Explore symmetry, structure, and visual beauty through coordinate
plane reflections, geometric patterns, and area of artistic designs.
6.GR · 6.NOS
Level
Guided practice with vocabulary support
🟠 Level 0 — Extra Support
Watch first: the worked example and hints are already shown for you.
One at a time: answer one question, check it, then go on.
Read aloud: press 🔊 Read aloud, then click any sentence to hear it.
Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
W
Warm-Up
2 questions
Warm-Up 1
Point A is at (3, 4) on the coordinate plane. What is
the reflection of A across the y-axis?
Vocabulary: A
reflection across the y-axis flips the
point horizontally. The x-coordinate changes sign; the y-coordinate
stays the same.
✓Correct! Reflecting across the y-axis changes the sign of x: (3, 4)
becomes (−3, 4).
✗Reflecting across the y-axis flips the x-coordinate: (3, 4) becomes
(−3, 4) (A).
Warm-Up 2
A square tile has a side length of 6 inches. What is
the area of the tile?
Hint: The area of a square
= side × side.
Area =square inches
✓Correct! 6 × 6 = 36 square inches.
✗Area of a square = side × side = 6 × 6 =
36 square inches.
P
Practice
5 questions
Practice 1
An artist draws a triangle with vertices at (1, 1),
(5, 1), and (3, 5). What is the area
of the triangle?
Strategy: The base goes from (1,1) to (5,1), so the
base = 4 units. The height goes from y = 1 to y = 5, so the height = 4
units. Area of a triangle = ½
× base × height.
Show your area calculation:
Sentence frame: "The base is ___ units and the height is ___ units.
Area = ½ × ___ × ___ = ___ square units."
✓Correct! Base = 4, height = 4. Area = ½ × 4 × 4
= 8 square units.
✗Base = 4, height = 4. Area = ½ × 4 × 4 =
8 square units (A).
Practice 2
Point B is at (−2, 5). What is the
reflection of B across the x-axis?
Hint: Reflecting across the
x-axis changes the sign of the
y-coordinate. The x-coordinate stays the same.
Explain the rule you used:
Sentence frame: "Reflecting across the x-axis changes the ___ sign.
So (−2, 5) becomes (___, ___)."
✓Correct! Reflecting across the x-axis: (−2, 5) becomes
(−2, −5).
✗Reflecting across the x-axis changes the y-sign: (−2, 5)
becomes (−2, −5) (B).
Practice 3
Sort each shape property into whether it relates to
Symmetry or Area.
Remember:Symmetry = balanced, mirror-image
properties. Area = how much space a shape
covers.
A butterfly's wings are mirror images
The floor is 120 square feet
Both halves of the design are identical
Base × height = 24 cm²
Folding along the center lines up perfectly
The garden covers 50 square meters
Symmetry
Area
✓All correct! Symmetry is about mirror images and balance. Area is
about the space a shape covers.
✗Some items are in the wrong group. Think: does it describe a
mirror/balance property, or how much space? Try again!
Practice 4
A mosaic design uses a parallelogram with a base of
10 cm and a height of 7 cm. What is
its area?
Formula:Area of parallelogram = base ×
height.
Area =cm²
Show your work:
Sentence frame: "Area = ___ × ___ = ___ cm²."
✓Correct! 10 × 7 = 70 cm².
✗Area of a parallelogram = base × height = 10 × 7 =
70 cm².
Practice 5
Two points are at (−4, 3) and
(−4, −2). What is the
distance between them?
Hint: Both points share the same x-coordinate, so the
distance is the difference of the y-coordinates. Use
absolute value: |3 − (−2)|.
Show how you found the distance:
Sentence frame: "The y-coordinates are ___ and ___. The distance is
|___ − ___| = ___ units."
✓Correct! |3 − (−2)| = |3 + 2| = 5 units.
✗|3 − (−2)| = |5| = 5 units (C).
★
Challenge
1 question
Challenge
An artist creates a symmetric design. One half contains a triangle
with vertices at (1, 0), (4, 0), and
(4, 6). The design is reflected across the y-axis.
What is the total area of both triangles combined?
Strategy: First find the area of one triangle (base =
3, height = 6). A reflection creates an identical triangle, so double
the area for the total.
Total area =square units
Show your complete reasoning:
Sentence frame: "One triangle has base ___ and height ___, so its
area is ½ × ___ × ___ = ___. Two triangles = ___
× 2 = ___ square units."
✓Correct! One triangle: ½ × 3 × 6 = 9. Reflected
copy is identical: 9 + 9 = 18 square units total.
✗One triangle: ½ × 3 × 6 = 9. Both triangles: 9
× 2 = 18 square units.