Answer the following questions. Show your work if needed.
Word Problem: Moving a Ramp
You are building a race track. A ramp starts at point (X=10, Y=0, Z=5). You want to move the whole ramp 5 units to the right. In your game, moving right means the X number gets bigger. What is the new X number for the start of the ramp?
SVG Diagram Needed: A number line representing the X-axis. A ramp icon is positioned at x=10. An arrow indicates movement 5 units to the right, ending at x=15. Labels should clearly mark the initial position (10), the movement (+5), and the final position (15).
(Keywords: number line, addition, coordinates, position, ramp)
Coordinates: Moving a Block
A block in your game is at position X=4, Y=7, Z=2. You move it:
What is its new X, Y, Z position?
SVG Diagram Needed: A simplified 3D coordinate system with X, Y, and Z axes. A block is shown at (4, 7, 2). Arrows indicate the movements: +3 on X, -2 on Y, +5 on Z. The new position (7, 5, 7) is highlighted. Each axis movement should be visually distinct (different color arrows or labels).
(Keywords: 3D coordinates, addition, subtraction, position, block)
Scale: Making a Cube Bigger
A cube has sides that are 2 units long. You want to make it 3 times bigger in all directions (length, width, and height). What will be the new length of each side of the cube?
SVG Diagram Needed: A cube with side length 2 units. A larger cube, scaled up by a factor of 3, is shown next to it with a side length of 6 units. Labels indicate the original side length (2) and the new side length (6). Potentially use different colors for the two cubes.
(Keywords: cube, scale, multiplication, dimensions)
Angles: Opening a Door
A door is closed. It is attached with a hinge. To open it all the way, it needs to turn 90 degrees. The door has already turned 30 degrees. How many more degrees does it need to turn to be open all the way?
SVG Diagram Needed: A diagram of a door with a hinge. An arc indicates the door's rotation. Show the initial 30-degree angle, and then the full 90-degree angle. The 60-degree difference (how much more it needs to open) should be highlighted and labeled.
(Keywords: angle, degrees, rotation, door, hinge, subtraction)
What If: Changing a Platform
You have a flat square platform. Each side of the square is 4 units long. You decide to make each side two times longer.
What is the new length of each side?
SVG Diagram Needed: A square with side length 4. Next to it, a larger square with side length 8. Labels indicate the original and new side lengths. A 'x2' label next to the arrow indicating the scaling would further clarify the doubling.
(Keywords: square, scale, multiplication, length, area)
The area of a square is found by multiplying the side length by itself (side \(\times\) side). What was the area of the platform before you made it bigger?
SVG Diagram Needed: A square with side length 4. The area (16) is visualized by dividing the square into a 4x4 grid. Labels show both the side length (4) and the calculated area (16).
(Keywords: square, area, multiplication, grid)
What is the area of the new, bigger platform?
SVG Diagram Needed: A square with side length 8 (the scaled-up square from 5a). The area (64) is visualized by dividing the square into an 8x8 grid. Labels show both the side length (8) and the calculated area (64).
(Keywords: square, area, multiplication, grid)