🎯Today's objective: Plot points in all four quadrants and find distances.
Need a hint?
Re-read the problem and underline the numbers and the question.
Pick one representation (model, table, or equation), show your
steps, and check that your answer makes sense for the situation.
The school is planning a new outdoor lunch area. The principal has a
map on a coordinate grid where each square =
1 meter. Four possible table locations have been
marked: A(3, 5), B(-4, 5),
C(-4, -2), and D(3, -2). Your team
must plot these points, connect them to form a rectangle, find the
length and width, and calculate the
perimeter of the lunch area.
The Investigation
The Problem: Plot points A(3, 5), B(-4, 5), C(-4,
-2), and D(3, -2) on a coordinate plane. Connect them in order to form
a rectangle. Find the length of side AB (the width),
the length of side BC (the height), and the
perimeter of the rectangle. Then answer: how many
square meters is the lunch area?
Visual Model: Coordinate Grid with Rectangle
Step-by-Step Investigation Guide
Set up the coordinate plane. Draw x and y axes.
Label the origin (0, 0). Number both axes from -6 to 6.
Guiding question: Which direction is positive for x? For y?
Plot the four points. Start at the origin each
time. Move right/left for x, then up/down for y. Mark and label A,
B, C, D.
Guiding question: For B(-4, 5), do you go left or right first?
Then up or down?
Connect the points. Draw line segments A to B, B to
C, C to D, D to A.
Guiding question: What shape do you see? How do you know it is a
rectangle?
Find the width (AB). A and B have the same y-value
(5). Width = |3 - (-4)| = |7| = 7 meters.
Guiding question: Why can we subtract x-values when the y-values
match?
Find the height (BC). B and C have the same x-value
(-4). Height = |5 - (-2)| = |7| = 7 meters.
Guiding question: This rectangle is actually a square! How do you
know?
Calculate perimeter and area. Perimeter = 2(7) +
2(7) = 28 m. Area = 7 x 7 = 49 sq m.
Guiding question: Is 49 square meters enough space for lunch
tables?
Language Support: Key Vocabulary
Coordinate plane
A flat surface with two number lines (x and y) that cross at the
origin.
Ordered pair
Two numbers (x, y) that tell the position of a point. Always x
first, then y.
Origin
The point (0, 0) where the x-axis and y-axis cross.
Quadrant
One of four sections of the coordinate plane, numbered I, II, III,
IV.
x-axis
The horizontal number line (left-right).
y-axis
The vertical number line (up-down).
Sentence Frames:
"Point _____ is in Quadrant _____ because the x-value is _____ and
the y-value is _____."
"The distance between _____ and _____ is _____ because I
subtracted _____ and took the absolute value."
"To plot (x, y), I start at the origin, move _____ on the x-axis,
then _____ on the y-axis."
Multiple Representations
Approach 1: Plotting and Counting
Plot all four points on grid paper. Count the grid squares along
each side. AB goes from x = -4 to x = 3, that is 7 squares. BC
goes from y = 5 to y = -2, that is 7 squares.
Approach 2: Absolute Value Formula
For horizontal distance: |x1 - x2| when y-values are equal. For
vertical distance: |y1 - y2| when x-values are equal. AB =
|3-(-4)| = 7. BC = |5-(-2)| = 7.
Approach 3: Coordinate Table
List each point with its quadrant: A(3,5) = Quadrant I B(-4,5)
= Quadrant II C(-4,-2) = Quadrant III D(3,-2) = Quadrant
IV The rectangle spans all four quadrants!
Team Roles
📚Facilitator
Read the lunch area scenario. Make sure everyone understands (x, y)
order. Call out each point for the Model Builder to plot.
✏️Model Builder
Draw the coordinate plane with labeled axes. Plot all four points
accurately. Connect them to form the rectangle. Label all sides.
🔎Precision Checker
Verify each point is in the correct quadrant. Check distance
calculations. Confirm perimeter and area formulas are applied
correctly.
📝Reporter
Prepare defense: name each point's quadrant, state the dimensions,
and present the perimeter and area with full calculations.
Timed Lab Phases
Launch Phase
03:00
Read the scenario. Assign roles. Review how to read an ordered
pair: x first, then y.
In (3, 5), which number is x and which is y?
What does a negative x-value mean on the grid?
Which quadrant has both values negative?
Checkpoint: Everyone can explain how to plot an ordered pair
starting from the origin.
Draw axes. Plot all four points. Connect them to form the
rectangle.
Is each point in the correct quadrant?
Do the four points form a rectangle when connected?
Label each vertex with its ordered pair.
Checkpoint: All 4 points plotted correctly. Rectangle drawn
and labeled.
Calculate side lengths, perimeter, and area.
AB: |3 - (-4)| = ? meters
BC: |5 - (-2)| = ? meters
Perimeter = 2(length) + 2(width) = ?
Area = length times width = ?
Checkpoint: All calculations complete with units (meters,
square meters).
Reporter prepares the defense using the coordinate grid as
evidence.
"Point A is in Quadrant _____ because _____."
"The width is _____ because we calculated |_____|."
"The lunch area has _____ square meters, which is enough for
_____ tables."
Checkpoint: Defense includes quadrant identification, distance
calculations, and perimeter/area.
Challenge Extensions
Extension Problem: The principal wants to add a
fountain at the exact center of the rectangle. What are the
coordinates of the center point? (Hint: average the x-values and
average the y-values.) Then find the distance from the fountain to
the nearest corner.
What If?
What if point D moved to (3, -5)? Would the shape still be a
rectangle? What would the new perimeter be?
Reflect the rectangle over the y-axis. What are the new
coordinates of each vertex?
If each lunch table needs 4 square meters of space, how many
tables fit in the 49 square meter area?
Real-Life Connections
Coordinate planes are used in GPS navigation, video game design,
architecture blueprints, and mapping apps like Google Maps.
Defense Preparation
Name the quadrant of each point. How do you know?
How did you find the length of side AB? Show the absolute value
calculation.
Why does this shape span all four quadrants?
What is the perimeter and area? Include correct units.
Sentence Starters:
"Point _____ is in Quadrant _____ because both its x and y are
_____."
"We found the distance by subtracting coordinates: |_____ -
(_____)| = _____."
"The perimeter is _____ meters because _____."
Rubric
Criteria
Excellent (4)
Proficient (3)
Developing (2)
Plotting
All 4 points in correct position with labels
4 points plotted, minor label issue
Some points plotted
Quadrants
All 4 quadrants correctly identified with reasoning
Quadrants identified
Some quadrants named
Distance
Both distances with absolute value shown
Correct distances stated
Attempted
Perimeter/Area
Both correct with units and formulas
Correct answers
One calculation correct
Exit Product
Your team submits: A Lunch Area Blueprint that
includes:
A coordinate grid with labeled axes (at least -6 to 6 on both)
All four points plotted and labeled with ordered pairs
The rectangle drawn with side lengths labeled
Distance calculations for width and height using absolute value
Perimeter (28 m) and area (49 sq m) with formulas shown
Each point's quadrant identified
Self-Assessment Checklist
I can plot points in all four quadrants of the coordinate plane.
I know that (x, y) means go right/left first, then up/down.
I can find horizontal distance using |x1 - x2|.
I can find vertical distance using |y1 - y2|.
I calculated perimeter and area correctly with units.
I can name the quadrant of any point by looking at the signs of x
and y.