Math for - The world I live in (presentation of worlds)

  1. Word Problem: You build a tall tower. It starts at ground level. The ground is $Y=0$. You stack 5 cube blocks. Each block is 3 units high. How high is your tower on the Y-axis?

    3 units3 units3 units3 units3 units15? units

  2. Coordinates: A red ball is at position $X=10, Y=2, Z=5$. You move it 4 units to the left. (Hint: 'left' means the X number gets smaller). What is its new X spot?

    SVG Diagram Needed: A simple 2D coordinate plane (X and Z only - Y is implied as up). Show a point labeled (10, 5) with a red circle, and an arrow showing movement 4 units to the left to a new point (6, 5).

    (Keywords: coordinates, x-axis, z-axis, movement, subtraction)

  3. Area: You have a flat square mat for your game. One side is 10 units long. What is the area of your mat in square units?

    SVG Diagram Needed: A square with each side labeled '10 units'. Inside the square, write 'Area = 100? square units'.

    (Keywords: square, area, multiplication)

  4. Speed and Distance: Your race car toy moves 8 units in 1 second. How far will it travel in 3 seconds if it keeps the same speed?

    SVG Diagram Needed: A number line showing a car moving from 0 to 8 in the first second, 8 to 16 in the second, and 16 to 24 in the third. Each segment should be labeled with '8 units' and '1 second'.

    (Keywords: distance, speed, time, multiplication, number line)

  5. What If (Scale): A game part is a box. It is 2 units wide, 4 units long, and 1 unit high.

    1. What if you want to make it two times taller? What is the new height?

      SVG Diagram Needed: A rectangular prism (3D box) labeled '2 units wide', '4 units long', and '1 unit high'. Next to it, a taller box with the same width and length, but the height is labeled '2? units' with a question mark.

      (Keywords: scaling, height, width, length, multiplication, 3D shape)

    2. Do the width and length change if you only make it taller?

      Static Image/Diagram Needed: Show the original 3D box from the previous visual (5a) and the scaled-up box from the previous visual. Emphasize with color/highlighting that only the height has changed. The question is if the width and length change, so the image needs to make it extremely obvious that they have stayed the same. A set of dimensions for each box would help. Could potentially be enhanced with an animation where the initial box stretches upward. If so, svg_diagram would be preferable.

      (Keywords: scaling, height, width, length, constant dimensions, 3D shapes)