6.AT.8 Lesson 8-6-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.6 Small Group · Group 1

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

Visual Models · Solve and Graph Inequalities · Solve · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do I solve an inequality and then graph it?
1Solve with inverse operations, then graph the solution set: open circle for < or >, closed for ≤ or ≥.
  • I solve an inequality the same way as an equation: use inverse operations to get the variable alone. But the answer is a range of values, so I show all of them on a number line. 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
  1. Solve x + 3 > 53. The inverse of adding 3 is subtracting 3.
  2. I subtract 3 from both sides: x + 3 − 3 > 53 − 3, so x > 50.
  3. The symbol > does not include 50, so I use an open circle at 50.
  4. 'Greater than' shades right. Check: x = 60 gives 60 + 3 = 63 > 53. True!
3Mathematical Word Bank
  • Solve and Graph Inequalities (Resolver y representar desigualdades) — Isolate the variable, then show the complete solution set on a number line.
  • Solve (Resolver) — To find the number that makes it true.
  • Graph (Graficar) — To show answers on a number line with circles and shading.
  • Solution (Solución) — A number that makes the equation or inequality true.
  • Substitute (Sustituir) — To put a number in place of a letter.
  • Solution set (Conjunto solución) — All the numbers that make the inequality true.
4Watch out
  • A common mistake in Solve and Graph Inequalities is shading the number line in the wrong direction after solving. For example, a student solves x + 4 > 10 correctly to get x > 6, but then shades LEFT toward smaller numbers instead of RIGHT toward greater numbers. The shading direction always matches the solved symbol, not the original problem: '>' and '≥' shade right (greater numbers), '<' and '≤' shade left (smaller numbers) — check this AFTER you solve, not before. To catch this mistake, substitute one shaded value and one unshaded value back into the original inequality: the shaded value should make it true, and the unshaded value should make it false.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    Final gate — describe the solution set. The vault rule is x > 7. What does the solution set mean?

    1. AAll numbers greater than 7, like 8, 9, 10, … (but NOT 7 itself)
    2. BOnly the number 7
    3. CAll numbers less than 7
    4. DEvery number, including 7
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    Is x = 5 a solution to x + 4 > 12?

    1. ANo, because 5 + 4 = 9, and 9 is not greater than 12
    2. BYes, because 5 + 4 = 9
    3. CYes, because 5 > 4
    4. DNo, because 5 < 12
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    Clue 1: Which value is a solution of x > 7?

    1. A9
    2. B7
    3. C5
    4. D3
    ✏️ Workspace & Solution Steps
  3. 4 MULTIPLE CHOICE

    Clue 2: Is 5 a solution of x ≤ 5?

    1. AYes, because 5 ≤ 5 is true
    2. BNo, because 5 is not less than 5
    3. CNo, because ≤ means only smaller numbers
    4. DYes, but only because 5 is odd
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Catch the Wrong Inverse Operation

    1. 1Inequality:x + 6 > 14
    2. 2Inverse operation:Add 6 to both sides
    3. 3Simplify:x > 20
    4. 4Graph:Open circle at 20, shade right

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Catch the Open vs. Closed Circle Mistake

    1. 1Inequality:x − 4 ≥ 9
    2. 2Inverse operation:Add 4 to both sides
    3. 3Simplify:x ≥ 13
    4. 4Graph:Open circle at 13, shade right

    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
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