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

4.2 Small Group · Group 2

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

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — 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
  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.
3Second Model — Try it together — then prove it
  1. Let's change 1/5 into a fraction out of 100, then a decimal and a percent.
  2. What do we multiply the denominator 5 by to get 100? (20)
  3. Now multiply the numerator by that same 20: 1 × 20 = ? (20) So 1/5 = 20/100.
  4. 20 out of 100 is what percent? (20%) And as a decimal? (0.2)
  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
  • 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.
5Watch 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

    Convert 7/20 to a percent.

    1. A35%
    2. B70%
    3. C20%
    4. D14%
    Rewrite each fraction
    Work it out
    Simplify
  2. 2 MULTIPLE CHOICE

    Which decimal is equivalent to 45%?

    1. A0.45
    2. B4.5
    3. C0.045
    4. D45.0
    0%50%100%
    Work
  3. 3 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A game shows your score as 7/8 complete. What percent is that?
    2. 2A classmate at our table answered:88%

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Convert 5/8 to a percent:5/8
    2. 2Divide the bottom by the top:8 ÷ 5 = 1.6
    3. 3Multiply by 100:1.6 × 100 = 160%
    4. 4Final answer:5/8 = 160%

    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
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