MPP.7 Lesson 10-2-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

10.2 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

symmetric · mirror image · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — Math creates beautiful designs in nature
1Bilateral symmetry — two sides that are mirror images — appears throughout nature, and it shapes human creations from art to music to architecture — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
2Worked Example — Watch me find the symmetry in a butterfly
  1. I look at the two sides of the butterfly, and they look like mirror images — the butterfly is symmetric.
  2. All butterflies have reflective symmetry. In plants and animals, this is called bilateral symmetry.
  3. To show it, I draw a line down the middle of the butterfly's body: everything on the left is reflected on the right.
3Second Model — Try it together — then prove it
  1. This plant grows in layers, and each layer is made up of two leaves — so 3 layers hold 3 × 2 = 6 leaves.
  2. In the first layer, one leaf is a mirror image of the other.
  3. To show the bilateral symmetry in the second layer, we draw a line down the middle of the layer, along the center of each leaf.
  4. Are the leaves EXACTLY symmetric? Nature comes close, but living things are never perfectly identical.
  5. Now prove it: say why that move had to work at all — not just that it did.
  6. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • symmetric (simétrico) — Having two halves that match — one side is a mirror image of the other.
  • mirror image (imagen reflejada) — A copy of a figure flipped across a line, so the two halves face each other.
  • bilateral symmetry (simetría bilateral) — Reflective symmetry in plants and animals — the two sides of the body mirror each other.
  • line of symmetry (eje de simetría) — The line you can draw through a figure so each side is a reflection of the other.
  • balance (equilibrio) — An even, steady arrangement — neither side feels heavier than the other.
5Watch out
  • Thinking a figure lacks bilateral symmetry just because its line of symmetry is not vertical — the mirror line can run in any direction, and the test is whether the two sides match across it.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    How many lines of symmetry does each figure have?

    FigureThink about the foldsLines of symmetry
    Square
    Rectangle (not a square)
    Equilateral triangle
    The letter H
    ✏️ Scratchpad / Reasoning
  2. 2 MATCHING GAME

    Match each transformation idea to its description.

    1. Reflection
    2. Rotation
    3. Translation
    4. Rotational symmetry
    • AFlip across a mirror line
    • BTurn around a center point
    • CSlide without turning or flipping
    • DFits onto itself in less than a full turn
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    Which is the best test for whether a figure has bilateral symmetry?

    1. AFind a line where one side is the mirror image of the other
    2. BCheck whether the figure has an even number of parts
    3. CCheck whether the figure is found in nature
    4. DCheck whether the figure looks beautiful to you
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    Your friend insists that only ONE of two flowers has bilateral symmetry, but both pass the mirror-image test — just across lines pointing in different directions. What is the best response?

    1. ABoth flowers have bilateral symmetry — a line of symmetry does not have to point the same direction in every figure
    2. BYour friend is right, because a real line of symmetry must always be vertical
    3. CNeither flower has bilateral symmetry, because flowers are not animals
    4. DAgree with your friend, because two people should not disagree about math
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 OPEN RESPONSE

    Where else do you see bilateral symmetry — in nature OR in something humans made?

    ✏️ Mathematical Justification & Response
  2. 6 OPEN RESPONSE

    The lesson says bilateral symmetry influences human creations 'from art to music to architecture.' Pick ONE of those three and describe how symmetry appears in it.

    ✏️ Mathematical Justification & Response
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The mathematical model proves the solution because each step preserves quantitative equivalence.
BUT An estimate provides a quick benchmark, but an exact proof is required for precision.
SO The quantities follow the standard rule, so the final result is verified with certainty.
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It