Grid Coordinates
Match Points to Coordinates (A)
Draw a line from each description to its coordinate.
Match Points to Coordinates (B)
Match each description.
Which Coordinate? (A)
Circle the correct coordinate.
3 across, 5 up
0 across, 4 up
6 across, 0 up
2 across, 7 up
Which Coordinate? (B)
Circle the correct coordinate.
8 across, 3 up
5 across, 5 up
1 across, 9 up
0 across, 0 up (the origin)
Write the Coordinates (A)
Write the coordinates for each point.
A point that is 4 right and 3 up: (__, __)
A point that is 7 right and 1 up: (__, __)
A point that is 0 right and 5 up: (__, __)
A point at the origin: (__, __)
Write the Coordinates (B)
Write the coordinates.
A point that is 9 right and 2 up: (__, __)
A point on the x-axis at position 6: (__, __)
A point on the y-axis at position 8: (__, __)
Sort: On an Axis or Not?
A point is on an axis if one coordinate is 0.
Coordinate Sums
Find what number is added to x to get the new x-coordinate.
Plot the Coordinates (A)
On grid paper, plot these points and join them in order.
Plot: (1, 1), (1, 5), (5, 5), (5, 1). Join them. What shape? ___
Plot: (2, 0), (4, 3), (6, 0). Join them. What shape? ___
Plot the Coordinates (B)
Plot and join these points.
Plot: (0, 0), (4, 0), (4, 3), (0, 3). Shape? ___
Plot: (1, 1), (3, 4), (5, 1). Shape? ___
Follow the Directions (A)
Start at the given point and follow directions.
Start at (2, 3). Move 4 right and 2 up. New position: (__, __)
Start at (5, 6). Move 3 left and 1 down. New position: (__, __)
Start at (0, 0). Move 6 right and 5 up. New position: (__, __)
Follow the Directions (B)
Follow the movements.
Start at (3, 7). Move 3 right and 4 down. New position: (__, __)
Start at (8, 2). Move 5 left and 3 up. New position: (__, __)
Start at (1, 1). Move right 4, up 3, right 2, up 1. Final position: (__, __)
Describe the Movement
What movement takes you from point A to point B?
From (2, 3) to (5, 3): move ___ right and ___ up
From (1, 1) to (1, 6): move ___ right and ___ up
From (4, 7) to (7, 2): move ___ right and ___ down
Coordinate Patterns
Circle the correct answer.
(1,1), (2,2), (3,3), (4,4) — these points lie on a...
(2,1), (2,3), (2,5), (2,7) — these points lie on a...
(1,4), (3,4), (5,4), (7,4) — these points lie on a...
Match Shapes to Coordinate Sets
Draw a line from each shape to the coordinates that would create it.
Coordinate Challenges (A)
Solve each problem.
Three corners of a rectangle are at (1, 2), (1, 6) and (5, 6). Where is the fourth corner?
A shape has corners at (2, 1), (6, 1), (6, 4) and (2, 4). What is the shape? What are its dimensions?
Coordinate Challenges (B)
Solve these problems.
Three corners of a square are (3, 1), (3, 5) and (7, 5). Where is the fourth corner? What is the side length?
A triangle has vertices at (0, 0), (6, 0) and (3, 4). Is it isosceles? Explain.
Coordinate Distances
Find the distance between each pair of points.
(1, 3) and (1, 8) — distance: ___ units (same x, so count y)
(2, 5) and (7, 5) — distance: ___ units (same y, so count x)
A rectangle has corners at (1, 2) and (5, 2). What is the width?
Perimeter from Coordinates
Find the perimeter of shapes defined by coordinates.
Rectangle with corners (0, 0), (6, 0), (6, 4), (0, 4). Perimeter = ___
Square with corners (2, 1), (7, 1), (7, 6), (2, 6). Perimeter = ___
Create Coordinate Shapes
Write coordinates for each shape.
A rectangle with a perimeter of 16 units. Coordinates: ___
An isosceles triangle. Coordinates: ___
Match Points to Coordinates (C)
Draw a line from each description to its coordinate.
Which Coordinate? (C)
Circle the correct coordinate.
