MPP.7 Lesson 10-2-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

10.2 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A symmetric garden design puts the same planting on each side of a center path. One side uses 14 tulips and 9 daisies. How many flowers does the WHOLE symmetric design use?

    1. A46 flowers
    2. B23 flowers
    3. C28 flowers
    4. D126 flowers
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Why do people find symmetry pleasing?

    1. AOur brains are wired to favor balance, and bilateral symmetry provides balance
    2. BSymmetric things are always brightly colored
    3. CSymmetry only appears in rare and expensive objects
    4. DSymmetric shapes are always larger than non-symmetric ones
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    There are over 17,000 species of butterflies, and ALL butterflies have reflective symmetry. About how many of those species have reflective symmetry?

    1. AAll 17,000+ of them
    2. BAbout half of them
    3. COnly the most colorful ones
    4. DNone — symmetry is only in plants
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 OPEN RESPONSE

    You and a friend are studying a building for an art project. The building's left half mirrors its right half. What can you say about the building in terms of bilateral symmetry?

    ✏️ Mathematical Justification & Response
  2. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Which is the best test for whether a figure has bilateral symmetry?
    2. 2A classmate at our table answered:Check whether the figure is found in nature

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 OPEN RESPONSE

    A butterfly's wings are bilaterally symmetric, but if you measured them the two halves would never be EXACTLY identical. Does that mean the butterfly is not symmetric? Write a rule for when 'symmetric' is still a useful description even though the two halves differ, and name one case where the difference would be big enough to matter.

    ✏️ Mathematical Justification & Response
📐 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.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It