Coordinates: numbers become an address in the plane

Where we are on the map

A second perpendicular number line turns the line into a plane.

Begin with a familiar image

An address states its parts in an agreed order. Coordinates do too: horizontal x first, vertical y second.

Precise meaning

For (x,y), x controls horizontal movement and y controls vertical movement. Aligned points with equal y are separated by the absolute difference of x-values.

The lesson’s support signal

meaning → model → calculation → check → explain in your own words

origin → move along x → move along y → point → distance

Worked example

A(−3,2) and B(4,2) share a height, so their distance is |4−(−3)|=7.

Example with a fading prompt

Change the numbers in the example and repeat the solution without copying its steps. Estimate first, calculate exactly, and check against the original condition.

Recall without a prompt

1. Define the main idea in one sentence.
2. Rebuild the support signal from memory.
3. Solve the example with different numbers and explain why every step is valid.

Find and correct the mistake

Plotting (2,−3) instead of (−3,2) reverses the coordinate order and produces a different point.

Transfer to a new setting

Apply the same relationship to something you can measure yourself. Name the quantities, units, and the boundary within which the model is valid. Check the answer by a second representation or an inverse operation.

Exercise

Required. Plot P(−4,−1), Q(3,−1), and R(3,5); find PQ, QR, and the rectangle’s perimeter.

With your own data. Create one everyday example with the same structure and show it in words, a formula, and a check.

Optional. Seven days later, change the numbers and repeat without the support map.

Open perspective

The coordinate plane becomes the main language of function graphs and geometric models.

Course contents