How many pattern block triangles would create 5 hexagons?
The Correct Answer and Explanation is :
The correct answer is: 30 pattern block triangles
To find out how many pattern block triangles are needed to create 5 hexagons, we first need to determine how many triangles fit into one hexagon.
A pattern block hexagon can be broken down into six equilateral triangles. You can think of it as dividing the hexagon into smaller sections, with each section being a triangle.
Step-by-Step Breakdown:
- Triangles per Hexagon: One hexagon is composed of 6 triangles.
- Triangles for 5 Hexagons: If one hexagon contains 6 triangles, then 5 hexagons will contain:
[
5 \text{ hexagons} \times 6 \text{ triangles per hexagon} = 30 \text{ triangles}.
]
Thus, 30 pattern block triangles are needed to create 5 hexagons.
Explanation:
Pattern blocks are common tools in education, particularly in math, for exploring geometry and fractions. Each hexagon can be subdivided into smaller shapes, including triangles, parallelograms, and trapezoids. When the hexagon is divided into triangles, it becomes easier to understand its structure. The hexagon is a symmetrical shape with equal-length sides, and each of the six triangles is equilateral, meaning all its sides are equal.
To determine how many triangles are needed for multiple hexagons, you simply multiply the number of triangles in one hexagon (which is 6) by the number of hexagons you’re dealing with. In this case, for 5 hexagons, multiplying 6 by 5 gives 30.
This concept helps students understand not only geometry but also how larger shapes are composed of smaller, simpler units, aiding spatial reasoning skills. It also introduces early multiplication concepts by illustrating how quantities can be scaled up consistently.