Problem Solving with Pattern Blocks
Tasks to Develop Proportional Reasoning and Fraction Understanding
There are 6 kinds of pattern blocks. The yellow, red, blue, and green blocks can be used to make some
shapes in different ways.
1. Most pattern blocks have sides that are 1 inch long. Can you find any sides that have a different
length? If so, write down the other length(s) as a full sentence.
2. Suppose it costs $300 to make a giant Hexagon out of wood. About how much should a giant Triangle
of wood cost?
3. Complete the following table using the relative sizes of the pattern block shapes.
Hexagon Trapezoid Rhombus Triangle
4. If the size of a Green Triangle is , what is the combined size of a hexagon, trapezoid, and triangle?
5. Can you make a design with 6 pattern blocks so that Trapezoids make half of the total area? Draw a
picture to show your answer.
6. The "Dancing Block People" are made out of three kinds of shapes. What percentage of the design is
made up of each shape? Show the steps you use to find the answer.
Reducing Pattern Blocks
The picture below shows that it is sometimes possible to "reduce" pattern blocks by replacing some
blocks with fewer shapes.
1 Trapezoid + 2 Rhombi (3 shapes ) reduces to 1 Hexagon + 1 Triangle (2 shapes)
7. Can you find more ways to reduce pattern blocks? Draw pictures and use words to explain your
reductions. (Hint: there are 6 more ways to reduce pattern blocks.)