Pattern Designer Rima went to a park and saw many beautiful patterns on the pathway tiles. Some tiles looked the same on both sides (symmetrical), while others did not (asymmetrical). Look at the patterns below. Tick ( $\checkmark$ ) the patterns that are symmetrical and cross ( $\times$ ) the ones that are asymmetrical. - Tile 1: A grid of rectangular shapes arranged horizontally with rows of circles between them. - Tile 2: A square grid pattern formed by square outlines and a central motif with concentric-like square blocks. - Tile 3: A square grid containing alternating circles and square shapes arranged in rows and columns. - Tile 4: A repeating pattern made of triangles (upright and inverted) and rectangles. - Tile 5: A pattern made of sun-like shapes with triangular rays and smaller star-like patterns. [Each tile has an empty checkbox beneath it to indicate symmetrical ( $\checkmark$ ) or asymmetrical ( $\times$ ).] --- Look at each tile pattern carefully. Identify the 2D shapes you can see and complete the table. | Tile | Tile 1 | Tile 2 | Tile 3 | Tile 4 | Tile 5 | | :--- | :--- | :--- | :--- | :--- | :--- | | Name of the shapes used | | | | | | | Drawing of the shapes | | | | | | --- Draw your own tile pattern using any 2D shapes. You can use more than two shapes. [A blank rectangular box is provided for drawing.] --- Let's Discuss and Write Compare your tile pattern with your friends' patterns and share your experience. * Which friend's design do you like the most? \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ * What do you like in his/her design? \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Answer: Symmetry Check: Tile 1: $\checkmark$ (Symmetrical) Tile 2: $\checkmark$ (Symmetrical) Tile 3: $\checkmark$ (Symmetrical) Tile 4: $\checkmark$ (Symmetrical) Tile 5: $\checkmark$ (Symmetrical) 2D Shapes Used: - Tile 1: Rectangle, Circle - Tile 2: Square, Rectangle - Tile 3: Square, Circle - Tile 4: Triangle, Rectangle - Tile 5: Circle, Triangle (Star/Sun motifs)

Step-by-step solution

Step 1: Analyze Symmetry of Each Tile

A shape or pattern is symmetrical if a line of symmetry divides it into two identical halves that mirror each other. Examining the patterns: Tile 1 has vertical and horizontal mirror symmetry; Tile 2 has 4-fold reflective symmetry across vertical, horizontal, and diagonal axes; Tile 3 has reflective lines across both centers and diagonals; Tile 4 has repeating alternating triangles and rectangles creating vertical mirror symmetry lines; Tile 5 has radiating rotational and bilateral reflection symmetries across its axes. Therefore, all five patterns are symmetrical and receive a tick mark ( $\checkmark$ ).

Step 2: Identify 2D Shapes in Tiles 1 to 3

In Tile 1, we observe horizontal bars, which are rectangles, along with full circular dots, which are circles. In Tile 2, the grid and inner concentric blocks are formed using squares and rectangular framing outlines. In Tile 3, the alternating grid elements consist of squares and circles.

Step 3: Identify 2D Shapes in Tiles 4 and 5

Tile 4 features rows of 3-sided polygons (triangles), both upright and inverted, alongside rectangular spacers. Tile 5 consists of circular centers with triangular points acting as sun rays and radiating stars.

Solve your own maths question free →