Skills / Ages 11 to 14 / Math
Plotting in four quadrants
Plotting points like (-2, 5) on a grid that runs both ways from zero. A negative first number goes left, a negative second number goes down, and the signs tell you which of the four quadrants the point is in.
Why it matters
The workbook turns a town map into points and finds distances between them, then draws a cabin outline from corners like (-3, 2) and (5, -4). If your child puts a negative point in the wrong place, every length and area on those pages comes out wrong.
What it looks like when your child can do it
- Given (-4, 1), your child goes left 4 from the center and up 1, and lands in the upper left.
- Your child names the quadrant of (2, -6) as IV from its signs alone, before plotting it.
- Given four corners, your child plots them, joins them in order, and gets a closed shape with no crossed sides.
How to teach it at the kitchen table
- 01
Extend the grid past zero
On graph paper, draw the across line and the up line through the middle of the page, crossing at (0, 0). Number both from -6 to 6. Right and up are positive. Left and down are negative.
- 02
Keep the same order
Nothing about the order changes. The first number is still across and the second is still up or down. A minus sign on the first number means go left. A minus sign on the second means go down.
- 03
Name the four quadrants
The two lines cut the page into four quadrants, numbered I, II, III and IV, starting at the top right and going counterclockwise. Quadrant I is (+, +), II is (-, +), III is (-, -) and IV is (+, -).
- 04
Read the signs before plotting
Before your child plots a point, ask which quadrant it should land in, from its signs. Then plot it and see whether the dot agrees. This one habit catches most slips.
- 05
Draw a street map
Put your house at (0, 0) on a sketch of your street, with east to the right and north up. A friend's house 3 blocks west and 2 blocks south is (-3, -2). A map gives every sign a direction your child can picture.
You will need: Graph paper · A pencil and a ruler · A sketch of your own street drawn on graph paper
Try it together
Try 1
Ask your child to plot (-2, 5) and name its quadrant.
Listen for Left 2, up 5, in Quadrant II. Watch that the minus sign on the first number sends your child left, not down.
Try 2
Ask your child to plot (6, -4) and (-6, 4). Are they the same point?
Listen for No. (6, -4) is right 6 and down 4, in Quadrant IV. (-6, 4) is left 6 and up 4, in Quadrant II. Moving the minus sign moves the point to a different quadrant.
Try 3
Without plotting, ask your child to name the quadrant for (-5, -1), (3, 7) and (-6, 0).
Listen for (-5, -1) is in Quadrant III and (3, 7) is in Quadrant I. (-6, 0) sits on the across line, 6 to the left of the center, so it is in no quadrant at all. The zero is the one to watch.
Try 4
Your house is (0, 0). The store is 5 blocks east and 3 blocks south. The library is 2 blocks west and 4 blocks north. Ask your child to write both as ordered pairs.
Listen for The store is (5, -3) and the library is (-2, 4). East and north are positive, west and south are negative, and the east or west move is always written first.
Try 5
Ask your child to plot (-2, 3), (5, 3), (5, -1) and (-2, -1), join them in order and back to the first, and say how wide and how tall the rectangle is.
Listen for 7 squares wide and 4 squares tall. From -2 across to 5 is 2 + 5 = 7, and from -1 up to 3 is 1 + 3 = 4. Counting the squares on the grid is a good check.
Watch for
- Swapping x and y. (-2, 5) plotted as left 5 and up 2 is a different point. Across first, every time.
- Losing the minus sign and going the wrong way. Have your child say the direction, left or down, before moving a finger.
If it is not there yet
- Back up to the first quadrant alone, plotting pairs like (3, 4), until across-then-up is automatic. Then open up the left half of the grid, and add the bottom half after that.
- Practice on a single number line that runs both ways. Find -4 and 3 on one line before putting two lines together.
A few days of this is normal, and it is time well spent. The lesson will still be there, and it will go faster.
Where this skill comes up
Grade 6 Math Practice Workbook · Lesson 15
Points, Distances, and a Map Grid
Needs it because the problem is built from plotted points.
Grade 6 Math Practice Workbook · Lesson 27
Drawing a Polygon on a Grid
Needs it because the vertices may be anywhere on the grid.