Orienting Yourself: The Use of Coordinates: common misconceptions

If your child says… “One number tells you exactly where I am.”

Ask together

Could another point be higher while staying two squares right?

What’s true

Several positions can share the same horizontal coordinate.

If your child says… “The zero always comes second on an axis.”

Ask together

Directly above O, how far right or left have you gone?

What’s true

The zero’s position tells us which axis contains the point.

If your child says… “A negative first number always means Quadrant III.”

Ask together

Which two quadrants lie left of the y-axis?

What’s true

Negative x allows Quadrants II and III, or the x-axis when y is zero.

If your child says… “The distance is minus three centimetres.”

Ask together

Does the ruler measure a negative length?

What’s true

The sign shows direction; the distance measures a nonnegative length.

If your child says… “The numbers are unchanged, so it is the same point.”

Ask together

Does moving left and up take you where moving right and down does?

What’s true

Exchanging unequal coordinates changes the position.

If your child says… “Both second coordinates are one, so the length is zero.”

Ask together

Do these endpoints overlap, or is there a gap?

What’s true

Equal second coordinates mean no vertical change, but the horizontal gap remains.

If your child says… “Three across and four up means seven units straight.”

Ask together

Does the straight segment follow both shorter sides?

What’s true

Adding across and up measures the bent route along the shorter sides.

If your child says… “Both signs change in a reflection.”

Ask together

Does folding along a vertical line change a corner’s height?

What’s true

Across the y-axis, heights stay unchanged while horizontal positions reverse.