Reflect Points Across Axes
I can reflect points across the x-axis and y-axis on the coordinate plane.
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🎯 Content Objective / Objetivo de contenido
I can reflect points across the x-axis and y-axis on 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
When you reflect the point (3, 2) over the y-axis, which coordinate changes its sign and which stays the same? Why?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Mirror Images on the Map
Captain Vega discovers that her treasure map has a magic mirror trick! When she folds the map along the x-axis, some clues match up perfectly with clues on the other side. For example, a marker at (2, 4) has a matching marker at (2, -4) when reflected over the x-axis. Another pair reflects over the y-axis: (5, 3) and (-5, 3). How does reflection change the coordinates?
Concept Launch
💡 How do you reflect a point across an axis?
A reflection is a flip of a point over a line, like a mirror image. The axis you flip over decides which coordinate changes its sign.
Reflect over the x-axis: the y-coordinate changes sign. Reflect over the y-axis: the x-coordinate changes sign.
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 |
|---|---|---|---|
| Reflection Reflexión |
A flipped image of a point on the other side of a line, the same distance away. Una imagen volteada de un punto al otro lado de una línea, a la misma distancia. |
(3, 2) reflected over the y-axis becomes (-3, 2) — x changes sign, y stays | |
| x-axis Eje x |
The line that goes across the grid. Flipping over it changes the y sign. La línea que va de lado en la cuadrícula. Voltear sobre ella cambia el signo de y. |
(4, 3) → (4, -3): the y flips from +3 to -3, like folding the paper along the horizontal line | |
| y-axis Eje y |
The line that goes up the grid. Flipping over it changes the x sign. La línea que va hacia arriba en la cuadrícula. Voltear sobre ella cambia el signo de x. |
(4, 3) → (-4, 3): the x flips from +4 to -4, like folding the paper along the vertical line | |
| Symmetry Simetría |
When a shape looks the same on both sides of a line. Cuando una figura se ve igual a ambos lados de una línea. |
A butterfly's wings are symmetric — fold it down the middle and both sides match | |
| 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?
A flip of a point or shape over an axis to make a mirror image 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
When you reflect the point (3, 2) over the y-axis, which coordinate changes its sign and which stays the same? Why?
👂 Listen For
Student states reflecting over the y-axis flips the sign of the x-coordinate while the y-coordinate stays the same, so (3,2) becomes (-3,2).
Extend: Push students to explain why the reflected point is the same distance from the y-axis as the original.
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 original point and then plot its reflection across the given axis.
✍️ Explore Discourse
What pattern do you notice about the coordinates when reflecting over the x-axis versus the y-axis?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
Reflect (4, -5) over the x-axis. Talk through how the coordinates change and where the new point lands.
👂 Listen For
Student flips the sign of the y-coordinate, so (4, -5) becomes (4, 5), and explains the x stays the same.
Extend: Ask students to predict where (4, -5) lands if reflected over the y-axis instead, and compare the two results.
Practice Check A
Point A is at (-3, 5). It is reflected over the x-axis to A', then A' is reflected over the y-axis to A''. What are the coordinates of A''?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
What is the reflection of (4, -3) over the x-axis?
✍️ 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 fold by which coordinate rule it follows on Vega's 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: "Reflect over the x-axis: the y-coordinate changes sign. Reflect over the y-axis: the x-coordinate changes sign." — and it works because ___.
Because Reflection means ___, but a tricky part is ___, so I have to ___.
A common mistake with Reflection is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using x-axis to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Reflect over the x-axis: the y-coordinate changes sign. Reflect over the y-axis: the x-coordinate changes sign. because ___
Reflect over the x-axis: the y-coordinate changes sign. Reflect over the y-axis: the x-coordinate changes sign. but ___
Reflect over the x-axis: the y-coordinate changes sign. Reflect over the y-axis: the x-coordinate changes sign. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Plot each original point and then plot its reflection across the given axis.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
What is the reflection of (4, -3) over the x-axis?
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 game designer creates a spaceship at (3, 2) and wants to place enemy ships as reflections to make the level symmetric. One enemy is reflected over the y-axis, and another is reflected over the x-axis.
✍️ Connection Reasoning
How do reflections help the game designer create a balanced, symmetric level?
The enemy reflected over the y-axis is at ___ because ___. The enemy reflected over the x-axis is at ___ because ___. Reflections help game designers because ___.
Turn & Talk — Connect
How is reflecting a point over an axis like looking at it in a mirror placed on that axis?
👂 Listen For
Student connects the axis to a mirror line and the reflected point to a mirror image, equal distance on the opposite side.
Extend: Push students to generalize a rule: what changes when you reflect over the x-axis versus the y-axis?
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
What is the reflection of (-5, 2) over the y-axis?
Bonus Exit Check
What is the reflection of (-2, 6) over the y-axis?
✍️ 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 states reflecting over the y-axis flips the sign of the x-coordinate while the y-coordinate stays the same, so (3,2) becomes (-3,2).
• Student flips the sign of the y-coordinate, so (4, -5) becomes (4, 5), and explains the x stays the same.
• Student connects the axis to a mirror line and the reflected point to a mirror image, equal distance on the opposite side.
• Student identifies they flipped x instead of y; the correct image over the x-axis is (2, -3).
Common mistake: A common mistake in Reflect Points Across Axes is skipping the key idea: "Reflect over the x-axis: the y-coordinate changes sign. Reflect over the y-axis: the x-coordinate changes sign." — 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, -5) — Over x-axis: (-3, 5) → (-3, -5). Then over y-axis: (-3, -5) → (3, -5). Both coordinates changed sign.
✓ Practice 2: (4, 3) — Reflecting over the x-axis changes the sign of the y-coordinate. The x stays the same (4), and the y changes from -3 to 3. The answer is (4, 3).
✓ Practice 3: (2, 6) — Reflecting over the y-axis changes the sign of the x-coordinate. x goes from -2 to 2, and y stays 6. The answer is (2, 6).
✓ Practice 4: (0, 5) — Points on the y-axis have x-coordinate = 0. (0, 5) is on the y-axis.
✓ Exit ticket: (5, 2) — Reflecting over the y-axis changes the sign of the x-coordinate. x goes from -5 to 5, and y stays 2. The reflection is (5, 2).