Unit 9 · Standard 6.NS.6b
Ordered Pairs in All Four Quadrants
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
I (+, +) top-right, II (-, +) top-left, III (-, -) bottom-left, IV (+, -) bottom-right
Quadrant
One of the four parts of a coordinate grid, numbered I to IV.
(-3, 2) means 3 left and 2 up from the origin
Negative coordinate
A coordinate less than zero. It means left or below the center point.
(3, 2) reflected over the y-axis is (-3, 2) — same distance, opposite side
Reflection
A flipped, mirror image of a point across a line.
The x-axis goes left-right; the y-axis goes up-down; they cross at (0, 0)
Axis
A line on the grid. The x-axis goes across; the y-axis goes up.
..., -3, -2, -1, 0, 1, 2, 3, ...
Integer
Whole numbers and their opposites, like -2, -1, 0, 1, 2.
Key Ideas & Notes
- 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.
- Plot each treasure clue on the expanded map and identify which quadrant it falls in.
Think About It
- How do you know which quadrant a point is in by looking at the signs of its coordinates?
- What do negative x-values and negative y-values mean on the map?
- Where is the point (0, 0) on the expanded map?
My Notes
Guided Examples
Example 1
In which quadrant is the point (-4, 5)?
Solution: The x-coordinate is negative (left) and the y-coordinate is positive (up). Left and up is Quadrant II.
Answer: B. Quadrant II
Example 2
A point has a positive x-coordinate and a negative y-coordinate. Which quadrant is it in?
Solution: Positive x (right) and negative y (down) = Quadrant IV (bottom-right).
Answer: D. Quadrant IV
Example 3
Which point is located on the x-axis?
Solution: A point is on the x-axis when its y-coordinate is 0. (4, 0) is on the x-axis.
Answer: A. (4, 0)
Write About the Math The Writing Revolution
I can explain my work using the words quadrant, negative coordinate, reflection, and axis.
1. Kernel Sentence subject + verb
Model: Quadrant is one of the four parts of a coordinate grid, numbered I to IV.Cuadrante es una de las cuatro partes de una cuadrícula de coordenadas, numeradas I a IV.
Write a kernel sentence about quadrant. Use a subject and a verb.Escribe una oración base sobre cuadrante. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Quadrant matters in mathCuadrante importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Quadrant matters in math because ___.Cuadrante importa en matemáticas porque ___.
Quadrant matters in math, but ___.Cuadrante importa en matemáticas, pero ___.
Quadrant matters in math, so ___.Cuadrante importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about quadrant.Di un hecho verdadero sobre quadrant.
Quadrant ___.
Ask a question about quadrant.Haz una pregunta sobre quadrant.
How does ___ ?¿Cómo ___ ?
Show excitement about quadrant.Muestra entusiasmo sobre quadrant.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with quadrant.Dile a un compañero qué hacer con quadrant.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
The point is in quadrant ___ because ___.El punto está en el cuadrante ___ porque ___.
Both signs are ___.Ambos signos son ___.
Four quadrants matter when ___.Los cuatro cuadrantes importan cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Which point is located on the x-axis?
- (4, 0)
- (0, 4)
- (4, 4)
- (-4, -4)
2. Point A is at (-5, 3). If you move 8 units to the right, what are the new coordinates?
- (3, 3)
- (-13, 3)
- (-5, 11)
- (-5, -5)
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A point starts in Quadrant I at (4, 6). Describe a move that puts it in Quadrant III. What must happen to both coordinates? Can you give the exact new coordinates after your move?
Sentence starter: To move from Quadrant I to Quadrant III, both coordinates must become ___. Starting at (4, 6), I could move ___ units left and ___ units down to reach (___,___), which is in Quadrant III because ___.
Reflect — Exit Ticket
A point has a negative x-coordinate and a negative y-coordinate. Which quadrant is it in?
- Quadrant I
- Quadrant II
- Quadrant III
- Quadrant IV
Answer Key & Teacher Guide
- Try It 1: A. (4, 0) — A point is on the x-axis when its y-coordinate is 0. (4, 0) is on the x-axis.
- Try It 2: A. (3, 3) — Moving right means adding to the x-coordinate: -5 + 8 = 3. The y stays the same. New point: (3, 3).
- Exit Ticket: C. 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.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Quadrant is one of the four parts of a coordinate grid, numbered I to IV.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).