Distance on the Coordinate Plane
I can find the distance between two points on the coordinate plane using absolute value.
How to Use This Deck
Click Present or press F11 for fullscreen. Use arrow keys to advance.
Blue boxes show exactly what to say, ask, and how long to spend.
Text boxes, polls, and drag-sort save automatically in the browser.
Press N or click 📝 in the toolbar for pacing tips and answers.
Launch the full HTML activity for independent practice.
File → Print or the print button for handout copies.
🎯 Content Objective / Objetivo de contenido
I can find the distance between two points on the coordinate plane using absolute value.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Two points sit on the same horizontal line: (2, 3) and (7, 3). How can you find the distance between them without counting every square?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Treasure Distances
Captain Vega has two treasure locations on her map: a buried chest at (-3, 2) and a hidden cave at (4, 2). Both are at the same height (y = 2) on the map. She needs to figure out how far apart they are so she knows how much rope to bring. Another pair of treasures is at (1, -3) and (1, 5) — same column, different rows. How far apart is each pair?
Concept Launch
💡 How do you find distance on the coordinate plane?
Distance is how far apart two points are, and it is never negative. When two points share a row or a column, you can find the distance using their coordinates.
If points are on the same side of zero, subtract; if they are on opposite sides of zero, add the absolute values.
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 |
|---|---|---|---|
| Distance Distancia |
How far apart two points are. It is never negative. Qué tan separados están dos puntos. Nunca es negativo. |
The distance from -3 to 4 on a number line is |-3| + |4| = 3 + 4 = 7 units | |
| Absolute value Valor absoluto |
How far a number is from zero. Qué tan lejos está un número de cero. |
|-3| = 3 and |4| = 4; to find distance: |4 - (-3)| = 7 | |
| Horizontal distance Distancia horizontal |
How far apart two points are going left or right. Qué tan separados están dos puntos yendo a la izquierda o a la derecha. |
From (-2, 3) to (5, 3): count from -2 to 5 = 7 units across | |
| Vertical distance Distancia vertical |
How far apart two points are going up or down. Qué tan separados están dos puntos yendo hacia arriba o hacia abajo. |
From (4, -1) to (4, 6): count from -1 to 6 = 7 units up | |
| Coordinate plane Plano cartesiano |
A grid with a line going across and a line going up that cross. Una cuadrícula con una línea horizontal y una vertical que se cruzan. |
Two number lines crossing at (0, 0), creating four quadrants | |
| 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?
How far apart two points are on the coordinate plane is the ___.
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
Two points sit on the same horizontal line: (2, 3) and (7, 3). How can you find the distance between them without counting every square?
👂 Listen For
Student finds the distance by subtracting the x-coordinates (7 - 2 = 5) since the points share a horizontal line.
Extend: Push students to explain why we can use absolute value to find distance even if the points were at negative coordinates.
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 pair of treasure locations and find the distance between them.
✍️ Explore Discourse
How did you use coordinates and absolute value to find the distance between two points in the same row or column?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
One point is at (-3, 1) and another is at (4, 1). How does absolute value help you find the distance across zero?
👂 Listen For
Student adds the absolute values (3 + 4 = 7) because the points are on opposite sides of zero.
Extend: Ask students to compare finding distance when both points are on the same side of zero versus opposite sides.
Practice Check A
Two points are at (-3, -7) and (-3, 5). What is the distance between them?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
What is the distance between (2, 3) and (2, 8)?
✍️ 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
Sort each block-distance problem by whether you SUBTRACT (same side of zero) or ADD absolute values (opposite sides of zero).
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: "If points are on the same side of zero, subtract; if they are on opposite sides of zero, add the absolute values." — and it works because ___.
Because Distance means ___, but a tricky part is ___, so I have to ___.
A common mistake with Distance is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Absolute value to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
If points are on the same side of zero, subtract; if they are on opposite sides of zero, add the absolute values. because ___
If points are on the same side of zero, subtract; if they are on opposite sides of zero, add the absolute values. but ___
If points are on the same side of zero, subtract; if they are on opposite sides of zero, add the absolute values. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Plot each pair of treasure locations and find the distance between them.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
What is the distance between (-4, 3) and (2, 3)?
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 drone starts at position (-4, 0) on a grid and needs to deliver a package to (3, 0), then fly to another delivery at (3, -5). It can only fly horizontally or vertically.
✍️ Connection Reasoning
How does the drone use coordinate distance to calculate the total flight path?
The horizontal distance from (-4, 0) to (3, 0) is ___ units because ___. The vertical distance from (3, 0) to (3, -5) is ___ units because ___. The total flight path is ___ units.
Turn & Talk — Connect
Why does distance on the coordinate plane always come out positive, even when the coordinates are negative?
👂 Listen For
Student explains distance is a length (how far apart) and absolute value guarantees a non-negative result.
Extend: Push students to generalize a rule for finding the distance between any two points on the same horizontal or vertical line.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
What is the distance between the points (3, -2) and (3, 5)?
Bonus Exit Check
What is the distance between (-4, 1) and (3, 1)?
✍️ 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 finds the distance by subtracting the x-coordinates (7 - 2 = 5) since the points share a horizontal line.
• Student adds the absolute values (3 + 4 = 7) because the points are on opposite sides of zero.
• Student explains distance is a length (how far apart) and absolute value guarantees a non-negative result.
• Student catches that the classmate ignored the negative sign; correct distance is |6| + |-2| = 8.
Common mistake: A common mistake in Distance on the Coordinate Plane is skipping the key idea: "If points are on the same side of zero, subtract; if they are on opposite sides of zero, add the absolute values." — 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: 12 units — Same x = -3. Distance = |5 - (-7)| = |5 + 7| = 12 units.
✓ Practice 2: 5 units — The x-coordinates match, so distance = |8 - 3| = 5 units.
✓ Practice 3: 7 units — The y-coordinates match, so distance = |3 - (-4)| = 7 units.
✓ Practice 4: 6 units — Both points have y = 3, so this is a horizontal distance. |2 - (-4)| = |2 + 4| = 6 units.
✓ Exit ticket: 7 units — Both points share x = 3, so this is a vertical distance. |5 - (-2)| = |5 + 2| = 7 units.