8.6 Small Group · Group 1

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

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

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

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 NUMBER LINE

Solve x + 3 > 9, then graph the solution on the number line.
✏️ Workspace & Solution Steps
2 FILL TABLE

Solve each inequality, describe the inverse operation, and describe the graph.

Inequality Inverse Operation Solution Graph Description
x + 11 ≥ 20
x − 3 < 7
x + 8 ≤ 20

✏️ Scratchpad / Reasoning

SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]

🗣️ 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