6.AT.9 Lesson 8-5-part2 Apply Day · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.5 · Part II

Second Practice Form · Independent Application and Spiral Review

Graph Inequalities · Number line

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 8.5 · Part II
1Graphing Inequalities on the Number Line
2The Structural Procedure
  1. Draw the boundary circle at the given constant number
  2. Open Circle (○) for < or > (boundary value is not included in solution set)
  3. Closed Circle (●) for ≤ or ≥ (boundary value is included). Shade right for >, left for <
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?).
  1. 1 MULTIPLE CHOICE

    A number line shows an open circle at 7, and the shading covers the numbers to the right of 7. Which inequality does this graph represent?

    1. Ax > 7
    2. Bx ≥ 7
    3. Cx < 7
    4. Dx ≤ 7
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Which graph represents x < 5?

    1. AOpen circle at 5, shaded left
    2. BClosed circle at 5, shaded left
    3. COpen circle at 5, shaded right
    4. DClosed circle at 5, shaded right
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Which graph represents x ≥ 3?

    1. AClosed circle at 3, shaded right
    2. BOpen circle at 3, shaded right
    3. CClosed circle at 3, shaded left
    4. DOpen circle at 3, shaded left
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Which graph represents x > 8?

    1. AOpen circle at 8, shaded right
    2. BClosed circle at 8, shaded right
    3. COpen circle at 8, shaded left
    4. DClosed circle at 8, shaded left
    ✏️ 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