6.AT.4 Lesson 4-5-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.5 Small Group · Group 2

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

Visual Models · Determine the Whole Given the Part and Percent · Part · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — 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 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.
3Second Model — Try it together — then prove it
  1. Sheng's car is now worth $26,600, which is 70% of what his parents paid for it. Find the original price.
  2. Name the pieces first: $26,600 is the part, 70% is the percent, and the purchase price is the unknown whole.
  3. Write the percentage statement as an equation, using the decimal form: 0.7v = 26,600.
  4. Solve by dividing both sides by 0.7: v = 26,600 ÷ 0.7 = 38,000. The car cost $38,000 when they bought it.
  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
  • 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.
5Watch 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

    Which equation says "30 is 25% of some number n"?

    1. A0.25n = 30
    2. B25n = 30
    3. Cn = 0.25 × 30
    4. Dn = 30 + 25
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    $42 is 60% of the original price. Should the original price be more or less than $42?

    1. AMore, because 60% is less than the whole
    2. BLess, because 60 is a big number
    3. CExactly $42
    4. DYou cannot tell
    ✏️ Workspace & Solution Steps
  3. 4 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
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:$42 is 60% of the original price. Should the original price be more or less than $42?
    2. 2A classmate at our table answered:Less, because 60 is a big number

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Find the error

    1. 1Setup:18 students is 30% of the class. How many students are in the class?
    2. 2Step 1:30% = 0.3
    3. 3Step 2:18 ÷ 0.3 = 60
    4. 4Step 3:There are 60% of students in the class.

    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