6.AT.4 Lesson 4-5-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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4.5 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 DRAG SORT

    Sort each number by the role it plays in "$42 is 60% of the original price."

    Target Categories: The part The percent The unknown whole
    • $42
    • 60%
    • the original price
    • the amount Akela paid
    • 0.6
    • 100%
  2. 2 FILL TABLE

    $42 is 60% of the original price. Complete the ratio table to reach 100%.

    PercentDollars
    60%
    10%
    100%
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    $20 is 50% of what number?

    1. A$40
    2. B$10
    3. C$25
    4. D$70
    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. 4 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
  3. 5 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
  4. 6 MULTIPLE CHOICE

    75 minutes is 15% of the school day. How long is the school day?

    1. A500 minutes
    2. B11.25 minutes
    3. C90 minutes
    4. D1,125 minutes
    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?
🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."
👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The ratio remains equivalent because both quantities are scaled by the exact same multiplicative factor.
BUT Two ratios may look similar, but inverting the order of terms fundamentally changes the comparison.
SO The recipe requires 3 parts flour to 2 parts water, so the unit rate is 1.5 cups of flour per cup of water.
📐 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