4 across, 6 up
7 across, 0 up
3 across, 3 up
9 across, 1 up
Which Coordinate? (D)
Circle the correct coordinate.
0 across, 9 up
10 across, 5 up
6 across, 8 up
1 across, 1 up
Write the Coordinates (C)
Write the coordinates for each point.
A point that is 8 right and 4 up: (__, __)
A point that is 3 right and 9 up: (__, __)
A point that is 10 right and 0 up: (__, __)
A point that is 5 right and 7 up: (__, __)
Sort: x-Coordinate Greater or Less Than 5?
Sort each point.
Coordinate Sums (B)
The x-coordinate and y-coordinate add up to the total. Find the missing value.
Match Coordinates to Quadrants
Draw a line from each description to the correct position.
Plot the Coordinates (C)
On grid paper, plot and join these points.
Plot: (0, 0), (3, 0), (3, 4), (0, 4). Join them. What shape? ___ What is the perimeter?
Plot: (2, 1), (5, 1), (5, 6), (2, 6). Join them. What shape? ___ What are the dimensions?
Plot the Coordinates (D)
Plot and join these points.
Plot: (1, 1), (1, 7), (6, 7), (6, 1). Shape? ___ Perimeter? ___
Plot: (0, 3), (4, 6), (8, 3). Shape? ___ Is it isosceles? ___
Follow the Directions (C)
Start at the given point and follow directions.
Start at (1, 1). Move 3 right, 2 up, 3 right, 2 up. Final position: (__, __)
Start at (7, 8). Move 4 left, 3 down. New position: (__, __)
Start at (0, 5). Move 6 right, 5 down. New position: (__, __)
Start at (4, 4). Move 2 left, 3 up, 1 right, 2 down. Final position: (__, __)
Follow the Directions (D)
Follow the movements.
Start at (5, 2). Move right 3, up 4. New position: (__, __)
Start at (9, 9). Move left 6, down 7. New position: (__, __)
Start at (2, 0). Move right 5, up 8, left 2, down 3. Final position: (__, __)
Coordinate Patterns (B)
Circle the correct answer.
(0, 2), (1, 3), (2, 4), (3, 5) — the y-coordinate is always...
(1, 2), (2, 4), (3, 6), (4, 8) — the y-coordinate is always...
(0, 0), (2, 1), (4, 2), (6, 3) — the pattern is y = ...
Describe the Movement (B)
What movement takes you from A to B?
From (0, 0) to (4, 7): move ___ right and ___ up
From (5, 8) to (5, 2): move ___ right and ___ down
From (3, 3) to (8, 3): move ___ right and ___ up
From (6, 1) to (2, 5): move ___ left and ___ up
Match Movements to New Positions
Start at (3, 4). Match each movement to the final position.
Sort: Horizontal or Vertical Movement?
Sort each movement.
Coordinate Challenges (C)
Solve each problem.
A square has corners at (1, 1) and (1, 5). Find the other two corners if it extends to the right.
Plot points (0, 0), (3, 0), (3, 2), (0, 2). What is the area of this rectangle?
A triangle has two corners at (0, 0) and (6, 0). The third corner is directly above the middle. If the triangle is 4 units tall, what are the coordinates of the third corner?
Coordinate Challenges (D)
Solve these problems.
The midpoint of a line segment is (4, 3). One end is at (2, 1). Where is the other end?
A rectangle has an area of 12 square units. One corner is at (0, 0). Write possible coordinates for the other 3 corners.
Coordinate Distances (B)
Find the distance between each pair of points.
(0, 0) and (0, 7) — distance: ___ units
(3, 5) and (9, 5) — distance: ___ units
(2, 3) and (2, 10) — distance: ___ units
A square has corners at (1, 1) and (6, 1). What is the side length? What is the perimeter?
Area from Coordinates
Find the area of shapes defined by coordinates.
Rectangle: (0, 0), (5, 0), (5, 3), (0, 3). Area = length × width = ___
Rectangle: (2, 1), (8, 1), (8, 4), (2, 4). Area = ___
Square: (1, 2), (4, 2), (4, 5), (1, 5). Area = ___
Coordinate Paths
Describe a path using coordinates.
