6.AT.4 Lesson 4-2-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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4.2 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort these values — which are greater than 50% and which are less than 50%?

    Target Categories: Greater than 50% Less than 50%
    • 2 NUMBER LINE

      Place each value on the number line: A = 3/8, B = 0.6, C = 85%

      ✏️ Workspace & Solution Steps
    SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
    1. 3 MULTIPLE CHOICE

      Convert 3/5 to a percent.

      1. A60%
      2. B35%
      3. C53%
      4. D65%
      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. 4 MULTIPLE CHOICE

      Convert 7/20 to a percent.

      1. A35%
      2. B70%
      3. C20%
      4. D14%
      Rewrite each fraction
      Work it out
      Simplify
      1. 1Same size piecesCommon denominator first.
      2. 2OperateOnly then add or subtract.
      3. 3SimplifyDivide out common factors.
    3. 5 MULTIPLE CHOICE

      Which decimal is equivalent to 45%?

      1. A0.45
      2. B4.5
      3. C0.045
      4. D45.0
      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?
    4. 6 MULTIPLE CHOICE

      What fraction is equal to 0.75?

      1. A3/4
      2. B7/5
      3. C3/5
      4. D7/10
      ✏️ Workspace & Solution Steps
    🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

    Group Discussion Prompt: How does your visual model justify your mathematical solution?

    🗣️ Partner A:
    Partner A: "I modeled this by identifying the relationship and..."
    👂 Partner B:
    Partner B: "I agree with your step because the standard mathematical rule states..."
    ✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

    Complete each sentence stem to demonstrate precise mathematical reasoning:

    BECAUSE The ratio remains equivalent because both quantities are scaled by the exact same multiplicative factor.
    BUT Two ratios may look similar, but inverting the order of terms fundamentally changes the comparison.
    SO The recipe requires 3 parts flour to 2 parts water, so the unit rate is 1.5 cups of flour per cup of water.
    📐 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