Tessellation worksheet for students to identify which shapes can create a pattern without gaps or overlaps.

To determine which shapes can tessellate, I need to check if each shape can cover a flat surface completely without any gaps or overlaps.

Let me work through each shape:

a. Parallelogram - Parallelograms can tessellate because they fit together perfectly when placed side by side and stacked. The angles add up to 360° at meeting points. → yes

b. Circle - Circles cannot tessellate because there will always be gaps between them when placed next to each other. → no

c. Star (5-pointed) - A regular 5-pointed star cannot tessellate on its own because the angles don't allow them to fit together without gaps. → no

d. Hourglass/bowtie shape - This shape (two triangles meeting at a point) can tessellate. When you flip and rotate copies, they fit together perfectly. → yes

e. Arrow/chevron shape - This irregular hexagon-like shape with an arrow end can tessellate. The indentations and protrusions fit together like puzzle pieces. → yes

f. Rounded rectangle - Rounded rectangles cannot tessellate because the curved corners create gaps between shapes. → no

g. Lightning bolt/zigzag - This zigzag shape can tessellate because the indentations of one piece fit into the protrusions of another. → yes

h. U-shape/cup shape - This shape with a curved bottom cannot tessellate properly due to the curved edge creating gaps. → no

i. T-shape - T-shapes can tessellate. They fit together in interlocking patterns where the stem of one T fits into the gap between the arms of others. → yes

Final Answer:
a. yes
b. no
c. no
d. yes
e. yes
f. no
g. yes
h. no
i. yes