Based on the analysis of each shape, here is the solution to the worksheet "Which Shapes Tessellate? Sheet 2".
A shape tessellates if it can cover a flat surface completely without any gaps or overlaps, using only copies of itself.
Here is the evaluation for each of the nine shapes:
1.
Cross Shape (Top Left): This shape tessellates. The arms of the cross can be arranged to fit into the gaps of adjacent crosses, creating a seamless pattern.
2.
Arrow/Chevron Shape (Top Middle): This shape tessellates. By alternating the orientation of the arrows, their points can fit into the notches of neighboring arrows, allowing them to tile the plane.
3.
Rhombus (Top Right): This shape tessellates. All quadrilaterals, including rhombuses, can tessellate by rotating and flipping them to fit together perfectly.
4.
Right-Angled Triangle (Middle Left): This shape tessellates. Any triangle can tessellate. Two identical triangles can be combined to form a parallelogram, which is known to tessellate.
5.
'E' Shape (Middle Middle): This shape does
not tessellate. The concave angles and indentations create gaps that cannot be filled by another 'E' shape when trying to arrange them in a pattern.
6.
Shape with Curved Sides (Middle Right): This shape does
not tessellate. Because it has curved edges, it is impossible to arrange multiple copies to cover a flat surface without leaving gaps or causing overlaps.
7.
Four-Pointed Star (Bottom Left): This shape tessellates. The points of one star can fit into the valleys of surrounding stars, allowing for a complete, gap-free tiling.
8.
Parallelogram (Bottom Middle): This shape tessellates. Parallelograms are one of the simplest shapes to tessellate; they can be slid (translated) along their sides to create a continuous pattern.
9.
Lightning Bolt Shape (Bottom Right): This shape tessellates. Although complex, its jagged edges can be designed to interlock with copies of itself. The "points" of the bolt can fit into the "valleys" of adjacent bolts, creating a repeating, gap-free pattern.
In summary, the shapes that tessellate are:
- The Cross
- The Arrow/Chevron
- The Rhombus
- The Right-Angled Triangle
- The Four-Pointed Star
- The Parallelogram
- The Lightning Bolt
The shapes that do
not tessellate are:
- The 'E' Shape
- The Shape with Curved Sides
Parent Tip: Review the logic above to help your child master the concept of tessellation worksheet pdf.
