6.AT.4 Lesson 4-5-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.5 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Determine the Whole Given the Part and Percent · Part · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — Working backwards to the whole
1Percent × whole = part. When the whole is unknown, divide the part by the percent in decimal form: whole = part ÷ decimal.
  • When you know a part and the percent it represents, the whole is what is missing. A double number line, a ratio table, or an equation will each get you there — the equation is the fastest once you trust it. 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 find the original price of the sweater
  1. Akela paid $42 for a sweater on sale, and that was 60% of the original price. The $42 is the part; the original price is the whole, which is 100%.
  2. On a double number line, I put $42 under 60%. To find a smaller step, I use 10%: if 60% is $42, then 10% is 42 ÷ 6 = $7.
  3. Now I count up to the whole: 100% is ten of those 10% steps, so 10 × $7 = $70.
  4. The equation says the same thing in one move: 0.6 × v = 42, so v = 42 ÷ 0.6 = 70. The original price was $70 — larger than the sale price, which is exactly what a discount should mean.
3Mathematical Word Bank
  • Determine the Whole Given the Part and Percent (Hallar el total dados la parte y el porcentaje) — Working backwards from a part and its percent to find the whole amount it came from.
  • Part (Parte) — The amount you already know — the piece of the whole that the percent describes.
  • Whole (Total) — The full amount the percent is measured against. The whole is always 100%.
  • Double number line (Recta numérica doble) — Two lines lined up — dollars on one, percents on the other — so matching marks show the same amount two ways.
  • Equation (Ecuación) — A math sentence with an equal sign. Here it says percent × whole = part, with the whole unknown.
  • Percent (Porcentaje) — A ratio comparing a number to 100. To compute with it, write it in decimal form: 60% = 0.6.
4Watch out
  • A common mistake when finding the whole is multiplying by the percent instead of dividing. For "$42 is 60% of the original price," computing 0.6 × 42 = $25.20 makes the original price SMALLER than the sale price — impossible for a discount. Since percent × whole = part, the whole is found by dividing: 42 ÷ 0.6 = $70. Whenever the percent is less than 100%, the whole must come out larger than the part, so a smaller answer is the tell.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    Which statement correctly names the pieces of "18 students is 30% of the class"?

    1. A18 is the part, 30% is the percent, the class size is the whole
    2. B18 is the whole, 30% is the part
    3. C30 is the part, 18 is the percent
    4. DThe class size is the part
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    A car is now worth $26,600, which is 70% of its purchase price. What was the purchase price?

    1. A$38,000
    2. B$18,620
    3. C$26,670
    4. D$45,200
    0%50%100%
    Work
    1. 1Whole100% is what number?
    2. 2Find 10%Divide by 10.
    3. 3BuildAdd or multiply to the percent.
    4. 4CheckIs it under or over the whole?
  2. 3 MULTIPLE CHOICE

    $10 is 50% of what number?

    1. A$20
    2. B$5
    3. C$60
    4. D$100
    0%50%100%
    Work
    1. 1Whole100% is what number?
    2. 2Find 10%Divide by 10.
    3. 3BuildAdd or multiply to the percent.
    4. 4CheckIs it under or over the whole?
  3. 4 MULTIPLE CHOICE

    $9 is 25% of what number?

    1. A$36
    2. B$2.25
    3. C$34
    4. D$225
    0%50%100%
    Work
    1. 1Whole100% is what number?
    2. 2Find 10%Divide by 10.
    3. 3BuildAdd or multiply to the percent.
    4. 4CheckIs it under or over the whole?
  4. 5 MULTIPLE CHOICE

    To find the whole from a part and a percent, you…

    1. ADivide the part by the percent in decimal form
    2. BMultiply the part by the percent
    3. CAdd the part and the percent
    4. DSubtract the percent from 100
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Find the error

    1. 1Setup:$42 is 60% of the original price. Find the original price.
    2. 2Step 1:60% = 0.6
    3. 3Step 2:0.6 × 42 = 25.20
    4. 4Step 3:The original price was $25.20.

    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