6.AT.6c Lesson 6-4-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.4 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · 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:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — 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.
  • A numerical expression is a math phrase made of numbers and operations, with no equal sign. Writing one for a whole situation keeps every part visible; evaluating it means finding its single value, following the order of operations. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
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.
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 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 1 MULTIPLE CHOICE

    Evaluate 6 + 2 × 5.

    1. A16
    2. B40
    3. C13
    4. D30
    Show each partial product, then add them
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.
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
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.
  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
  3. 4 MULTIPLE CHOICE

    Evaluate 4².

    1. A16
    2. B8
    3. C6
    4. D44
    Rewrite the whole expression each lineWhat I simplified
    1. 1GroupingInside ( ) first.
    2. 2ExponentsThen powers.
    3. 3× ÷Left to right.
    4. 4+ −Left to right.
  4. 5 MULTIPLE CHOICE

    Which is a numerical expression?

    1. A8 × 3 + 2
    2. B8 × 3 = 24
    3. Cx + 5
    4. D24
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Find the error

    1. 1Expression:Evaluate 3 + 4 × 2²
    2. 2Step 1:3 + 4 = 7
    3. 3Step 2:7 × 2² = 7 × 4 = 28

    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
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