to changing an improper fraction to a mixed number
and vice versa.
Now consider using the pattern block pieces to develop rules and procedures
for adding and subtracting fractions.
Use the pattern blocks to help give meaning to division of fractions.
For instance, one interpretation for a ÷ b is how many
of b are in a? So, if the yellow hexagon represents 1, then 1/2
÷ 1/6 means how many pieces are in 1/2? Because 3 green triangles
(each with value 1/6) are in the red trapezoid (with value 1/2), then
1/2 ÷ 1/6= 3.
F. Angle Measures
Determine which pieces have the same angles. Use the white rhombus together
with the square to determine the measure of one of the angles in the
white rhombus. Use this relationship to find the measures of the angles
of the other pieces. Make a conjecture: what seems to be the sum of
the angle measures of any quadrilateral? How could you prove this?
Use these pieces, particularly the white rhombus, to measure the angles
of other objects around the room. You will often need to give an estimate
or an interval in which the true measure lies.
G. Factors, prime numbers, and composite numbers
Use only the orange pieces. Take a group of the squares. Determine how
many different rectangles you can make. Record the dimensions. Try the
same process for a different number of squares. Combine results from
all the members of the class. Use the results to introduce the terms
factor, prime, and composite.
Reinforce these numbers with the Opening the Gate activity (a Florida
project for building algebraic thinking), entitled Step Forward and
Take a Bow. Give each student a number. Have them line themselves
up in numerical order. Generate a series of number descriptions. If
your number specifies the condition, you must step forward and take
a bow. For instance, if your number is a factor of 12, step forward
and take a bow.
H. Odd and even
Use only the orange squares. Take several different numbers of squares.
Can you make a rectangle with the squares? For which numbers can you
make rectangles? For which can you not make a rectangle? How does this
idea help you with even and odd?
III. Transformations and
A. Creating Flips
Draw a line and use the pattern blocks to build a figure on one side
of the line. Build what you think will be its image after being flipped
over the line. Check your work with a MIRA or a mirror. You could also
check your work by tracing around the blocks in your original figure
and its image and then folding the paper along the reflection line to
determine if the two tracings match up. Are the figures congruent? Why
or why not?
B. Lines of symmetry
Build a figure with a line of symmetry. Check your result using one
of the strategies in A.
Determine the number of lines of symmetry for each of the pattern block
pieces. Build a figure with a line of symmetry. Check your result using
one of the strategies in A. Build figures with more than one line of
C. Turning symmetry
Build a figure with turning symmetry. Trace your figure on paper. Use
your tracing together with the built figure to verify that your creation
has turning symmetry.
Build a figure with turning or rotation symmetry. Determine the number
of degrees necessary to have turning symmetry. Trace your figure on
paper. Use your tracing together with the built figure to verify that
your creation has turning symmetry.
D. Similar figures
Build two figures that are similar. How do you know that they are similar?
IV. Area and perimeter ideas
A. Find perimeters
Identify a unit to serve as the unit of length. Build figures and determine
B. Find areas
Identify a unit to serve as the unit of area. Build figures and determine
C. Relationships between area and perimeter
Build two or more figures with the same area but different perimeters.
Justify your answer.
Build two figures with the same perimeter but different areas. Justify
Compare the perimeters and areas of figures that are similar. What conjectures
can you make about the ratio of the perimeters or the ratio of the areas
of similar figures?
V. Algebraic Ideas
Build a pattern with the blocks. Have students duplicate and then extend
the pattern. Have students design their own patterns. Which ones have
the same structure? How could you describe that structure?
B. Marshalls and non-Marshalls
Create at least three examples of some category of figure called a Marshall
(or whatever crazy name you choose.) Create three non-examples. Give
students other figures and have them determine which satisfy the requirements
and which do not. Have students then create their own categories.
C. Problem solving with patterns
Suppose you put 100 squares in a row. What would be the perimeter? What
would be the area? Suppose you had n squares. Now find the perimeter
and the area.
Build some other figure in a logical manner that can be extended. Determine
how many pieces would be used in 2, 3, or 4 copies of the figure or
in 2, 3, or 4 extensions of the pattern. How many pieces would be used
in n copies of the figure or n extensions?
Have students select a handful of blocks and then create graphs that
illustrate the number of blocks of each type selected. What questions
can you ask about your graph? Compare your graph to that of another
student. What questions can you ask when you use both graphs?
A. Tessellations and tiling
Read A Cloak for the Dreamer. Have students create cloak patterns.
Read Sam Johnson and the Blue Ribbon Quilt. Have students use
the blocks to create quilt patterns.
How many figures can you make using just 1 square, 2 squares, 3 squares,
and 4 squares? What about 5 squares (pentominoes)?
Charles, Linda Holden and Micaelia Randolph Brummett. Connections:
Linking Mathematics with Manipulatives. Sunnyvale, CA: Creative Publications,
Marilyn Burns Manipulative Videos (Pattern Blocks)
Learning with Pattern Blocks by Cuisenaire