Describe a path from (0, 0) to (5, 5) using only right and up moves. How many ways can you go?
A robot starts at (1, 1). It moves: right 3, up 2, left 1, up 3. Write the coordinate after each move.
Coordinate Reasoning
Circle the correct answer.
All points on the line y = 3 have...
A point with equal coordinates lies on...
Moving a shape 2 right changes...
The origin is...
Write Coordinate Rules
Find the rule for each set of coordinates.
(1, 3), (2, 4), (3, 5), (4, 6). Rule: y = ___
(1, 2), (2, 4), (3, 6), (4, 8). Rule: y = ___
(0, 5), (1, 4), (2, 3), (3, 2). Rule: y = ___
Match Points to Coordinates (D)
Draw a line from each description to its coordinate.
Which Coordinate? (E)
Circle the correct coordinate.
3 along, 9 up
5 along, 0 up
0 along, 0 up
12 along, 5 up
Coordinate Differences
Find the difference between the x-coordinates.
Sort: Points Above or Below y = 5
Sort each point based on whether its y-coordinate is above, at, or below 5.
Write the Coordinates (D)
Write the coordinates.
A point that is 0 right and 0 up (origin): (__, __)
A point on the x-axis at position 10: (__, __)
A point on the y-axis at position 6: (__, __)
A point equidistant from both axes at distance 5: (__, __)
Follow the Directions (E)
Start at the given point and follow directions.
Start at (0, 0). Move right 4, up 3, left 2, up 5. Final position: (__, __)
Start at (5, 5). Move left 3, down 4, right 6, up 1. Final position: (__, __)
Start at (8, 3). Move left 5, up 4, right 3, down 2. Final position: (__, __)
Midpoints
Find the midpoint (middle point) between each pair of coordinates.
Midpoint between (0, 0) and (6, 0): (__, __)
Midpoint between (2, 4) and (8, 4): (__, __)
Midpoint between (1, 3) and (5, 7): (__, __)
Midpoint between (0, 0) and (10, 10): (__, __)
Coordinate Reflections
Find the reflected coordinate.
Reflect (3, 2) across the y-axis: (__, __)
Reflect (5, 4) across the x-axis: (__, __)
Reflect (2, 3) across the line y = x (swap coordinates): (__, __)
Reflect (6, 1) across the y-axis: (__, __)
Points on a Grid
A survey counted points plotted by students in each quadrant area of a 10×10 grid.
| x < 5, y < 5 | |
| x ≥ 5, y < 5 | |
| x < 5, y ≥ 5 | |
| x ≥ 5, y ≥ 5 |
Which area had the most points?
Total points plotted?
Were points roughly evenly distributed?
What fraction were in the top-right area?
Coordinate Errors
Students made coordinate errors. Count the type of error.
| Item | Tally | Total |
|---|---|---|
Swapped x and y | ||
Read wrong axis | ||
Off by one | ||
No error |
Coordinate Patterns (C)
Find the rule for each pattern.
(2, 6), (3, 7), (4, 8), (5, 9). Rule: y = x + ___
(1, 3), (2, 5), (3, 7), (4, 9). Rule: y = 2x + ___
(0, 10), (1, 9), (2, 8), (3, 7). Rule: y = ___
(2, 4), (4, 8), (6, 12). Rule: y = ___
Coordinate Reasoning (B)
Circle the correct answer.
A point on the x-axis has y = ___
Moving a shape 3 left changes the x-coordinate by ___
The midpoint of (0,0) and (8,0) is ___
A point with coordinates (a, a) lies on the line ___
Map Reading with Coordinates
Use coordinates to describe a simple map.
School is at (3, 4). Library is at (7, 4). How far apart are they? ___
Park is at (1, 6). Swimming pool is at (1, 2). How far apart are they? ___
Which two locations above are further apart? ___
What is the midpoint between school and library? ___
Design a Coordinate Map
Design your own map using coordinates.
