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

8.5 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort by circle type: open or closed.

    Target Categories: Open circle (not included) Closed circle (included)
    • x > 4
    • x < 12
    • n > 0
    • x ≥ 7
    • x ≤ 3
    • n ≥ 15
  2. 2 NUMBER LINE

    Read the graph description and write the inequality it represents. Then graph it.

    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 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
  2. 4 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
  3. 5 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
  4. 6 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
🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."
👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The ratio remains equivalent because both quantities are scaled by the exact same multiplicative factor.
BUT Two ratios may look similar, but inverting the order of terms fundamentally changes the comparison.
SO The recipe requires 3 parts flour to 2 parts water, so the unit rate is 1.5 cups of flour per cup of water.
📐 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