Coordinates, translations and polygons
Reading first-quadrant coordinates, describing translations and plotting points to complete polygons
About four lessons of 45 to 60 minutes
A coordinate is an exact address
A map reference such as B4 narrows a search to one square. Coordinates are even more precise: the ordered pair (3, 5) identifies one exact point by moving across 3, then up 5.
Once every vertex has an address, a shape can be moved without turning or resizing it. Add the same translation to every vertex and the whole polygon slides across the grid.
- A point at (3, 5)move across the x-axis first, then up the y-axis
- Translate 4 right and 2 upadd 4 to every x-coordinate and 2 to every y-coordinate
- Three plotted verticesjoin the specified points with straight sides to form a polygon
What students will be able to do
Pupils will read and plot ordered pairs in the first quadrant, describe and calculate horizontal and vertical translations, and plot and join vertices to complete polygons.
- I can read a coordinate by moving across first and then up.
- I can plot a point accurately in the first quadrant.
- I can describe a translation in horizontal and vertical units.
- I can apply the same translation to every vertex.
- I can plot and join points in order to complete a polygon.
Standards this unit teaches
- uk-ks2-y4-ma-gpd-01UK National Curriculum (England)First-quadrant coordinates
Describe positions on a 2-D grid as coordinates in the first quadrant.
- uk-ks2-y4-ma-gpd-02UK National Curriculum (England)Translations
Describe movements between positions as translations of a given unit to the left or right and up or down.
- uk-ks2-y4-ma-gpd-03UK National Curriculum (England)Plot points and complete polygons
Plot specified points and draw sides to complete a given polygon.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
- Coordinate
- an ordered pair that gives the exact position of a point
- x-coordinate
- the first number, showing how far to move across
- y-coordinate
- the second number, showing how far to move up
- Origin
- the point (0, 0) where the two axes meet
- Translation
- a slide that does not turn or resize a shape
- Vertex
- a corner point where two sides of a polygon meet
Teach it: concrete, pictorial, abstract
The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.
1. Read coordinates across, then up
PictorialStart at the origin. Follow the x-axis across to the first number, then move parallel to the y-axis up to the second number. Say the instruction while pointing: across 3, up 5, so (3, 5).
- Which coordinate is read first?
- How are (2, 6) and (6, 2) different?
2. Plot points at grid-line intersections
PictorialCoordinates name points, not grid squares. Mark a small, precise cross where the vertical x-line and horizontal y-line intersect, then label it with its ordered pair.
Plot A(4, 2).
- Begin at the origin.
- Move 4 units across along the x-axis.
- Move 2 units up, parallel to the y-axis.
- Mark and label the intersection A(4, 2).
Answer: A is plotted at the intersection x = 4, y = 2.
- Should the mark fill a square or identify an intersection?
- What label proves which point you plotted?
3. Describe and apply translations
AbstractA translation slides a point or shape. Moving 3 right adds 3 to the x-coordinate; moving 2 up adds 2 to the y-coordinate. The shape keeps the same side lengths and orientation.
Translate P(2, 3) by 4 right and 2 up.
- Horizontal move: x changes from 2 to 2 + 4 = 6.
- Vertical move: y changes from 3 to 3 + 2 = 5.
Answer: P' is (6, 5).
- Which coordinate changes for a horizontal translation?
- What stays unchanged when a shape is translated?
4. Plot and join vertices to complete polygons
AbstractPlot each specified vertex accurately, label it, then join the points in the stated order with straight line segments. If one vertex is missing from an axis-aligned rectangle, use equal opposite sides to determine its coordinate.
A rectangle has vertices (1, 1), (5, 1) and (5, 4). Find the fourth vertex.
- The missing vertex must share x = 1 with the first point.
- It must share y = 4 with the third point.
Answer: The fourth vertex is (1, 4).
- Why must the vertices be joined in order?
- How can parallel sides help find a missing rectangle vertex?
Common misconceptions and how to address them
MisconceptionCoordinates are read up first and then across.
Why it happens: Everyday descriptions often mention vertical position first.
How to address it: Use the repeated phrase 'along the corridor, up the stairs': x across first, y up second.
MisconceptionA translation can include a turn.
Why it happens: Both are transformations and both move a shape.
How to address it: Trace a vertex arrow and compare orientation. A translation gives every vertex the same straight movement and never changes the facing direction.
MisconceptionOnly one vertex needs the translation applied.
Why it happens: The pupil focuses on the labelled point and redraws the rest by eye.
How to address it: Write the new coordinate for every vertex before joining any sides.
Guided practice (with answers)
1. Read the point 3 across and 6 up.
Answer: (3, 6).
2. Translate (2, 5) by 3 right and 1 down.
Answer: (5, 4).
3. Translate (7, 2) by 4 left and 5 up.
Answer: (3, 7).
4. A rectangle has vertices (2, 2), (6, 2), (6, 5). What is the fourth vertex?
Answer: (2, 5).
Independent practice worksheets
The grid-map and turns sets provide age-equivalent coordinate and movement practice. Ask pupils to annotate each horizontal and vertical change.
Differentiation
- Use an arrow card labelled x across, y up beside every grid.
- Keep translations to one direction before combining horizontal and vertical moves.
- Plot points with one coordinate held constant to make rows and columns visible.
- Find every possible fourth vertex for a square when two adjacent vertices are given.
- Write the translation that maps one whole polygon onto another.
- Design a polygon, translate it, and challenge a partner to infer the movement.
Assessment: exit ticket
Check coordinate order, translation calculation and polygon completion.
1. Plot and label the point (5, 3).
Answer: The point at x = 5, y = 3.
2. Translate (4, 6) by 2 left and 3 down.
Answer: (2, 3).
3. A rectangle has (1, 2), (4, 2) and (4, 6). Find its fourth vertex.
Answer: (1, 6).
Teacher notes and timings
- The statutory Year 4 coordinate work is limited to the first quadrant, so all coordinates are non-negative.
- Say and write translations as horizontal movement followed by vertical movement to match coordinate order.
- A translation preserves every length, angle and orientation. Use that invariant to check pupils' completed shapes.