6.AT.6c Lesson 6-4-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.4 Small Group · Group 2

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

Write and Evaluate Numerical Expressions with Exponents · Numerical expression · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — Write the expression, then evaluate it in order
1Evaluate in this order: grouping symbols, then powers, then multiplication and division left to right, then addition and subtraction left to right — 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 price the theater order
  1. Sofia buys 2 member tickets at $15, 4 non-member tickets at $20, and 8 student tickets at $2 each. I write one expression for each ticket type: 2 × 15, 4 × 20, and 8 × 2.
  2. The whole order is the three costs added together: 2 × 15 + 4 × 20 + 8 × 2.
  3. Now I evaluate. There are no grouping symbols and no powers yet, so multiplication comes first, left to right: 30 + 80 + 16.
  4. Then I add: 30 + 80 + 16 = 126. The tickets cost $126.
3Second Model — Try it together — then prove it
  1. Suppose the student tickets cost 2³ dollars each instead of $2. The expression becomes 2 × 15 + 4 × 20 + 8 × 2³.
  2. Powers come before multiplying, so evaluate 2³ first: 2 × 2 × 2 = 8.
  3. Now multiply, left to right: 30 + 80 + 64.
  4. Then add: 30 + 80 + 64 = 174. The order now costs $174.
  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
  • Write and Evaluate Numerical Expressions with Exponents (Escribir y evaluar expresiones numéricas con exponentes) — Turning a situation into a number sentence without an equal sign, then finding its value in the correct order.
  • Numerical expression (Expresión numérica) — A math phrase built from numbers and operations, with no equal sign and no variable.
  • Evaluate (Evaluar) — To find the single value an expression is worth by carrying out its operations in order.
  • Order of operations (Orden de las operaciones) — The agreed order for evaluating: grouping symbols, then exponents, then multiply and divide left to right, then add and subtract left to right.
  • Power (Potencia) — A short way to write repeated multiplication of the same factor, such as 2³ for 2 × 2 × 2.
  • Base (Base) — In a power, the number being multiplied by itself. In 2³ the base is 2.
5Watch out
  • A common mistake with powers is multiplying the base by the exponent: reading 3² as 3 × 2 = 6 instead of 3 × 3 = 9. A second is evaluating strictly left to right, so 3 + 4 × 2 becomes 14 instead of 11. The order of operations exists so one expression has exactly one value: grouping symbols, then powers, then × and ÷ left to right, then + and − left to right.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    What does 2³ mean?

    1. A2 × 2 × 2
    2. B2 × 3
    3. C3 × 3
    4. D2 + 2 + 2
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Sofia buys 4 tickets at $20 each and 2 tickets at $15 each. Which expression shows the total?

    1. A4 × 20 + 2 × 15
    2. B4 + 20 + 2 + 15
    3. C(4 + 2) × (20 + 15)
    4. D4 × 2 + 20 × 15
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    What is the total of 2 × 15 + 4 × 20 + 8 × 2³?

    1. A174
    2. B126
    3. C210
    4. D1,392
    Show each partial product, then add them
  2. 4 MULTIPLE CHOICE

    Miguel evaluates 12 − 2 × 3 and gets 30. Margaret gets 6. Who is right?

    1. AMargaret, because multiplication comes before subtraction
    2. BMiguel, because he worked left to right
    3. CBoth are right
    4. DNeither is right
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Evaluate 4².
    2. 2A classmate at our table answered:8

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Find the error

    1. 1Expression:Evaluate 20 − 3²
    2. 2Step 1:3² = 6
    3. 3Step 2:20 − 6 = 14

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

    ✏️ Corrected Mathematical Work & Explanation
📐 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