6.AT.4 Lesson 4-2-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.2 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Visual Models · Fractions, Decimals, and Percents · Percent · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How can one value be written as a fraction, a decimal, AND a percent?
1To turn a fraction into a percent, build an equivalent fraction with a denominator of 100: ask “what do I multiply the denominator by to get 100?” and multiply the numerator by that same number. The new numerator is the percent.
  • Equivalent forms name the same value in different ways. Percent means "out of 100," so a fraction is already a percent once its denominator is 100. 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
  1. A player scored 3/4 of the points. Percent means out of 100, so I want an equivalent fraction with 100 on the bottom.
  2. What do I multiply the denominator 4 by to get 100? 4 × 25 = 100, so my scale factor is 25.
  3. I have to multiply the top by that same 25: 3 × 25 = 75. So 3/4 = 75/100.
  4. 75 out of 100 is 75%. And 75/100 as a decimal is 0.75, because hundredths sit two places after the point.
  5. So 3/4 = 75/100 = 0.75 = 75%. All three name the same score.
3Mathematical Word Bank
  • Fractions, Decimals, and Percents (Fracciones, decimales y porcentajes) — Three equivalent ways to name the same part of a whole.
  • Percent (Porcentaje) — A way to compare a number to 100, shown with the % sign.
  • Decimal (Decimal) — A number with a dot, like 0.5, that shows a part less than one.
  • Equivalent (Equivalente) — Having the same value, just written a different way.
  • Benchmark (Referencia) — A familiar number you use to guess, like 50% or 1/2.
  • Discount (Descuento) — Money taken off the first price to make it cheaper.
4Watch out
  • A common mistake in Relate Fractions, Decimals, and Percents is treating the numerator and denominator as the percent's digits — turning 3/5 into "35%" by just reading the 3 and the 5. Percent means out of 100, so the fix is to build an equivalent fraction with denominator 100: 5 × 20 = 100, so multiply the top by 20 too — 3/5 = 60/100 = 60%. A second version of this mistake is scaling only ONE part of the fraction (writing 3/5 = 3/100 or 60/5). Whatever you multiply the denominator by, you must multiply the numerator by the same number. When a denominator will not reach 100 evenly (8, 3, 7), divide the numerator by the denominator instead and then multiply by 100.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A game shows your score as 7/8 complete. What percent is that?

    1. A87.5%
    2. B78%
    3. C75%
    4. D88%
    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
  2. 2 MULTIPLE CHOICE

    Your arcade scoreboard reads 0.25 of the level cleared. What percent and fraction match this score?

    1. A25% and 1/4
    2. B2.5% and 1/4
    3. C25% and 1/5
    4. D250% and 1/40
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    A player powered up 3/5 of the energy bar. Which decimal and percent name the same amount?

    1. A0.6 and 60%
    2. B0.35 and 35%
    3. C0.6 and 6%
    4. D0.65 and 65%
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Convert 3/5 to a percent:3/5
    2. 2Read the digits as the percent:The numerator is 3 and the denominator is 5, so the student writes 35%.
    3. 3Final answer:3/5 = 35%

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Level 2 Extension — Find the Decimal-to-Percent Mistake

    1. 1Convert 0.4 to a percent:0.4
    2. 2Move the decimal point:0.4 → 0.04
    3. 3Write the percent:0.04 = 4%
    4. 4Final answer:0.4 = 4%

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find the Conversion Error

    1. 1Convert 2/3 to a percent:2/3
    2. 2Divide numerator by denominator:2 ÷ 3 = 0.67
    3. 3Move decimal two places:0.67 → 67%
    4. 4Final answer:2/3 = 67%

    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
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