Math Activity
10.2
10.25
673
MATH ACTIVITY 10.2
Virtual
Manipulatives
Areas of Pattern Blocks Using Different Units
Purpose: Explore areas of pattern block pieces using different units of area.
Materials: Pattern Block Pieces in the Manipulative Kit or Virtual Manipulatives.
*1. Two of the pattern block triangles cover the blue parallelogram. So if the triangle is
the unit of area, then the parallelogram has an area of 2 triangular units.
www.mhhe.com/bbn
a. Use your pattern blocks to find the areas of
the trapezoid and the hexagon if the triangle
is the unit of area.
b. Using the triangle as the unit of area, approxArea of 1
Area of 2
imate the area of the square and the tan paral- triangular unit
triangular units
lelogram. Draw sketches and explain your
reasoning. Will the area of the square be greater or less than 2 triangular units? Will
the area of the tan parallelogram be greater or less than 1 triangular unit?
2. Suppose the pattern block hexagon is the unit of area.
a. What are the areas of the trapezoid, blue parallelogram, and triangle?
b. What are the approximate areas of the square and tan parallelogram? Draw
diagrams to support your conclusions.
Research Statement
The 7th national mathematics
assessment found that students
performed better on questions
that were accompanied by
manipulatives than on items
that asked them to outline
figures on a grid.
Martin and Strutchens 2000
ben19456_ch10.indd 673
Area of 1 hexagonal unit
3. Normally a square is used for the unit of area.
a. Trace a pattern block hexagon on paper, and show that its area is approximately
2_23 times the area of the square.
b. If the square is used as the unit of area and the area of the hexagon is 2_23 times the
area of the square, find the areas of the trapezoid, blue parallelogram, and triangle
in terms of square units.
c. By placing two tan parallelograms and a triangle together as shown below, it can
be shown that the total area of two tan parallelograms equals the area of the square
pattern block. Experiment with the pattern block pieces to find how this can be
illustrated. Explain your reasoning.
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