Year 4 Maths: Describing Translations

What is a Translation?

Hello, Year 4! Today, we are going to learn about translations in maths. A translation is a way to move a shape from one place to another on a grid without changing its size or shape. Think of it like sliding a piece of paper across a table!

Key Rules of Translations

1. No Rotation or Flipping: When we translate a shape, it stays the same. We do not turn it or flip it over.
2. Direction Matters: We can move shapes up, down, left, or right.
3. Distance Counts: We need to know how far we are moving the shape. We describe translations using two numbers: one for moving left or right (the x-axis) and one for moving up or down (the y-axis).

How to Describe a Translation

When describing a translation, we write it as:

$$

\text{Translation} = (x, y)

$$

• x: how far left or right to move
  • Positive x moves the shape to the right.
  • Negative x moves the shape to the left.
• y: how far up or down to move
  • Positive y moves the shape up.
  • Negative y moves the shape down.

Examples

1. Example 1: A shape is at point (2, 3) and we want to translate it 2 units to the right and 1 unit down.
   • We write this as:
   $$(2, -1)$$
   • So the new point is:
   $$(2 + 2, 3 – 1) = (4, 2)$$
2. Example 2: A shape is at point (1, 1) and we translate it 3 units to the left and 2 units up.
   • We write this as:
   $$(-3, 2)$$
   • So the new point is:
   $$(1 – 3, 1 + 2) = (-2, 3)$$

Tips and Tricks

• Draw It Out: Sometimes, drawing the shapes and the grid helps you see the translation better.
• Use a Coordinate Plane: Remember that the first number tells you about left and right (x-axis), and the second number tells you about up and down (y-axis).
• Start from the Origin: If you are confused, start from the point (0,0) and move from there!

Practice Questions

Easy Questions

1. What is the translation for moving 3 units to the right and 2 units up?
2. If a shape is at (1, 1) and we translate it (0, 2), where does it go?
3. Describe the translation (4, -3).
4. Translate the shape at (2, 2) by (1, 0). Where does it go?
5. Translate the shape at (0, 0) by (-5, 5). Where does it go?
6. What happens if we translate a shape (0, 0) by (0, 0)?
7. If a shape is at (3, 4) and we move it (-3, 2), where does it go?
8. Describe the translation (2, 1).
9. If we have a shape at (5, 5) and we translate it (0, -2), where does it go?
10. What does it mean to translate a shape (2, 0)?

Medium Questions

11. Translate the shape at (4, 3) by (3, 2). What is the new position?
12. A shape is at (1, 1). What is its new position after translating it (-1, -1)?
13. Describe the translation (5, 0) in words.
14. If we start at (2, 2) and move to (2, 5), what translation did we use?
15. What will be the position of a shape at (0, 0) after translating it (7, -3)?
16. If a shape moves from (4, 4) to (0, 1), what is the translation?
17. Translate the shape at (3, 3) by (-1, 4). Where does it go?
18. Describe a translation that moves a shape from (1, 2) to (4, 5).
19. If a point at (2, 3) is translated by (0, -2), what is the new point?
20. What does the translation (-2, -3) mean for a shape at (5, 5)?

Hard Questions

21. A shape is translated from (0, 0) to (3, 4). What is the translation in terms of (x, y)?
22. If we translate a shape at (3, 5) by (4, 0), what will its new coordinates be?
23. A shape moves from (1, 1) to (2, 3). Describe the translation in numeric form.
24. If a shape is translated (2, 5) and ends up at (3, 6), where did it start?
25. Describe the translation from (5, 5) to (0, 0).
26. If a shape at (10, 10) is translated by (-7, -5), what are the new coordinates?
27. A shape at (6, 6) is translated (0, -8). Where does it end up?
28. Find the translation that moves a point from (2, 2) to (7, 3).
29. If a point moves from (0, 0) to (5, 5), can you describe the translation in one sentence?
30. A shape is translated from (-2, -2) to (1, 1). What is the translation in (x, y) form?

Answers

Easy Answers

1. (3, 2)
2. (1, 3)
3. Move right 4 and down 3.
4. (3, 2)
5. (-5, 5)
6. It stays at (0, 0).
7. (0, 6)
8. Move right 2 and up 1.
9. (5, 3)
10. No movement.

Medium Answers

11. (7, 5)
12. (0, 0)
13. Move right 5.
14. (0, 3)
15. (7, -3)
16. (-4, -3)
17. (2, 7)
18. (3, 3)
19. (2, 1)
20. Move left 2 and down 3.

Hard Answers

21. (3, 4)
22. (7, 5)
23. (1, 2)
24. (1, -1)
25. Move left 5 and down 5.
26. (3, 5)
27. (6, -2)
28. (5, 1)
29. Move right 5 and up 5.
30. (3, 3)

I hope this helps you understand translations better! Keep practicing, and you’ll be a pro in no time!