6.AT.9 Lesson 8-5-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.5 Small Group · Group 1

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

Visual Models · Graph Inequalities · Number line · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do I graph an inequality on a number line?
1Closed circle for ≤ or ≥ (included), open circle for < or > (not included); shade right for greater, left for less.
  • Graphing an inequality shows every value that makes it true. I draw a circle at the boundary number and shade the side that works. The circle tells me if the boundary is included. 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. Graph t ≥ 2. The boundary number is 2.
  2. The symbol ≥ includes 2, so I draw a closed (filled) circle at 2.
  3. 'Greater than or equal to' means larger values work, so I shade to the right.
  4. Now the graph shows 2, 3, 4, and every value above 2.
3Mathematical Word Bank
  • Graph Inequalities (Representar desigualdades en una recta numérica) — Show every solution to an inequality on a number line with a boundary point and an arrow.
  • Number line (Recta numérica) — A straight line where numbers are placed in order; numbers get smaller to the left and larger to the right.
  • Open circle (Círculo abierto) — An empty circle showing a number is NOT included.
  • Closed circle (Círculo cerrado) — A filled-in circle showing a number IS included.
  • Solution set (Conjunto solución) — All the numbers that make the inequality true.
  • Inequality (Desigualdad) — A math sentence that compares two sides with <, >, ≤, or ≥.
4Watch out
  • A common mistake in Graph Inequalities is treating ≥ and ≤ the same as > and < and drawing the wrong circle. For example, students often graph x ≥ 6 with an OPEN circle (as if it were x > 6), which wrongly excludes 6 even though 6 itself makes x ≥ 6 true. A second common mistake is choosing the right circle but shading the wrong direction — for x < 9 students sometimes shade right instead of left. Always check the symbol twice: once for the circle (does it have an 'or equal to' line?) and once for the shading direction (does the symbol point toward larger or smaller numbers?).
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A number line shows a closed circle at 8 and is shaded to the left. Which inequality does this represent?

    1. Ax ≤ 8
    2. Bx < 8
    3. Cx ≥ 8
    4. Dx > 8
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Clue: the witness ran more than 15 feet, so d > 15. On the number line, what do you draw?

    1. AOpen circle at 15, shade right
    2. BClosed circle at 15, shade right
    3. COpen circle at 15, shade left
    4. DClosed circle at 15, shade left
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Clue: the getaway car held at most 4 suspects, so s ≤ 4. How is this graphed?

    1. AClosed circle at 4, shade left
    2. BOpen circle at 4, shade left
    3. CClosed circle at 4, shade right
    4. DOpen circle at 4, shade right
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Read:Graph n ≥ 8 on the number line.
    2. 2Circle choice:Open circle at 8
    3. 3Shade direction:Shade right
    4. 4Final graph:Open circle at 8, shaded right

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Level 2 Extension — Crack the Graphing Mistake

    1. 1Clue inequality:k > 19 (the loot weighed more than 19 pounds)
    2. 2Circle type:Closed circle at 19
    3. 3Shade direction:Shade right
    4. 4Final graph:Closed circle at 19, shaded right

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find the Graphing Error

    1. 1Inequality:x > 6
    2. 2Circle type:Closed circle at 6
    3. 3Shade direction:Shade right
    4. 4Graph:Closed circle at 6, shaded 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