6.AT.8 Lesson 8-7-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.7 · Part II

Supported Application · Guided Entry to Today's Problem

Equations and Inequalities Problem Solving · Model

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 8.7 · Part II
1Modeling Real-World Scenarios with Equations & Inequalities
2Strategy Model — step by step
  1. Define the variable and units in the scenario
  2. Look for keywords: 'equals/is' (=) vs 'at least/limit' (≥, ≤, >, <)
  3. Write the algebraic model, solve with inverse operations, and check in context
3Mathematical Word Bank
  • Equations and Inequalities Problem Solving (Resolución de problemas con ecuaciones y desigualdades) — Use an equation for one exact value or an inequality for a range of values in a real situation.
  • Model (Modelar) — To show a real-life situation with an equation or inequality.
  • Equation (Ecuación) — A math sentence with an equal sign showing both sides are the same.
  • Inequality (Desigualdad) — A math sentence that compares two sides with <, >, ≤, or ≥.
  • Reasonableness (Razonabilidad) — Checking if your answer makes sense.
  • Variable (Variable) — A letter that stands for a number that is unknown or can change.
4Watch out
  • A common mistake in Equations and Inequalities Problem Solving is matching the wrong model to a key phrase. For 'the getaway car held no more than 6 bags,' students often write the equation b = 6 instead of the inequality b ≤ 6, because they see one number and assume it must be exact. The same mistake happens in reverse: for 'the reward split equally among 5 people gave each $40,' students sometimes write the inequality 5p ≥ 40 instead of the equation 5p = 40, because 'split equally' sounds like it could mean a range. Before you submit, ask: does this phrase give one exact value (equation, =) or a limit/range (inequality, <, >, ≤, ≥)?
  1. 1 MULTIPLE CHOICE

    A bus can carry at most 48 passengers. There are already 31 on board. Which inequality shows how many more can board?

    1. A31 + p ≤ 48
    2. B31 + p > 48
    3. C31 + p = 48
    4. Dp − 31 ≤ 48
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    (Lesson 8.4) Which inequality represents: 'The temperature is less than 40 degrees'?

    1. At < 40
    2. Bt > 40
    3. Ct ≤ 40
    4. Dt = 40
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    (Lesson 8.4) Which inequality represents: 'You must be at least 48 inches tall to ride'?

    1. Ah ≥ 48
    2. Bh > 48
    3. Ch < 48
    4. Dh ≤ 48
    ✏️ 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
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.8 Lesson 8-7-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.7 · Part II

On-Level Application · Standard Rigor

Equations and Inequalities Problem Solving · Model

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 8.7 · Part II
1Modeling Real-World Scenarios with Equations & Inequalities
2The Structural Procedure
  1. Define the variable and units in the scenario
  2. Look for keywords: 'equals/is' (=) vs 'at least/limit' (≥, ≤, >, <)
  3. Write the algebraic model, solve with inverse operations, and check in context
3Mathematical Word Bank
  • Equations and Inequalities Problem Solving (Resolución de problemas con ecuaciones y desigualdades) — Use an equation for one exact value or an inequality for a range of values in a real situation.
  • Model (Modelar) — To show a real-life situation with an equation or inequality.
  • Equation (Ecuación) — A math sentence with an equal sign showing both sides are the same.
  • Inequality (Desigualdad) — A math sentence that compares two sides with <, >, ≤, or ≥.
  • Reasonableness (Razonabilidad) — Checking if your answer makes sense.
  • Variable (Variable) — A letter that stands for a number that is unknown or can change.
4Watch out
  • A common mistake in Equations and Inequalities Problem Solving is matching the wrong model to a key phrase. For 'the getaway car held no more than 6 bags,' students often write the equation b = 6 instead of the inequality b ≤ 6, because they see one number and assume it must be exact. The same mistake happens in reverse: for 'the reward split equally among 5 people gave each $40,' students sometimes write the inequality 5p ≥ 40 instead of the equation 5p = 40, because 'split equally' sounds like it could mean a range. Before you submit, ask: does this phrase give one exact value (equation, =) or a limit/range (inequality, <, >, ≤, ≥)?
  1. 1 MULTIPLE CHOICE

    A student solved 4n = 52 and got n = 13. Is the answer reasonable if n represents the number of notebooks in a box?

    1. AYes — 13 notebooks per box is reasonable
    2. BNo — 13 is too many notebooks
    3. CNo — the answer should be 48
    4. DYes — but only if n is a fraction
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Room 2: The vault keypad clue reads, 'A number of stolen coins plus 6 equals 14.' Solve x + 6 = 14 to find the code x.

    1. Ax = 8
    2. Bx = 20
    3. Cx = 6
    4. Dx = 2
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Room 3: A sign warns, 'The safe holds at most 20 gold bars.' Which inequality models the number of bars x?

    1. Ax ≤ 20
    2. Bx ≥ 20
    3. Cx > 20
    4. Dx = 20
    ✏️ 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.8 Lesson 8-7-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.7 · Part II

Extension &amp; Non-Routine Application

Equations and Inequalities Problem Solving · Model

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 8.7 · Part II
1Modeling Real-World Scenarios with Equations & Inequalities
2The Structural Procedure
  1. Define the variable and units in the scenario
  2. Look for keywords: 'equals/is' (=) vs 'at least/limit' (≥, ≤, >, <)
  3. Write the algebraic model, solve with inverse operations, and check in context
3Mathematical Word Bank
  • Equations and Inequalities Problem Solving (Resolución de problemas con ecuaciones y desigualdades) — Use an equation for one exact value or an inequality for a range of values in a real situation.
  • Model (Modelar) — To show a real-life situation with an equation or inequality.
  • Equation (Ecuación) — A math sentence with an equal sign showing both sides are the same.
  • Inequality (Desigualdad) — A math sentence that compares two sides with <, >, ≤, or ≥.
  • Reasonableness (Razonabilidad) — Checking if your answer makes sense.
  • Variable (Variable) — A letter that stands for a number that is unknown or can change.
4Watch out
  • A common mistake in Equations and Inequalities Problem Solving is matching the wrong model to a key phrase. For 'the getaway car held no more than 6 bags,' students often write the equation b = 6 instead of the inequality b ≤ 6, because they see one number and assume it must be exact. The same mistake happens in reverse: for 'the reward split equally among 5 people gave each $40,' students sometimes write the inequality 5p ≥ 40 instead of the equation 5p = 40, because 'split equally' sounds like it could mean a range. Before you submit, ask: does this phrase give one exact value (equation, =) or a limit/range (inequality, <, >, ≤, ≥)?
  1. 1 MULTIPLE CHOICE

    A school van can carry at most 14 passengers. There are already 9 passengers on board. Let p be the number of additional passengers who can get on. Which inequality models this situation?

    1. A9 + p ≤ 14
    2. B9 + p ≥ 14
    3. C9 + p < 14
    4. Dp − 9 ≤ 14
    ✏️ 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