6.AT.4 Lesson 4-1-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.1 Small Group · Group 2

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

Understand Percent · Percent · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What a percent really says
1A percent is a ratio comparing a number to 100. The whole is always 100%, so a percent above 100 means MORE than one whole — 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 turn a vote into a percent
  1. Students voted on a mascot, and 4 out of every 10 voters chose the tiger. I want to know how many that is out of 100.
  2. "4 out of every 10" is a ratio, so I write an equivalent ratio with 100 as the second term. Multiplying both terms by 10 gives 40 out of 100.
  3. On a decimal grid of 100 squares, I shade 40 squares — one square for each percent.
  4. 40 out of 100 is written 40%. So 40% of the students voted for the tiger.
3Second Model — Try it together — then prove it
  1. Shanice's gray kitten weighs 4 ounces. The orange kitten weighs 1.5 times as much. What percent of the gray kitten's weight is the orange kitten's weight?
  2. The gray kitten is the whole, so its weight is 100%.
  3. Draw a tape diagram: one full tape is 100%. The orange kitten needs 1.5 tapes — one whole tape plus half of another.
  4. One whole is 100% and half a whole is 50%, so 100% + 50% = 150%. The orange kitten weighs 150% of the gray kitten's weight — more than one whole, which matches it being the heavier kitten.
  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
  • 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.
5Watch 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

    Claim: “A percent can never be more than 100.” Always, sometimes, or never true?

    1. ANever true — a percent counts per 100, and nothing stops the count passing 100
    2. BAlways true — 100% is the whole, and nothing is more than the whole
    3. CSometimes true — it depends whether the percent describes a part or a change
    4. DAlways true — percents above 100 are just written wrong
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Which percent means MORE than one whole?

    1. A120%
    2. B100%
    3. C80%
    4. D0.8%
    ✏️ Workspace & Solution Steps
  3. 3 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:What does the word percent mean?
    2. 2A classmate at our table answered:Per part

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Find the error

    1. 1Setup:A player scored 150% of the weekly goal of 200 points.
    2. 2Step 1:150% is more than one whole.
    3. 3Step 2:So the player scored 150 points.
    4. 4Step 3:The player beat the 200-point goal.

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 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