BUILD · CHAPTER 1
BUILD — Building the Cartesian Plane
Think first. Use AI purposefully. Verify always.
01 · DISCOVER
Start with a question.
How could a single number line describe a position above it? What would a second, perpendicular number line add?
Make a prediction before exploring. You do not need a rule yet.
02 · UNDERSTAND
Two number lines. One shared origin.
Place two number lines at right angles, with their zero marks together. The horizontal axis gives a left–right reference; the vertical axis gives an up–down reference. Together they provide a frame for the whole plane.
03 · KEY IDEAS
Key Ideas
- The x-axis is horizontal; the y-axis is vertical.
- Their intersection is the origin, named O.
- In the usual orientation, right and up are positive; left and down are negative.
- Use equal intervals for equal units on each axis. Here both axes use the same unit size.
04 · VISUALISE
Explore the idea.
Build the frame
A horizontal number line gives a left–right reference.
05 · METHOD
From understanding to a method.
Draw perpendicular axes, align their zero marks, label x and y, and mark the scale and positive directions.
06 · ONE WORKED EXAMPLE
Follow each step.
Build a plane where one grid interval represents one unit. Locate the origin and show the positive directions.
- Draw the horizontal x-axis.
- Draw the vertical y-axis at right angles to it.
- Label their intersection O; both scales read zero here.
- Mark equal unit intervals. Positive x points right; positive y points up.
07 · AIMS METHOD
Your turn to reason.
Attempt independently. Investigate the information. Make connections with the visual. Scrutinise your reasoning.
Someone labels the horizontal line y and the vertical line x. Does this match the convention used in this module?
Your written reasoning is not automatically graded or sent anywhere.08 · AIMS PRACTICE SPRINT
Vary the situation. Keep the idea.
Work through 10 questions on this concept. Select an answer before checking it; use the feedback to revise your reasoning.
Start practice sprint09 · CHECK & FEEDBACK
Correct answers receive an explanation. Incorrect answers receive a hint and another attempt. This is practice, not an examination.
TEXTBOOK CONNECTION · BUILD
Now connect with your textbook.
Choose one item. Try it independently, then use an AIMS hint or compare the reasoning.
Textbook Guided Example
End-of-Chapter Practice
Original AIMS explanations linked to verified textbook references. Completion remains untracked.