Describing Movements
Describe movements between positions as translations of a given unit to the left/right and up/down
What a learner can do afterwards
- Describe moving from (2,3) to (5,3) as 3 units to the right
- Translate a shape 4 units right and 2 units up and state the new coordinates
- Predict where a point will be after a given translation
1 · Read
You already know how to read coordinates and slide shapes on a grid. Now you will describe that slide in a clear way: how many units left or right, and how many units up or down.
A point starts at (2, 3) and ends at (5, 3). The y-number stays 3, so the point did not move up or down. The x-number went from 2 to 5, a change of 3. The movement is 3 units to the right.
A shape has a corner at (1, 1). You slide it 4 units right and 2 units up. Add 4 to the x-number: 1 + 4 = 5. Add 2 to the y-number: 1 + 2 = 3. The corner is now at (5, 3).
Right and up add to your numbers. Left and down subtract. Check the x-number for left and right, and the y-number for up and down, one at a time.
A movement on a grid is just adding or subtracting units from the x-number for left and right, and the y-number for up and down.
More to read
Translations intro
A translation slides a shape without turning it or flipping it. Every point of the shape moves the same distance in the same direction. If one corner moves 3 squares right, all the corners move 3 squares right. The shape looks exactly the same, just in a new place. Think of pushing a book across a table without spinning it. To describe a slide, count how far along it went and how far up or down it went. From (2, 3) to (5, 3) is 3 squares to the right, because the first number grew by 3 and the second number stayed the same.
Translating shapes
When you translate a shape on a grid, each corner follows the same rule. Sliding 4 squares right and 2 squares up means adding 4 to every x-coordinate and 2 to every y-coordinate. A corner at (3, 1) lands on (7, 3). Check every corner with the same rule and the whole shape moves as one piece. A quick way to check your work is to pick one corner and test the rule on it first. If that corner lands in the right place, use the same rule for the rest. If a corner lands somewhere odd, recount the squares before moving on.
Translations review
Slides to the right make the x-coordinate grow, and slides to the left make it shrink. Slides up make the y-coordinate grow, and slides down make it shrink. Moving from (2, 3) to (5, 3) changes only the first number, so the slide is flat to the right. Nothing moved up or down. To predict a landing spot, start at the point and count squares step by step. Say the moves out loud as you count, like right 1, right 2, right 3. Landing on the square you predicted shows your rule was correct.
Moving in the plane
Points on a grid can travel in any direction, and each trip has a clear description. Left and right change the first number. Up and down change the second number. A trip of 2 left and 3 down from (4, 5) ends at (2, 2). Both numbers shrink because left and down both count backwards. Before you move a full shape, predict where one special point will land. Write your prediction down, then slide the shape and compare. Matching predictions build confidence that you really understand slides.
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2 · Watch
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Where it sits
Learn first
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.