L4 · Grids in Context: Maps and Games Clinic

Learning goal

“I can model a polygon on a grid by listing its vertices in order, describe the vertices' locations, use coordinates in map and game problems (routes, shortest grid paths, hidden points), and combine everything from this unit without help.”

Polygon — a closed flat shape with straight sides (triangles, rectangles and pentagons are polygons).

Vertex — a corner point of a polygon, located here by its ordered pair (plural: vertices). A polygon is modelled on a grid by listing its vertices in order around the shape.

Route — a path described as a sequence of moves (right, up, left, down) with unit counts, from a start point to an end point.

Legend — the key on a map that tells what each symbol or label stands for; on our grids, the list that matches landmarks to their coordinates.

Worked example

A rectangular garden plot has corners at (2, 2), (8, 2), (8, 5) and (2, 5). Model it and describe it. Step 1: Plot the vertices IN ORDER: (2, 2) bottom-left, (8, 2) bottom-right, (8, 5) top-right, (2, 5) top-left, and join back to the start. Step 2: Read the shape off the numbers: bottom vertices share second number 2 (a horizontal side); top vertices share second number 5; left vertices share first number 2; right vertices share first number 8. Horizontal and vertical sides only - a rectangle. Step 3: Measure from the pairs: width = 8 - 2 = 6 units (across); height = 5 - 2 = 3 units (up). Step 4: Describe any vertex on request: the top-right vertex is (8, 5) - 8 units from the vertical axis and 5 units from the horizontal axis. Say it plainly: a polygon on a grid IS its list of vertices, in order. Everything about it - shape, width, height - can be read straight off that list.

Check yourself — explain it

A polygon is modelled on a grid by…

Paired problem — example still visible

A square plot has vertices (1, 3), (5, 3), (5, 7) and (1, 7). What is its side length? -> 4 units (across: 5 - 1 = 4; up: 7 - 3 = 4 - equal, as a square requires).

Faded completion — last step is yours

"A rectangle's bottom side runs from (3, 2) to (9, 2). Its width is ___ units." -> 6 (9 - 3)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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