6.AT.4 Lesson 4-1-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.1 · Part II

Supported Application · Guided Entry to Today's Problem

Understand Percent · Percent

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 4.1 · Part II
1Understanding Percent
2Strategy Model — step by step
  1. Percent means 'per hundred' (% = /100)
  2. On a 100-grid, each square represents 1% = 0.01 = 1/100
  3. Fraction to Percent: Scale fraction to a denominator of 100
3Mathematical Word Bank
  • Understand Percent (Comprender el porcentaje) — A percent is a ratio that compares a number to 100, so every percent answers the question “how many out of 100?”
  • Percent (Porcentaje) — A ratio that compares a number to 100. The word means “per hundred,” and the symbol is %.
  • Per hundred (Por cada cien) — The meaning hidden inside the word percent: for every group of 100. It is why every percent can be written as a fraction over 100.
  • Decimal grid (Cuadrícula decimal) — A 10-by-10 grid of 100 squares. Shading squares shows a percent directly, one square per percent.
  • Part-to-whole (Parte a todo) — A comparison of one part against the whole amount. In a percent, the whole is always 100%.
  • Greater than 100% (Mayor que 100 %) — More than one whole. A percent above 100 means the amount is larger than the thing it is being compared to.
4Watch out
  • A common mistake with percent is scaling only one term of the ratio: reading 7 out of 10 as 7%. A percent compares to 100, so BOTH terms must be multiplied by the same factor — 10 × 10 = 100, so 7 × 10 = 70, giving 70%. Reading it as 7% describes seats that are nearly empty when they are nearly full. A second mistake is treating a percent as an amount: 150% of a 200-point goal is 1.5 × 200 = 300 points, not 150 points.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each percent by how it compares to one whole.

    Target Categories: Less than one whole More than one whole
    • 45%
    • 150%
    • 99%
    • 200%
    • 0.5%
    • 101%
  2. 2 MATCHING GAME

    Match each comparison to its percent.

    1. 4 out of 10
    2. 23 out of 100
    3. 1.5 times the whole
    4. the whole itself
    • A40%
    • B23%
    • C150%
    • D100%
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    Which percent means MORE than one whole?

    1. A120%
    2. B100%
    3. C80%
    4. D0.8%
    ✏️ Workspace & Solution Steps
📐 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 4-1-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.1 · Part II

On-Level Application · Standard Rigor

Understand Percent · Percent

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 4.1 · Part II
1Understanding Percent
2The Structural Procedure
  1. Percent means 'per hundred' (% = /100)
  2. On a 100-grid, each square represents 1% = 0.01 = 1/100
  3. Fraction to Percent: Scale fraction to a denominator of 100
3Mathematical Word Bank
  • Understand Percent (Comprender el porcentaje) — A percent is a ratio that compares a number to 100, so every percent answers the question “how many out of 100?”
  • Percent (Porcentaje) — A ratio that compares a number to 100. The word means “per hundred,” and the symbol is %.
  • Per hundred (Por cada cien) — The meaning hidden inside the word percent: for every group of 100. It is why every percent can be written as a fraction over 100.
  • Decimal grid (Cuadrícula decimal) — A 10-by-10 grid of 100 squares. Shading squares shows a percent directly, one square per percent.
  • Part-to-whole (Parte a todo) — A comparison of one part against the whole amount. In a percent, the whole is always 100%.
  • Greater than 100% (Mayor que 100 %) — More than one whole. A percent above 100 means the amount is larger than the thing it is being compared to.
4Watch out
  • A common mistake with percent is scaling only one term of the ratio: reading 7 out of 10 as 7%. A percent compares to 100, so BOTH terms must be multiplied by the same factor — 10 × 10 = 100, so 7 × 10 = 70, giving 70%. Reading it as 7% describes seats that are nearly empty when they are nearly full. A second mistake is treating a percent as an amount: 150% of a 200-point goal is 1.5 × 200 = 300 points, not 150 points.
  1. 1 MULTIPLE CHOICE

    The orange kitten weighs 1.5 times as much as the gray kitten. What percent of the gray kitten's weight is that?

    1. A150%
    2. B15%
    3. C50%
    4. D1.5%
    0%50%100%
    Work
  2. 2 MULTIPLE CHOICE

    What percent is 9 out of 100?

    1. A9%
    2. B90%
    3. C0.9%
    4. D19%
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Which is exactly one whole?

    1. A100%
    2. B50%
    3. C10%
    4. D1%
    ✏️ Workspace & Solution Steps
📐 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 4-1-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.1 · Part II

Extension & Non-Routine Application

Understand Percent · Percent

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 4.1 · Part II
1Understanding Percent
2The Structural Procedure
  1. Percent means 'per hundred' (% = /100)
  2. On a 100-grid, each square represents 1% = 0.01 = 1/100
  3. Fraction to Percent: Scale fraction to a denominator of 100
3Mathematical Word Bank
  • Understand Percent (Comprender el porcentaje) — A percent is a ratio that compares a number to 100, so every percent answers the question “how many out of 100?”
  • Percent (Porcentaje) — A ratio that compares a number to 100. The word means “per hundred,” and the symbol is %.
  • Per hundred (Por cada cien) — The meaning hidden inside the word percent: for every group of 100. It is why every percent can be written as a fraction over 100.
  • Decimal grid (Cuadrícula decimal) — A 10-by-10 grid of 100 squares. Shading squares shows a percent directly, one square per percent.
  • Part-to-whole (Parte a todo) — A comparison of one part against the whole amount. In a percent, the whole is always 100%.
  • Greater than 100% (Mayor que 100 %) — More than one whole. A percent above 100 means the amount is larger than the thing it is being compared to.
4Watch out
  • A common mistake with percent is scaling only one term of the ratio: reading 7 out of 10 as 7%. A percent compares to 100, so BOTH terms must be multiplied by the same factor — 10 × 10 = 100, so 7 × 10 = 70, giving 70%. Reading it as 7% describes seats that are nearly empty when they are nearly full. A second mistake is treating a percent as an amount: 150% of a 200-point goal is 1.5 × 200 = 300 points, not 150 points.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A robotics club had a fundraising goal of $500. By Friday, they collected $750. What percent of their goal did they achieve?

    1. A150%
    2. B75%
    3. C125%
    4. D50%
    0%50%100%
    Work
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 OPEN RESPONSE

    A car dealership sold 50 cars last month: 20 sedans, 15 SUVs, 10 trucks, and 5 vans. The owner will order 100 cars for next month and wants the order to match last month's sales pattern. Write each type as a percent, then say how many of each to order — and explain why percents make this easier than the raw counts.

    ✏️ 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