What is a Translation?

Hello Year 4! Today, we’re going to learn about translations in maths. A translation is a way to move shapes around on a grid without changing their size or shape. Imagine sliding a toy car across a smooth floor. The car doesn’t change; it just moves to a new spot!

Key Rules of Translations

  1. Slide, Don’t Change: When you translate a shape, it stays the same size and shape. You’re just moving it to a different location.
  2. Direction Matters: You can move shapes up, down, left, or right. It’s important to remember which way you’re moving your shape.
  3. Count the Squares: Use a grid to help you. Count how many squares you move in each direction.

How to Draw a Translation

  1. Start with a Shape: Draw a shape on a grid. Let’s say we have a triangle.
  2. Decide on the Move: Let’s say we want to move the triangle 3 squares to the right and 2 squares up.
  3. Count the Squares: From the triangle’s starting point, count 3 squares to the right and then 2 squares up.
  4. Draw the New Shape: Mark the new position of the triangle. You’ve just translated it!

Example

  • Original Triangle: Imagine it has points at (2, 3), (3, 5), and (1, 5) on a grid.
  • Translate it 2 squares to the left and 1 square down.
  • New Points:
    • (2 – 2, 3 – 1) = (0, 2)
    • (3 – 2, 5 – 1) = (1, 4)
    • (1 – 2, 5 – 1) = (-1, 4)

The new triangle is at (0, 2), (1, 4), and (-1, 4).

Tips and Tricks

  • Use a Pencil: If you make a mistake, it’s easier to erase and try again!
  • Draw Lightly: Start by lightly sketching your shape so you can adjust it easily.
  • Check Your Work: After translating, double-check that you counted the squares correctly!

Questions

Easy Level Questions

  1. What is a translation?
  2. How many squares do you move a shape in a translation?
  3. If you move a shape 4 squares to the right, what direction is that?
  4. If a square is at (3,3) and you move it 1 square up, where does it go?
  5. Draw a square at (0,0) and translate it 2 squares to the right.
  6. How does a translated shape compare to the original shape?
  7. If you move a triangle 3 squares left, what direction is that?
  8. What happens to the size of the shape when you translate it?
  9. Draw a rectangle and translate it 1 square down.
  10. If a shape starts at (1,1) and moves 2 squares right, where is it now?

Medium Level Questions

  1. Translate a circle from (2,2) to (5,2). What are the new coordinates?
  2. If a triangle is at (4,4) and is moved 3 squares up, where does it go?
  3. Move a rectangle located at (1,1) 2 squares left and 3 squares down. Where is it now?
  4. Draw a shape at (1,3) and translate it 4 squares right and 2 squares up. What are the new coordinates?
  5. If a square at (5,5) is translated 1 square down and 1 square left, what are the new coordinates?
  6. How many squares do you move to translate a shape 2 squares left?
  7. If a shape is at (0,0) and it is translated to (2,3), how far did it move?
  8. What is the new position of a shape at (3,3) after translating it 3 squares down?
  9. Draw a triangle at (2,2) and translate it 2 squares left. What is its new position?
  10. If you have a shape at (1,4) and you move it 3 squares up, where will it be?

Hard Level Questions

  1. Translate a hexagon from (3,3) to (5,7). What movements did you make?
  2. If a parallelogram is at (2,5) and you move it 4 squares to the left and 2 squares down, what are the new coordinates?
  3. Draw a star at (3,3) and translate it 6 squares right and 3 squares down. What are the new coordinates?
  4. If a shape moves from (5,5) to (3,1) through translation, what movements were made?
  5. Translate a triangle from (1,1) to (1,3) and then to (3,3). What are the movements?
  6. If a shape is at (2,2) and is translated 3 squares up and 1 square right, where does it go?
  7. What happens to the coordinates of a shape if it is translated 5 squares left and 2 squares up?
  8. If you translate a shape from (4,4) to (4,2), how many squares did you move and in which direction?
  9. Move a rectangle from (0,0) to (5,5) by making two translations. What could those translations be?
  10. If a shape at (6,6) is translated to (2,2), what are the movements made in each direction?

Answers

Easy Level Answers

  1. A way to move shapes around on a grid without changing them.
  2. You move them in the number of squares you choose.
  3. Right.
  4. (3, 4).
  5. A square at (2,0).
  6. It stays the same size and shape.
  7. Left.
  8. It doesn’t change.
  9. A rectangle at (1,0).
  10. (3,1).

Medium Level Answers

  1. (5,2).
  2. (4,7).
  3. (1,-2).
  4. (5,5).
  5. (4,4).
  6. 2 squares.
  7. 2 squares right and 3 squares up.
  8. (3,3).
  9. (0,2).
  10. (1,7).

Hard Level Answers

  1. 2 squares right and 4 squares up.
  2. (-2,3).
  3. (9,0).
  4. 2 squares left and 4 squares down.
  5. (0,2) and then (2,2).
  6. (3,3).
  7. The x-coordinate decreases and the y-coordinate increases.
  8. 4 squares left and 2 squares down.
  9. Move to (4,0) and then to (5,5).
  10. 4 squares left and 4 squares down.

Great job, Year 4! Now you can practice translating shapes on your own!