Shapes on a coordinate grid
Draw polygons in all four quadrants of the coordinate plane from given vertex coordinates; find the length of a horizontal or vertical side from the coordinates of its endpoints (which share an x- or a y-coordinate) by subtracting when both endpoints lie on the same side of the axis, and by adding their distances from the axis (absolute values) when the side crosses it; and use these lengths to find perimeters, areas, missing vertices and distances in real-world and mathematical problems such as maps and plans
Lesson
Set out your lesson
“Shapes on a coordinate grid means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Paper shapes or a ruler and pencil
- Shape or angle name cards
Extra for the adult
Worked example. A rectangle has four right angles. Naming the property is the check.
Optional challenge. For Shapes on a coordinate grid, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Shapes on a coordinate grid, not mastery.
Share and support
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Practice this concept
Start practiceShapes on a coordinate grid practice
Practice key ideas from Shapes on a coordinate grid.
Free · no login · no ads · Practice answers and completion are not saved. Parent observation remains the lesson record.
Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
PhET Interactive Simulations · Practice link — not the full lesson
Area Builder
Before you open · source notes
Area Builder supports hands-on exploration for Shapes on a coordinate grid. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
Before you openAsk the learner what they changed in the sim or page and what they observed.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Area Builder.” External page; Gakuva does not copy, host, embed, or redistribute materials.
Unknown — link only
Check understanding
- Plot (−3, 2), (4, 2), (4, −1) and (−3, −1), join them to form a rectangle, and find its side lengths (7 and 3 units), perimeter (20 units) and area (21 square units)
- Explain that (−5, 6) to (−5, 1) is 6 − 1 = 5 units, while (2, −4) to (2, 3) is |−4| + |3| = 7 units because that side crosses the x-axis
- Find how far the library at (−6, 3) is from the park at (2, 3) on a town map where each grid unit is 100 m (800 m)
“If your child plots the corners of a vegetable patch at (−3, 2), (4, 2), (4, −1) and (−3, −1) on a grid where each square is 1 metre, could they draw it and work out how long each side is, even where the patch crosses the axes?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 11–12
Standards