Ordered Pairs in All Four Quadrants
I can plot ordered pairs in all four quadrants of the coordinate plane.
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🎯 Content Objective / Objetivo de contenido
I can plot ordered pairs in all four quadrants of the coordinate plane.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
What do the signs of the coordinates in an ordered pair tell you about which quadrant the point is in?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Expanding the Treasure Map
Captain Vega realized her treasure map only covered one corner of the island! She needs to expand the map in all directions — north, south, east, and west of the base camp at the origin (0, 0). Now clues can have negative coordinates: (-4, 3) means 4 units west and 3 units north. A clue at (2, -5) means 2 units east and 5 units south. Which quadrant is each clue in?
Concept Launch
💡 How do you plot points in all four quadrants?
The coordinate plane has four parts called quadrants. A negative coordinate means you move left (for x) or down (for y) from the origin instead of right or up.
The signs of (x, y) tell you the quadrant: (+,+) is I, (-,+) is II, (-,-) is III, (+,-) is IV.
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Quadrant Cuadrante |
One of the four parts of a coordinate grid, numbered I to IV. Una de las cuatro partes de una cuadrícula de coordenadas, numeradas I a IV. |
I (+, +) top-right, II (-, +) top-left, III (-, -) bottom-left, IV (+, -) bottom-right | |
| Negative coordinate Coordenada negativa |
A coordinate less than zero. It means left or below the center point. Una coordenada menor que cero. Significa a la izquierda o debajo del centro. |
(-3, 2) means 3 left and 2 up from the origin | |
| Reflection Reflexión |
A flipped, mirror image of a point across a line. Una imagen reflejada de un punto al otro lado de una línea. |
(3, 2) reflected over the y-axis is (-3, 2) — same distance, opposite side | |
| Axis Eje |
A line on the grid. The x-axis goes across; the y-axis goes up. Una línea en la cuadrícula. El eje x va de lado; el eje y va hacia arriba. |
The x-axis goes left-right; the y-axis goes up-down; they cross at (0, 0) | |
| Integer Número entero |
Whole numbers and their opposites, like -2, -1, 0, 1, 2. Números enteros y sus opuestos, como -2, -1, 0, 1, 2. |
..., -3, -2, -1, 0, 1, 2, 3, ... |
Which Word Fits?
One of the four regions of the coordinate plane, numbered I to IV, is a ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
What do the signs of the coordinates in an ordered pair tell you about which quadrant the point is in?
👂 Listen For
Student matches sign combinations to quadrants (e.g., (+,+) is I, (-,+) is II).
Extend: Push students to explain how to tell which quadrant a point is in without plotting it.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Plot each treasure clue on the expanded map and identify which quadrant it falls in.
✍️ Explore Discourse
How do the signs of the x- and y-coordinates tell you which quadrant a point is in?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
Plot (-3, -4). Which quadrant is it in, and how do the negative coordinates change the directions you move from the origin?
👂 Listen For
Student moves left for negative x and down for negative y, landing in quadrant III.
Extend: Ask students to predict the quadrant of (-3, 4) and compare how it differs from (-3, -4).
Practice Check A
Point A is at (-5, 3). If you move 8 units to the right, what are the new coordinates?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
In which quadrant is the point (-3, 5)?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Coordinate Treasure Hunt
Plot points to find the treasure! Target: (4, 3)
✍️ Justify Your Thinking
Captain Vega spotted four enemy ships. Drag each ship's coordinates into the correct quadrant of the map.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "The signs of (x, y) tell you the quadrant: (+,+) is I, (-,+) is II, (-,-) is III, (+,-) is IV." — and it works because ___.
Because Quadrant means ___, but a tricky part is ___, so I have to ___.
A common mistake with Quadrant is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Negative coordinate to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
The signs of (x, y) tell you the quadrant: (+,+) is I, (-,+) is II, (-,-) is III, (+,-) is IV. because ___
The signs of (x, y) tell you the quadrant: (+,+) is I, (-,+) is II, (-,-) is III, (+,-) is IV. but ___
The signs of (x, y) tell you the quadrant: (+,+) is I, (-,+) is II, (-,-) is III, (+,-) is IV. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Plot each treasure clue on the expanded map and identify which quadrant it falls in.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
In which quadrant is the point (-4, 5)?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A city uses a coordinate grid to map locations. City Hall is at the origin (0, 0). The library is at (-3, 4), the park is at (5, -2), the school is at (2, 3), and the hospital is at (-4, -1).
✍️ Connection Reasoning
How do four-quadrant coordinates help a city map locations in every direction from the center?
The library is in Quadrant ___ because its x is ___ and its y is ___. The park is in Quadrant ___ because ___. Four-quadrant coordinates help because ___.
Turn & Talk — Connect
How are the four quadrants like a tic-tac-toe of positive and negative directions on the coordinate plane?
👂 Listen For
Student connects each quadrant to a unique sign pattern for x and y.
Extend: Push students to generalize what happens to a point that lands exactly on an axis instead of inside a quadrant.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A point has a negative x-coordinate and a negative y-coordinate. Which quadrant is it in?
Bonus Exit Check
What are the coordinates of a point 4 units right and 2 units down from the origin?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Student matches sign combinations to quadrants (e.g., (+,+) is I, (-,+) is II).
• Student moves left for negative x and down for negative y, landing in quadrant III.
• Student connects each quadrant to a unique sign pattern for x and y.
• Student says (5, -2) is right and down, in quadrant IV, from the signs alone.
Common mistake: A common mistake in Ordered Pairs in All Four Quadrants is skipping the key idea: "The signs of (x, y) tell you the quadrant: (+,+) is I, (-,+) is II, (-,-) is III, (+,-) is IV." — always check your work against this rule before you submit.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: (3, 3) — Moving right means adding to the x-coordinate: -5 + 8 = 3. The y stays the same. New point: (3, 3).
✓ Practice 2: Quadrant II — Negative x with positive y places the point in Quadrant II.
✓ Practice 3: (4, -2) — Right is +x and down is -y, so the point is (4, -2).
✓ Practice 4: Quadrant II — The x-coordinate is negative (left) and the y-coordinate is positive (up). Left and up is Quadrant II.
✓ Exit ticket: Quadrant III — Quadrant III is where both x and y are negative. This means the point is left of the origin and below the origin.