I'll solve this tessellation problem by analyzing each shape to determine if it can tessellate (cover a plane without gaps or overlaps).
Let me start by examining each shape one by one.
First, let's look at the triangle (top left):
- Triangles can always tessellate because any triangle can be arranged with its mirror image to form a parallelogram, which can then tile the plane.
- The worksheet already shows an example of tessellating triangles at the bottom.
Next, the circle (top row, second from left):
- Circles cannot tessellate because they have curved edges and will always leave gaps between them when placed next to each other.
The trapezoid (top row, third from left):
- Trapezoids can tessellate. Any quadrilateral (including trapezoids) can tessellate the plane by rotating it 180 degrees around the midpoint of each side.
The ring/donut shape (top row, fourth from left):
- This shape cannot tessellate because it has a hole in the middle, which creates gaps that cannot be filled by identical shapes.
The rectangle (top row, far right):
- Rectangles can tessellate easily by arranging them in rows and columns.
The arrow shape (second row, far left):
- This arrow shape can tessellate. It appears to be a pentagon that can be arranged with rotations and translations to fill the plane without gaps.
The cross shape (second row, second from left):
- Cross shapes can tessellate. They can be arranged in a grid pattern where the arms of one cross fit into the spaces between adjacent crosses.
The square (second row, third from left):
- Squares can obviously tessellate, as they are one of the most basic tessellating shapes.
The ellipse/oval (second row, fourth from left):
- Ellipses cannot tessellate because, like circles, they have curved edges that will always leave gaps between them.
The downward arrow (second row, far right):
- This arrow shape can tessellate. Similar to the other arrow, it can be arranged with rotations and translations to fill the plane.
Now I'll provide the final answers for each shape:
Triangle: Yes
Circle: No
Trapezoid: Yes
Ring/Donut: No
Rectangle: Yes
Arrow (left): Yes
Cross: Yes
Square: Yes
Ellipse/Oval: No
Downward Arrow: Yes
Parent Tip: Review the logic above to help your child master the concept of tessellation worksheet pdf.