Place 5 locations on a 10×10 grid. Write their coordinates: Location 1: ___ Location 2: ___ Location 3: ___ Location 4: ___ Location 5: ___
Find the distance between two of your locations: ___
Give directions from one location to another using coordinate language: ___
Coordinate Perimeter and Area (B)
Find P and A from coordinates.
Square: corners at (0,0), (5,0), (5,5), (0,5). P = ___ A = ___
Rectangle: corners at (1,1), (7,1), (7,4), (1,4). P = ___ A = ___
Which shape above has greater area? ___
Match Points to Quadrant Position
Draw a line.
Coordinate Sums (C)
The x + y sum is given. Find the missing coordinate.
Plot and Join Coordinates (E)
Plot and join each set of coordinates, then name the shape.
(0, 4), (3, 0), (6, 4), (3, 8). Shape: ___. Is it a regular shape? ___
(0, 0), (4, 0), (5, 3), (1, 3). Shape: ___. What type of quadrilateral? ___
Coordinate Translations (E)
Describe or perform each translation.
Rectangle corners: (1,1), (4,1), (4,3), (1,3). Translate right 3, up 2. New corners: ___, ___, ___, ___
Triangle corners: (0,0), (3,0), (0,4). Translate right 2, up 1. New corners: ___, ___, ___
Coordinate Facts Quiz
Circle the correct answer.
A point on the y-axis has x = ___
Moving a point 5 units down changes the y-coordinate by ___
The midpoint of (2, 4) and (8, 4) is ___
Two points with the same y-coordinate form a ___ line.
Sort: On Axis or Interior?
Sort each point.
Symmetry on a Grid
Use coordinates to describe symmetric shapes.
A shape has corners (1,2), (3,2), (3,5), (1,5). Draw its reflection across x = 4. New corners: ___, ___, ___, ___
The same shape is reflected across y = 3. New corners: ___, ___, ___, ___
Negative Coordinates Introduction
Some grids extend to negative numbers.
If the x-axis goes from -5 to 5, and y from -5 to 5, plot and name the origin: ___
A point at (-3, 2) is ___ units left and ___ units up from the origin.
What coordinate is 4 units left of (1, 3)? ___
Coordinate Geometry Problems (E)
Solve.
A square has two corners at (2,1) and (2,5). The square extends to the right. Write all four corners.
A right-angled triangle has the right angle at (0,0), one side along the x-axis to (6,0), and another along the y-axis to (0,4). What is its perimeter?
Coordinate Art
Create a picture using coordinates.
Design a simple picture (house, boat, rocket) using only straight lines. List the coordinates for each line segment:
Describe what your picture looks like:
Coordinate Sequences
Find the next coordinate in each sequence.
Compare Coordinate Distances
Which distance is greater?
From (1,1) to (6,1) or from (1,1) to (1,5)?
From (0,0) to (6,0) or from (0,0) to (0,8)?
From (2,2) to (2,9) or from (1,4) to (8,4)?
Match Coordinate to Quadrant
Draw a line.
Translation Bonds (B)
If a point at x is translated right by d, find the new x.
Points on a Grid (C)
Circle the correct answer.
Which axis is the horizontal one?
The point (0, 3) is on...
The distance from (2, 3) to (2, 8) is...
Point (-3, 0) is to the ___ of the origin.
Sort: First or Second Quadrant?
Sort points by quadrant.
Plotting and Joining Shapes
Plot coordinates and join them to make shapes.
Plot and join: (1,1), (5,1), (5,4), (1,4). What shape? ___. Perimeter: ___
Plot: (0,0), (4,0), (2,4). What shape? ___ Is it isosceles? ___
Coordinates and Maps (B)
Maps use grid references.
On a map, the library is at (4, 7) and the school is at (9, 7). Distance between them: ___
The park is halfway between them. Park coordinates: ___
If you walk from (2, 3) to (7, 8), how far east and north did you travel? E: ___ N: ___
Coordinate Sequences (B)
Continue each sequence of x or y values.
Compare Distances Between Coordinate Points
Tick which distance is greater.
From (0,0) to (7,0) vs from (0,0) to (0,5)
From (1,2) to (5,2) vs from (3,1) to (3,7)
Describing Positions Using Direction and Distance
Use compass directions and distances.
