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

4.4 Small Group · Group 2

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

Visual Models · Percent of a Number · Percent · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do I find the percent of a number?
1Write the percent as a decimal (move the point 2 places left), then multiply it by the base: part = percent × base — 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. The claw machine costs 60 tickets, and it is 25% off. I need 25% of 60.
  2. Step 1 — find the base (the whole): the number after “of” is 60.
  3. Step 2 — the percent as a decimal: 25% means 25 out of 100, so 25 ÷ 100 = 0.25.
  4. Step 3 — multiply: 0.25 × 60 = 15.
  5. The discount is 15 tickets. Check: 15 is about a quarter of 60, so that makes sense.
3Second Model — Try it together — then prove it
  1. Find 40% of 80. Step 1 — what is the base? (80, the number after “of”)
  2. Step 2 — 40% as a decimal? (40 ÷ 100 = 0.40)
  3. Step 3 — multiply: 0.40 × 80 = ? (32)
  4. Does 32 make sense? 40% is a little less than half, and half of 80 is 40. ✓
  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
  • Percent of a Number (Porcentaje de un número) — A part of a number found by multiplying the number by the percent written as a decimal.
  • Percent (Porcentaje) — A way to compare a number to 100, shown with the % sign.
  • Base (Base) — The whole amount you start with — the number right after the word “of.”
  • Part (Parte) — How much of the base (the whole) you get. It is your answer.
  • Equation (Ecuación) — A number sentence with an equal sign. The percent one is: part = percent × base.
  • Discount (Descuento) — Money taken off the first price to make it cheaper.
5Watch out
  • A common mistake in Find the Percent of a Number is multiplying by the percent number itself instead of its decimal form — for example, finding 30% of 80 by computing 30 × 80 = 2,400 instead of 0.30 × 80 = 24. Always divide the percent by 100 to get the decimal, then multiply that decimal by the base.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    What is 20% of 150?

    1. A30
    2. B20
    3. C35
    4. D75
    0%50%100%
    Work
  2. 2 MULTIPLE CHOICE

    An arcade prize costs 240 tickets. If you have a coupon for 15% off, how many tickets do you save?

    1. A36 tickets
    2. B24 tickets
    3. C15 tickets
    4. D204 tickets
    0%50%100%
    Work
  3. 3 MULTIPLE CHOICE

    A student scored 72 out of 90 on a test. What percent did they score?

    1. A80%
    2. B72%
    3. C75%
    4. D90%
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Level 2 Extension — Discount Dash Color-by-Code Error

    1. 1Find 20% of 50:20% of 50
    2. 2Use the percent:Use 20 as the part
    3. 3Write the answer:20% of 50 = 20

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A student scored 72 out of 90 on a test. What percent did they score?
    2. 2A classmate at our table answered:75%

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Find 15% of 60:15% of 60
    2. 2Change the percent to a decimal:15% = 0.15
    3. 3Multiply by the wrong number:0.15 × 15 = 2.25
    4. 4Final answer:15% of 60 = 2.25

    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