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

6.3 Small Group · Group 2

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

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 MULTIPLE CHOICE

    Which expression shows 5³ as repeated multiplication?

    1. A5 × 5 × 5
    2. B5 × 3
    3. C5 + 5 + 5
    4. D3 × 3 × 3 × 3 × 3
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    What is the value of 6²?

    1. A36
    2. B12
    3. C62
    4. D8
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A synth pattern repeats 7 × 7 × 7. How do you write that as a power?
    2. 2A classmate at our table answered:21³

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 4 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Expression:2⁴
    2. 2Student's thinking:2 × 4
    3. 3Calculate:= 8

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 5 ERROR ANALYSIS

    Find the Exponent Error

    1. 1Expression:2³
    2. 2Student's thinking:2 × 3
    3. 3Calculate:= 6

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

    ✏️ Corrected Mathematical Work & Explanation
  4. 6 OPEN RESPONSE

    A bacteria colony doubles every hour. Starting with 1 bacterium, write a power expression for the number after 6 hours. Explain why exponential growth is so much faster than adding the same number each hour.

    ✏️ 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