Plotting points in the first quadrant

What it looks like when your child can do it

• — Given (5, 2), your child puts a finger on the corner, slides 5 along the bottom, then 2 up, and marks the point.
• — Shown a dot on a grid, your child reads its pair back with the across number first, like (2, 6).
• — Your child can show where (0, 4) and (4, 0) sit and say why they are different spots.

How to teach it at the kitchen table

1. 01

   Draw the grid together

   On graph paper, draw a line along the bottom and a line up the left side, meeting at a corner. Number both from 0 to 10 on the grid lines, not in the spaces. The bottom line is the x-axis, the side line is the y-axis, and the corner is (0, 0).

2. 02

   Across first, then up

   An ordered pair is written (x, y). The first number says how far across the bottom. The second says how far up. A saying helps: walk across the hall before you climb the stairs.

3. 03

   Plot with a finger, then a pencil

   For (3, 4), your child puts a finger on (0, 0), slides right 3, then up 4, and marks a dot where two grid lines cross. Say the moves out loud: across 3, up 4.

4. 04

   Swap the numbers on purpose

   Plot (3, 4) and (4, 3) on the same grid. They land in different spots. Seeing the two dots apart shows why the order in an ordered pair matters.

5. 05

   Read points back

   Now you draw a few dots and your child writes each pair. Reading a point back is the reverse move, and it catches a child who has been guessing.

You will need: Graph paper · A pencil and a ruler · Colored pencils to tell points apart

Try it together

1. Try 1

   Ask your child to plot the point (6, 2).

   Listen for  The dot sits 6 across and 2 up. A dot at 2 across and 6 up means the numbers were swapped, which is the mistake to watch for.

2. Try 2

   Draw a dot at 1 across and 5 up. Ask your child to write its ordered pair.

   Listen for  (1, 5). The across number is written first. If your child writes (5, 1), have them trace the path from the corner with a finger.

3. Try 3

   Ask your child to plot (4, 0) and (0, 4) and say where each one sits.

   Listen for  (4, 0) sits on the bottom line, 4 across and not up at all. (0, 4) sits on the side line, 4 up. Zeros are where the order most often gets mixed up.

4. Try 4

   A bean plant grows 2 cm each week. Make a table: week 0, 0 cm; week 1, 2 cm; week 2, 4 cm; week 3, 6 cm. Plot each row as a point, weeks first.

   Listen for  (0, 0), (1, 2), (2, 4) and (3, 6). The four dots fall in a straight line rising to the right. A dot off that line is usually a pair written backwards.

5. Try 5

   Plot (2, 1), (6, 1), (6, 4) and (2, 4), then join them in that order and back to the first. What shape is it, and how many squares across and up?

   Listen for  A rectangle 4 squares across and 3 squares up, because 6 - 2 = 4 and 4 - 1 = 3. If the sides cross, a point was plotted in the wrong place.

Watch for

• — Swapping x and y. (3, 4) plotted as 3 up and 4 across lands in the wrong spot. Say across first, up second, every time.
• — Numbering the spaces instead of the lines. The numbers go on the grid lines, and a dot goes where two lines cross, not in the middle of a square.

If it is not there yet

• — Play a hide-and-find game on a small grid numbered 0 to 5. You hide a dot on your own paper and your child calls out pairs until they find it. Keep the grid small until across-then-up is automatic.
• — Go back to a single number line and find numbers like 3 and 7 on it before putting two lines together.
• — Write across under the bottom line and up beside the side line, and leave those labels on the page for a week.

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 12

  Four Quadrants

  Needs it because the child already plots (3, 4); the new part is the signs.

• Grade 6 Math Practice Workbook · Lesson 24

  Two Quantities That Change Together

  Needs it because the pairs from the table are plotted.