7.3 Small Group · Group 1

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

Visual Models · Integers and Absolute Value · Integer · Procedural Fluency

Name: Date: Period: Learning Goal:

■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What is absolute value?

1Absolute value is a distance from zero, so it is never negative. It works the same for fractions and decimals as it does for whole numbers.

An integer is a whole number that can be positive, negative, or zero. The absolute value of a number is how far it is from zero on the number line. Distance is never negative. 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

Integers and Absolute Value (Enteros y valor absoluto) — Integers are whole numbers and their opposites; absolute value is their distance from zero.
Integer (Número entero) — Whole numbers and their opposites, like -2, -1, 0, 1, 2.
Positive (Positivo) — A number bigger than zero, to the right of zero on a number line.
Negative (Negativo) — A number smaller than zero, to the left of zero on a number line.
Absolute value (Valor absoluto) — How far a number is from zero. It is never negative.
Opposite (Opuesto) — Two numbers the same distance from zero, on opposite sides, like 3 and -3.

4Watch out

A common mistake in Integers and Absolute Value is judging size by the digits alone instead of position on the number line — students think -8 is 'more' than -3 because 8 > 3, when really -8 sits farther left (colder, deeper, or lower) and is actually the SMALLER integer. Absolute value measures distance from zero and is always positive or zero, but that distance does not decide which integer is greater — only left-to-right order on the number line does. Before you submit, ask: am I comparing distance from zero (absolute value) or position on the number line (greater/less than)?

SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]

1 MATCHING GAME
Match each integer to its absolute value.
1. -5
2. 3
3. -8
4. 0
5. -1
6. 7
- A5
- B3
- C8
- D0
- E1
- F7
2 NUMBER LINE

Plot these integers on the number line: -6, -2, 0, 4, 7
✏️ Workspace & Solution Steps

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 mathematical model proves the solution because each step preserves quantitative equivalence.

BUT An estimate provides a quick benchmark, but an exact proof is required for precision.

SO The quantities follow the standard rule, so the final result is verified with certainty.

📐 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