6.AT.4 Lesson 4-3-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.3 Small Group · Group 1

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

estimate · benchmark percent · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — 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.
  • The word approximately tells you an exact answer is not required. Benchmarks, rounding and compatible numbers get you close, fast. 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 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.
3Mathematical 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.
4Watch 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

    What is 10% of 220?

    1. A22
    2. B2.2
    3. C220
    4. D44
    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?
  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
    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?
  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
  5. 5 MULTIPLE CHOICE

    Estimate 24% of 81 with benchmarks.

    1. AAbout 20
    2. BAbout 40
    3. CAbout 8
    4. DAbout 2
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 OPEN RESPONSE

    The word 'approximately' appears in the storage problem. What does it tell you about the answer you need?

    💬 Sentence Starter: 'Approximately' tells me ___ .<br>So instead of computing exactly, I can ___ .
    ✏️ 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
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