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

6.4 Small Group · Group 2

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

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 FILL TABLE

    Sofia buys 2 member tickets ($15), 4 non-member tickets ($20), and 8 student tickets (2³ dollars). Build the total.

    Ticket typeExpressionCost
    Member
    Non-member
    Student
    ✏️ Scratchpad / Reasoning
  2. 2 DRAG SORT

    Sort each item into the stage of the order of operations where it is handled.

    Target Categories: Grouping symbols Exponents Multiply / divide Add / subtract
    • ( )
    • 2³
    • × and ÷ left to right
    • + and − left to right
    • [ ]
    • 5²
SECTION 2 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 3 MULTIPLE CHOICE

    Evaluate 6 + 2 × 5.

    1. A16
    2. B40
    3. C13
    4. D30
    Show each partial product, then add them
  2. 4 MULTIPLE CHOICE

    Evaluate 3 + 4 × 2.

    1. A11
    2. B14
    3. C24
    4. D9
    Show each partial product, then add them
SECTION 3 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 5 MULTIPLE CHOICE

    Evaluate 4².

    1. A16
    2. B8
    3. C6
    4. D44
    Rewrite the whole expression each lineWhat I simplified
  2. 6 MULTIPLE CHOICE

    Which is a numerical expression?

    1. A8 × 3 + 2
    2. B8 × 3 = 24
    3. Cx + 5
    4. D24
    ✏️ Workspace & Solution Steps
🗣️ 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