6.AT.6c Lesson 6-4-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.4 · Part II

Supported Application · Guided Entry to Today's Problem

Write and Evaluate Numerical Expressions with Exponents · Numerical expression

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 6.4 · Part II
1Order of Operations (PEMDAS)
2Strategy Model — step by step
  1. Grouping Symbols: Parentheses, brackets, fraction bars inner to outer
  2. Exponents: Evaluate all powers
  3. Multiply & Divide left to right; Add & Subtract left to right
3Mathematical 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.
4Watch 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.
  1. 1 MULTIPLE CHOICE

    Evaluate 5² + 3.

    1. A28
    2. B13
    3. C16
    4. D64
    Rewrite the whole expression each lineWhat I simplified
    1. 1GroupingInside ( ) first.
    2. 2ExponentsThen powers.
    3. 3× ÷Left to right.
    4. 4+ −Left to right.
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It
6.AT.6c Lesson 6-4-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.4 · Part II

On-Level Application · Standard Rigor

Write and Evaluate Numerical Expressions with Exponents · Numerical expression

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.4 · Part II
1Order of Operations (PEMDAS)
2The Structural Procedure
  1. Grouping Symbols: Parentheses, brackets, fraction bars inner to outer
  2. Exponents: Evaluate all powers
  3. Multiply & Divide left to right; Add & Subtract left to right
3Mathematical 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.
4Watch 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 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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 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. 3 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
📐 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
6.AT.6c Lesson 6-4-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.4 · Part II

Extension & Non-Routine Application

Write and Evaluate Numerical Expressions with Exponents · Numerical expression

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.4 · Part II
1Order of Operations (PEMDAS)
2The Structural Procedure
  1. Grouping Symbols: Parentheses, brackets, fraction bars inner to outer
  2. Exponents: Evaluate all powers
  3. Multiply & Divide left to right; Add & Subtract left to right
3Mathematical 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.
4Watch 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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Evaluate the numerical expression 3 × 4² − 8.

    1. A40
    2. B136
    3. C16
    4. D24
    Show each partial product, then add them
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 OPEN RESPONSE

    Seven friends split the bill for a pizza party. They order 4 pizzas at 3² dollars each, plus a one-time $6 delivery fee. Write ONE numerical expression for what each friend owes, evaluate it, and explain why the grouping symbols 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