6.AT.4 Lesson 4-3-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.3 · Part II

Supported Application · Guided Entry to Today's Problem

estimate · benchmark percent

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 4.3 · Part II
1Estimating Percents of Numbers
2Strategy Model — step by step
  1. Use benchmark percents: 10% (move decimal left 1), 1% (move left 2), 50% (half), 25% (quarter)
  2. Combine benchmarks (e.g. 15% = 10% + 5%; 75% = 50% + 25%)
  3. Round numbers to compatible values for quick mental estimates
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

    To estimate 8.6% of 216 by rounding, which numbers should you use?

    1. A10% of 220
    2. B8% of 300
    3. C86% of 216
    4. D1% of 216
    ✏️ Workspace & Solution Steps
  2. 2 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?
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 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
6.AT.4 Lesson 4-3-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.3 · Part II

On-Level Application · Standard Rigor

estimate · benchmark percent

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 4.3 · Part II
1Estimating Percents of Numbers
2The Structural Procedure
  1. Use benchmark percents: 10% (move decimal left 1), 1% (move left 2), 50% (half), 25% (quarter)
  2. Combine benchmarks (e.g. 15% = 10% + 5%; 75% = 50% + 25%)
  3. Round numbers to compatible values for quick mental estimates
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.
  1. 1 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
  2. 2 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
  3. 3 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
📐 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
6.AT.4 Lesson 4-3-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

4.3 · Part II

Extension &amp; Non-Routine Application

estimate · benchmark percent

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 4.3 · Part II
1Estimating Percents of Numbers
2The Structural Procedure
  1. Use benchmark percents: 10% (move decimal left 1), 1% (move left 2), 50% (half), 25% (quarter)
  2. Combine benchmarks (e.g. 15% = 10% + 5%; 75% = 50% + 25%)
  3. Round numbers to compatible values for quick mental estimates
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.
  1. 1 MULTIPLE CHOICE

    A jacket originally priced at $78.99 is on sale for 25% off. Which is the best estimate of the discount amount?

    1. A$20
    2. B$10
    3. C$40
    4. D$8
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Two students estimate 8.6% of 216. Ana uses 10% of 220 = 22. Ben uses 10% of 200 = 20. Whose estimate is closer to the exact answer, 18.576?

    1. ABen's — 20 is 1.4 away; Ana's 22 is 3.4 away
    2. BAna's — 22 is closer to 18.576
    3. CThey are equally close
    4. DNeither is a valid estimate
    ✏️ Workspace & Solution Steps
  3. 3 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
📐 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