Start at (3, 2). Move 4 right and 3 up. New position: ___
Start at (8, 6). Move 5 left and 2 down. New position: ___
Describe how to get from (1, 1) to (6, 4) in two moves:
Coordinate Transformations on a Grid (C)
Perform transformations.
Reflect point (3, 5) over x-axis. New point: ___
Reflect point (3, 5) over y-axis. New point: ___
Translate (3, 5) by (−4, +2). New point: ___
Rotate (3, 0) by 90° anticlockwise around origin. New point: ___
Quadrant Positions of Class Points
Students plotted random points. Count by quadrant.
| Item | Tally | Total |
|---|---|---|
Quadrant 1 | ||
Quadrant 2 | ||
Quadrant 3 | ||
Quadrant 4 |
Coordinate Vocabulary (B)
Match each term to its definition.
Coordinate Translation Bonds (C)
Find the missing coordinate after translation.
Reading Coordinates (C)
Circle the correct coordinate.
A point 3 right and 5 up from origin is:
The x-coordinate of (−4, 7) is:
A point on the y-axis has x-value:
The origin has coordinates:
Sort Points by x-value (Smallest to Largest)
Sort from smallest to largest x-coordinate.
Midpoints Between Coordinates
Find the midpoint between two points.
Midpoint between (2, 4) and (8, 4): ___
Midpoint between (0, 0) and (6, 10): ___
Midpoint between (−3, 2) and (5, 8): ___
Drawing Shapes on a Coordinate Grid (B)
Use coordinates to draw shapes.
Draw a right-angled triangle with vertices at (0,0), (4,0), and (0,3). Label sides and find area: ___
Draw a square with one corner at (1,1) and side length 4. List all vertices: ___
Coordinate Sequences: Straight Lines (B)
Continue each coordinate sequence (they form straight lines).
Street Maps and Coordinates
Use coordinate grids for navigation.
A city block grid: your house is at (2, 3), school at (7, 3). Each block = 200 m. Distance to school: ___
From school (7, 3), the park is at (7, 8). Distance from school to park: ___ m
Total round trip house → school → park → house: ___
Compare Distances on a Grid (B)
Which distance is greater?
From (1,1) to (7,1) = 6 units vs from (2,2) to (2,6) = 4 units
From (0,0) to (5,0) = 5 units vs from (0,0) to (0,8) = 8 units
Grid Map: Objects Found
Each icon = 1 object found in a grid square.
| Quadrant 1 objects | |
| Quadrant 2 objects | |
| Quadrant 3 objects | |
| Quadrant 4 objects |
Total objects?
Which quadrant had the most?
Difference between quadrant 1 and 3?
What fraction were in quadrant 2?
Coordinates in Real Mapping Applications
Think about coordinate grids in GPS and mapping.
GPS uses latitude and longitude. Sydney is at about (151°E, 34°S). What type of coordinate is this? ___
On a local scale, a map grid has each square = 1 km. If your home is at (3, 7) and the shops at (8, 7), distance: ___ km
Why is understanding coordinates important for navigation and technology?
Creating a Coordinate Picture
Use coordinates to create a picture.
Connect these points in order to make a shape: (0,0) → (3,0) → (3,4) → (0,4) → (0,0). What shape? ___
Add a point at (1.5,5). Connect it to (0,4) and (3,4). What new shape is created? ___
What is the total area of the original rectangle plus the new triangle? ___
Negative Coordinates in Context
Explore negative coordinates.
A submarine is at coordinates (2, −5) on a sea map where positive y is above sea level. Is the submarine above or below sea level? ___
Plot these points: (3, 2), (−3, 2), (−3, −2), (3, −2). What shape do they make? ___. Area: ___
What does the point (0, 0) represent on a map of a town?
Home Activity: Coordinate Treasure Hunt
Make a coordinate treasure hunt!
- 1Draw a grid on paper. Hide a treasure at a secret coordinate. Give clues.
- 2Use grid paper to draw a picture by connecting coordinates.
- 3Play Battleships using a coordinate grid.
- 4Set up a grid in your backyard with string or chalk and use coordinates to navigate.