Pattern Block Geometry Activities 1. Use the pattern blocks to complete the following tasks: How many triangles cover a trapezoid? How many triangles cover a blue rhombus? How many blue rhombi cover a hexagon? How many trapezoids cover a hexagon? How many triangles cover a hexagon? 2. Use the pattern blocks and the above information to answer the following questions. What part of a trapezoid is a triangle? What part of a blue rhombus is a triangle? What part of a hexagon is a blue rhombus? What part of a hexagon is a trapezoid? What part of a hexagon is a triangle? 3. Using pattern blocks, make the shape on the left. Make the same shape beside it using four blocks. By comparing the two shapes, determine how the tan rhombus and the square are related.
The Correct Answer and Explanation is:
Pattern Block Geometry Activities – Answer Key and Explanation
1. Pattern Block Equivalencies (Using Standard Pattern Blocks)
- How many triangles cover a trapezoid?
3 triangles can cover 1 trapezoid. - How many triangles cover a blue rhombus?
2 triangles make up 1 blue rhombus. - How many blue rhombi cover a hexagon?
3 blue rhombi cover 1 hexagon. - How many trapezoids cover a hexagon?
2 trapezoids cover 1 hexagon. - How many triangles cover a hexagon?
6 triangles cover 1 hexagon.
2. Fractional Relationships
- What part of a trapezoid is a triangle?
Since 3 triangles = 1 trapezoid, 1 triangle = 1/3 of a trapezoid. - What part of a blue rhombus is a triangle?
Since 2 triangles = 1 rhombus, 1 triangle = 1/2 of a rhombus. - What part of a hexagon is a blue rhombus?
Since 3 rhombi = 1 hexagon, 1 rhombus = 1/3 of a hexagon. - What part of a hexagon is a trapezoid?
Since 2 trapezoids = 1 hexagon, 1 trapezoid = 1/2 of a hexagon. - What part of a hexagon is a triangle?
Since 6 triangles = 1 hexagon, 1 triangle = 1/6 of a hexagon.
3. Comparing Shapes: Tan Rhombus and Square
When you make a complex shape with multiple pattern blocks, then recreate it using only four blocks, you often find relationships between shapes. For example, if the first shape includes a tan rhombus, and you can replace it with a square and another shape (like a triangle) to make the same total shape, then you can compare their area.
Let’s say you used a tan rhombus in the original and replaced it with 1 square + 1 triangle in the new shape. From this comparison, we determine that:
- A tan rhombus is equal in area to 1 square + 1 triangle, or about 1.5 triangles, if a square equals 1 triangle.
This shows that different shapes can represent equivalent areas when built from pattern blocks, helping students understand geometry and fractions visually and conceptually.
Explanation (300 words)
Pattern blocks are an excellent hands-on tool for learning geometry and fractions. In this activity, we examine how different shapes relate to each other in terms of area and composition.
First, by placing smaller blocks into larger ones, we explore how many equilateral triangles it takes to cover other shapes. For example, it takes 3 triangles to completely fill a trapezoid, 2 for a blue rhombus, and 6 for a regular hexagon. This concrete approach teaches how larger shapes are composed of smaller, repeatable units.
Next, we convert these shape compositions into fractions. For instance, if it takes 3 triangles to form a trapezoid, then each triangle is 1/3 of a trapezoid. This teaches students how fractions describe parts of a whole. Similarly, if a hexagon is made up of 6 triangles, then one triangle represents 1/6 of that hexagon. These comparisons foster a deeper understanding of equivalent fractions, area, and geometry.
Lastly, students explore equivalent shape compositions. By building a shape with different sets of blocks and comparing the two versions, students discover relationships between shapes. If a tan rhombus is replaced by a square and a triangle, it shows an equivalency. This kind of activity supports spatial reasoning and helps learners recognize that shapes can differ in appearance but be equal in area.
Overall, pattern block geometry helps build strong foundational understanding in geometry, fractions, and mathematical reasoning through interactive exploration.
