6.AT.4 Lesson 4-5-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.5 · Part II

Supported Application · Guided Entry to Today's Problem

Determine the Whole Given the Part and Percent · Part

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 4.5 · Part II
1Finding the Whole Given Part & Percent
2Strategy Model — step by step
  1. Identify the given part and the percentage it represents
  2. Convert the percent to a decimal or fraction
  3. Divide the part by the percent decimal to find the total whole (100%)
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%
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 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?
  2. 3 MULTIPLE CHOICE

    (Lesson 4.4) What is 20% of 150?

    1. A30
    2. B20
    3. C35
    4. D75
    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?
📐 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
6.AT.4 Lesson 4-5-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.5 · Part II

On-Level Application · Standard Rigor

Determine the Whole Given the Part and Percent · Part

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 4.5 · Part II
1Finding the Whole Given Part & Percent
2The Structural Procedure
  1. Identify the given part and the percentage it represents
  2. Convert the percent to a decimal or fraction
  3. Divide the part by the percent decimal to find the total whole (100%)
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
  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
📐 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
6.AT.4 Lesson 4-5-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.5 · Part II

Extension & Non-Routine Application

Determine the Whole Given the Part and Percent · Part

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 4.5 · Part II
1Finding the Whole Given Part & Percent
2The Structural Procedure
  1. Identify the given part and the percentage it represents
  2. Convert the percent to a decimal or fraction
  3. Divide the part by the percent decimal to find the total whole (100%)
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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Marcus completed 18 math problems, which represents exactly 60% of his homework assignment. How many total problems are on the assignment?

    1. A30 problems
    2. B28 problems
    3. C24 problems
    4. D36 problems
    0%50%100%
    Work
  2. 2 MULTIPLE CHOICE

    A shop reports that this week's $60 in sales is 120% of last week's. Was last week better or worse, and by how much?

    1. AWorse — last week was $50, so sales rose by $10
    2. BBetter — last week was $72, so sales fell
    3. CWorse — last week was $48
    4. DYou cannot tell without knowing the number of items sold
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 OPEN RESPONSE

    A toy store's puzzle stock was 25% 300-piece, 15% 500-piece, and the rest 1,000-piece. During a sale the store sold ALL of its 300-piece and 500-piece puzzles — 120 puzzles in total. How many of each type did the store have before the sale? Explain your reasoning.

    ✏️ Mathematical Justification & Response
📐 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