6.AT.8 Lesson 8-1-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.1 · Part II

Supported Application · Guided Entry to Today's Problem

Write Equations · Equation

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 8.1 · Part II
1Equations & Solutions
2Strategy Model — step by step
  1. An equation is a mathematical sentence stating two expressions are equal
  2. A solution is a value for the variable that makes the equation true
  3. Check: Substitute the value into the equation and verify that both sides balance
3Mathematical Word Bank
  • Write Equations (Escribir ecuaciones) — Represent a relationship with expressions joined by an equal sign.
  • Equation (Ecuación) — A math sentence with an equal sign showing both sides are the same.
  • Variable (Variable) — A letter that stands for a number that is unknown or can change.
  • Equal sign (Signo igual) — The = sign, showing both sides are the same.
  • Expression (Expresión) — A math phrase with numbers and letters, but no equal sign.
  • Constant (Constante) — A fixed number in an expression or equation that does not change.
4Watch out
  • A common mistake in Write Equations is writing subtraction and division clues in the wrong order — putting the number from the clue first instead of the variable first. For 'a number decreased by 8 equals 5,' students often write 8 − n = 5 instead of the correct n − 8 = 5; for 'a number divided by 4 equals 6,' they write 4 ÷ n (or 4n) instead of n / 4 = 6. Always start with the variable, then attach the operation in the order the words describe it, and check by substituting your answer back in.
  1. 1 MULTIPLE CHOICE

    Is n = 3 a solution of n + 5 = 9?

    1. ANo, because 3 + 5 = 8, which does not equal 9
    2. BYes, because 3 is smaller than 9
    3. CYes, because 3 + 5 is close to 9
    4. DYou cannot tell without solving first
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Which equation represents: 'A number divided by 4 equals 8'?

    1. An / 4 = 8
    2. B4n = 8
    3. Cn − 4 = 8
    4. Dn + 4 = 8
    ✏️ 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 8-1-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.1 · Part II

On-Level Application · Standard Rigor

Write Equations · Equation

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 8.1 · Part II
1Equations & Solutions
2The Structural Procedure
  1. An equation is a mathematical sentence stating two expressions are equal
  2. A solution is a value for the variable that makes the equation true
  3. Check: Substitute the value into the equation and verify that both sides balance
3Mathematical Word Bank
  • Write Equations (Escribir ecuaciones) — Represent a relationship with expressions joined by an equal sign.
  • Equation (Ecuación) — A math sentence with an equal sign showing both sides are the same.
  • Variable (Variable) — A letter that stands for a number that is unknown or can change.
  • Equal sign (Signo igual) — The = sign, showing both sides are the same.
  • Expression (Expresión) — A math phrase with numbers and letters, but no equal sign.
  • Constant (Constante) — A fixed number in an expression or equation that does not change.
4Watch out
  • A common mistake in Write Equations is writing subtraction and division clues in the wrong order — putting the number from the clue first instead of the variable first. For 'a number decreased by 8 equals 5,' students often write 8 − n = 5 instead of the correct n − 8 = 5; for 'a number divided by 4 equals 6,' they write 4 ÷ n (or 4n) instead of n / 4 = 6. Always start with the variable, then attach the operation in the order the words describe it, and check by substituting your answer back in.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    A witness statement reads: 'A number c of security cameras plus 6 more equals 19.' Which equation matches?

    1. Ac + 6 = 19
    2. B6c = 19
    3. Cc − 6 = 19
    4. Dc / 6 = 19
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    A detective found some fingerprints on Monday and 14 more on Tuesday, for a total of 30. Which equation represents this?

    1. Af + 14 = 30
    2. Bf − 14 = 30
    3. C14f = 30
    4. Df / 14 = 30
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    Which equation represents: 'A number divided by 4 equals 8'?

    1. An / 4 = 8
    2. B4n = 8
    3. Cn − 4 = 8
    4. Dn + 4 = 8
    ✏️ 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 8-1-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.1 · Part II

Extension & Non-Routine Application

Write Equations · Equation

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 8.1 · Part II
1Equations & Solutions
2The Structural Procedure
  1. An equation is a mathematical sentence stating two expressions are equal
  2. A solution is a value for the variable that makes the equation true
  3. Check: Substitute the value into the equation and verify that both sides balance
3Mathematical Word Bank
  • Write Equations (Escribir ecuaciones) — Represent a relationship with expressions joined by an equal sign.
  • Equation (Ecuación) — A math sentence with an equal sign showing both sides are the same.
  • Variable (Variable) — A letter that stands for a number that is unknown or can change.
  • Equal sign (Signo igual) — The = sign, showing both sides are the same.
  • Expression (Expresión) — A math phrase with numbers and letters, but no equal sign.
  • Constant (Constante) — A fixed number in an expression or equation that does not change.
4Watch out
  • A common mistake in Write Equations is writing subtraction and division clues in the wrong order — putting the number from the clue first instead of the variable first. For 'a number decreased by 8 equals 5,' students often write 8 − n = 5 instead of the correct n − 8 = 5; for 'a number divided by 4 equals 6,' they write 4 ÷ n (or 4n) instead of n / 4 = 6. Always start with the variable, then attach the operation in the order the words describe it, and check by substituting your answer back in.
  1. 1 MULTIPLE CHOICE

    Marisol tests values in the equation 7 + m = 23. Which value of m makes the equation true?

    1. Am = 16
    2. Bm = 30
    3. Cm = 23
    4. Dm = 9
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A torn note reads: 'A suspect's case minutes m, after 9 fewer, leaves 24.' Which equation fits?

    1. Am − 9 = 24
    2. Bm + 9 = 24
    3. C9m = 24
    4. Dm / 9 = 24
    ✏️ 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