Math Geometry worksheets for primary math students, based on the ... - Free Printable

To solve this problem, we need to understand what a translation is in geometry. A translation means sliding a shape from one position to another without turning it or flipping it. The shape stays exactly the same; it just moves to a new spot.

Here is how to complete the patterns for each grid:

Part 1: The Cross Shape (Top Grid)

1. Look at the grey cross in the top grid. It is made of 5 squares.
2. To "complete the pattern," you usually repeat the shape by sliding it over.
3. Let's slide the cross to the right. Count how many dots are between the right edge of the first cross and where the next one should start. In these grids, shapes often repeat every 4 or 5 units. Let's try sliding it 4 dots to the right.
4. Draw an identical grey cross starting 4 dots to the right of the original one.
5. You can also slide it up or down if there is space, but usually, these problems ask for a horizontal or vertical repeat. Looking at the space, you can fit another cross to the right and maybe one below or above depending on the specific rule intended. However, the most standard "pattern" completion is simply repeating the motif.
6. Action: Draw the same grey cross shape again, shifted to the right (and potentially down/left/up if more copies are needed to fill a pattern, but typically one or two repetitions are enough to show the translation). Let's assume we translate it 4 units right and 4 units down to create a repeating tile pattern if space allows, or just 4 units right for a simple row. Given the empty space, drawing one more copy to the right and one more copy below the original creates a nice block pattern.

Let's look closer at the dot spacing. The cross occupies a 3x3 area of dots (with corners missing). If we move it 4 dots to the right, it will sit neatly next to it. If we move it 4 dots down, it will sit neatly below.

Recommendation for Top Grid:
- Copy the grey cross.
- Paste it 4 dots to the right of the original cross.
- Paste another copy 4 dots below the original cross.
- Paste a fourth copy 4 dots right and 4 dots down from the original (diagonally).
This fills the grid with a repeating translated pattern.

Part 2: The Triangle Shape (Bottom Grid)

1. Look at the grey triangle. It is pointing up. Its base is 3 dots wide.
2. We need to slide (translate) this triangle to other positions.
3. Let's slide it to the right. The base is 3 dots wide. To make a neat pattern, we might slide it so the next triangle starts a few dots away. Let's try sliding it 4 dots to the right.
4. Draw an identical triangle 4 dots to the right.
5. Now, let's slide it up. Move the original triangle 3 dots up (or 4, depending on desired spacing). Let's say 3 dots up to keep them close.
6. Action: Draw the same triangle in new positions by sliding it. For example:
- One copy 4 dots to the right.
- One copy 3 dots up.
- One copy 4 dots right and 3 dots up.

Simpler Approach for Student:
Just pick one direction and repeat the shape.
- Top Grid: Draw the same cross shape again, but move it 4 spaces to the right. Then draw another one 4 spaces below the first one.
- Bottom Grid: Draw the same triangle again, but move it 4 spaces to the right. Then draw another one 3 spaces above the first one.

The key is: Do not rotate or flip the shapes. Just slide them like stickers.

Final Answer:
To complete the translation patterns:

For the top grid (Cross):
1. Find the original grey cross.
2. Draw an identical cross 4 dots to the right of the original one.
3. Draw another identical cross 4 dots below the original one.
4. Draw a fourth identical cross 4 dots to the right and 4 dots below the original one.
(This creates a repeating pattern of crosses.)

For the bottom grid (Triangle):
1. Find the original grey triangle.
2. Draw an identical triangle 4 dots to the right of the original one.
3. Draw another identical triangle 3 dots above the original one.
4. Draw a fourth identical triangle 4 dots to the right and 3 dots above the original one.
(This creates a repeating pattern of triangles.)

*Note: The exact number of dots you slide can vary slightly, but the shape must remain upright and unchanged in size. Sliding it 3-4 dots in any direction (up, down, left, right) is correct as long as you don't run off the page.*