6.AT.4 Lesson 4-3-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.3 Small Group · Group 2

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

estimate · benchmark percent · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — Approximately — the problem is asking for an estimate
1Anchor the whole at 100%, mark benchmark percents, and place the amount between the landmarks it falls beside — 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 set up the double number line
  1. The whole is 6 GB — that is 100%.
  2. I mark the bottom line in benchmark jumps of 25%: 0%, 25%, 50%, 75%, 100%.
  3. Equivalent ratios give the top line: 25% of 6 GB is 1.5 GB, so the top reads 0, 1.5, 3, 4.5, 6.
  4. 4 GB used lands between 4.5 (75%) and 3 (50%), close to 4.5 — so about 70% of the storage is used.
3Second Model — Try it together — then prove it
  1. The Green-Team recycled 216 pounds of material; 8.6% was metal.
  2. Round both: 8.6% is about 10%, and 216 is about 220.
  3. 10% of 220 = 0.1 × 220 = 22. About 22 pounds of metal.
  4. Compatible numbers work too: 10% of 200 = 20. Both estimates agree — around 20 pounds.
  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
  • estimate (estimación) — A reasoned answer that is close enough to be useful, found without exact computation.
  • benchmark percent (porcentaje de referencia) — A friendly percent — 1%, 10%, 25%, 50%, 75%, 100% — used as a landmark for estimating.
  • compatible numbers (números compatibles) — Numbers close to the originals that are easy to compute with mentally.
  • double number line (recta numérica doble) — Two parallel number lines that pair amounts with their percents at the same positions.
  • the whole (el todo) — The quantity that counts as 100% in a problem — and it can change between questions.
5Watch out
  • Keeping the same whole for every question — when the problem says 'of the used storage,' the whole changes from 6 GB to 4 GB, and estimates anchored to the old whole are wrong before any arithmetic happens.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    For which problem is ESTIMATING clearly the right tool, rather than exact computation?

    1. ADeciding if a $58 jacket at 25% off fits your $45 budget
    2. BProgramming a bank to compute interest on every account
    3. CReporting a medicine dose
    4. DScoring a state test
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    The Green-Team recycled 216 pounds; 8.6% was metal. Using compatible numbers 10% and 200, the estimate is:

    1. A20 pounds
    2. B2 pounds
    3. C208 pounds
    4. D86 pounds
    0%50%100%
    Work
  3. 3 MULTIPLE CHOICE

    Photos use 3.5 GB of the 4 GB of used storage. About what percent of the USED storage is photos?

    1. AAbout 87%
    2. BAbout 58%
    3. CAbout 35%
    4. DAbout 99%
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Why did the whole change between the two storage questions?

    1. AThe second question asks about the used storage, so 4 GB becomes 100%
    2. BThe phone gained storage between the questions
    3. CThe whole never changes in a percent problem
    4. DBecause photos are more important than mail
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 OPEN RESPONSE

    Write your own estimation problem about percent, using a real situation from your life. Then solve it with a benchmark and say whether your estimate runs high or low.

    ✏️ Mathematical Justification & Response
  2. 6 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Why did the whole change between the two storage questions?
    2. 2A classmate at our table answered:The whole never changes in a percent problem

    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