6.AT.5 Lesson 6-3-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.3 Small Group · Group 2

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

Powers and Exponents · Exponent · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What does an exponent mean?
1A power like 2³ is a short way to write repeated multiplication: 2 × 2 × 2 — 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
  1. I want to find the value of 2³.
  2. The small 3 tells me to multiply 2 by itself 3 times.
  3. So I write 2 × 2 × 2.
  4. First 2 × 2 = 4. Then 4 × 2 = 8.
  5. So 2³ = 8.
3Second Model — Try it together — then prove it
  1. Now let's find 5². How many times do we multiply 5 by itself?
  2. The exponent is 2, so we write 5 × 5.
  3. What is 5 × 5? Yes, 25. So 5² = 25.
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • Powers and Exponents (Potencias y exponentes) — A power uses a base and an exponent to show repeated multiplication.
  • Exponent (Exponente) — A small number that tells how many times to multiply a number by itself.
  • Base (Base) — The number that gets multiplied by itself.
  • Power (Potencia) — A number written with a base and an exponent, like 2³.
  • Evaluate (Evaluar) — To find the value by putting numbers in for the letters.
5Watch out
  • A common mistake in Powers and Exponents is multiplying the base by the exponent instead of using the base as a repeated factor — for example, thinking 2³ = 2 × 3 = 6 instead of 2³ = 2 × 2 × 2 = 8. Before you submit, rewrite the power as repeated multiplication first, then multiply step by step.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Evaluate each exponential expression. Show the repeated multiplication and the final value.

    PowerRepeated MultiplicationValue
    4³
    2⁶
    5³
    10⁴
    ✏️ Scratchpad / Reasoning
  2. 2 DRAG SORT

    Sort each power by whether its value is greater than 50 or not.

    Target Categories: Value > 50 Value ≤ 50
    SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
    1. 3 MULTIPLE CHOICE

      A synth pattern repeats 7 × 7 × 7. How do you write that as a power?

      1. A7³
      2. B3⁷
      3. C7 × 3
      4. D21³
      ✏️ Workspace & Solution Steps
    2. 4 MULTIPLE CHOICE

      The bass line doubles for 2⁶ counts. What is the value of 2⁶?

      1. A64
      2. B12
      3. C32
      4. D36
      ✏️ Workspace & Solution Steps
    3. 5 MULTIPLE CHOICE

      What is the value of 4³?

      1. A64
      2. B12
      3. C43
      4. D7
      ✏️ Workspace & Solution Steps
    SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
    1. 6 ERROR ANALYSIS

      Level 2 Extension — Spot the Beat-Builder Bug

      1. 1Track says:Play 3⁴ beats
      2. 2Producer's thinking:3 × 4
      3. 3Calculate:= 12

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

      ✏️ Corrected Mathematical Work & Explanation
    🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

    Group Discussion Prompt: How does your visual model justify your mathematical solution?

    🗣️ Partner A:
    Partner A: "I modeled this by identifying the relationship and..."
    👂 Partner B:
    Partner B: "I agree with your step because the standard mathematical rule states..."
    ✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

    Complete each sentence stem to demonstrate precise mathematical reasoning:

    BECAUSE The ratio remains equivalent because both quantities are scaled by the exact same multiplicative factor.
    BUT Two ratios may look similar, but inverting the order of terms fundamentally changes the comparison.
    SO The recipe requires 3 parts flour to 2 parts water, so the unit rate is 1.5 cups of flour per cup of water.
    📐 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