6.AT.9 Lesson 8-5-part2 Apply Day · Practice
MASTERY CHECK
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8.5 · Part II

Application Practice for Today's Problem

Graph Inequalities · Number line

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 8.5 · Part II
1Graphing Inequalities on the Number Line
2Strategy Model — step by step
  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?).
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Which graph represents x ≤ 10?

    1. AClosed circle at 10, shaded left
    2. BOpen circle at 10, shaded left
    3. CClosed circle at 10, shaded right
    4. DOpen circle at 10, shaded right
    ✏️ Workspace & Solution Steps
  2. 2 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
  3. 3 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
  4. 4 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. 5 OPEN RESPONSE

    A theme park has two rides. Ride A requires height h > 48 inches. Ride B requires height h ≥ 48 inches. A child is exactly 48 inches tall. Which ride can they go on? Explain using number line graphs for both inequalities.

    💬 Sentence Starter: For Ride A (h > 48), the graph has a ___ circle at 48. Since 48 > 48 is ___, the child ___ ride A. For Ride B (h ≥ 48), the graph has a ___ circle at 48. Since 48 ≥ 48 is ___, the child ___ ride B.
    ✏️ Mathematical Justification & Response
📐 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