8.4 Small Group · Group 1

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

Visual Models · Write Inequalities · Inequality · Procedural Fluency

Name: Date: Period: Learning Goal:

■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do I write an inequality from words?

1'At least' means ≥ and 'at most' means ≤; 'more than' means > and 'fewer/less than' means <.

An inequality compares two amounts using <, >, ≤, or ≥. I use one when many values are allowed, not just one. I pick a variable and match the words to the right symbol. 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

Write Inequalities (Escribir desigualdades) — Represent a range of possible values with <, >, ≤, or ≥.
Inequality (Desigualdad) — A math sentence that compares two sides with <, >, ≤, or ≥.
Greater than (Mayor que) — The > sign, showing one number is bigger.
Less than (Menor que) — The < sign, showing one number is smaller.
At least / At most (Al menos / A lo más) — 'At least' means ≥. 'At most' means ≤.
Variable (Variable) — A letter that stands for a number that is unknown or can change.

4Watch out

A common mistake in Write Inequalities is using a strict symbol (> or <) for a phrase that actually includes the boundary value. For 'the suspect is at least 18 years old,' students often write a > 18 instead of the correct a ≥ 18 — this wrongly excludes 18 itself, even though 'at least 18' means 18 counts as a match. The same error happens in reverse with 'at most': for 'the getaway bag holds at most 12 items,' students write n < 12 instead of n ≤ 12. Always ask: does the key phrase include the number ('at least,' 'at most,' 'no more than,' 'no fewer than' → use ≥ or ≤) or exclude it ('more than,' 'fewer than' → use > or <)?

SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]

1 NUMBER LINE

Place markers on the number line for each value, then decide: is 5 > 3 true or false? Is 2 ≥ 7 true or false?
✏️ Workspace & Solution Steps
2 FILL TABLE

Identify the key phrase, symbol, and write the inequality for each situation.

Situation Key Phrase Symbol Inequality
A package weighs less than 50 pounds.
You need at least $25 to buy the game.
No more than 30 students can join the club.

✏️ 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

Situation	Key Phrase	Symbol	Inequality
A package weighs less than 50 pounds.
You need at least $25 to buy the game.
No more than 30 students can join the club.