5.5 Small Group · Group 1

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

Volume with Whole-Number Edges · Volume · Procedural Fluency · Real-World Applications

Name: Date: Period: Learning Goal:

■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do we find the volume of a box?

1To find the volume of a box, multiply all three edges: V = length × width × height.

Volume is how much space is inside a 3D shape. For a rectangular prism (a box), volume = length × width × height, measured in cubic units. 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

My time capsule box is 6 long, 4 wide, and 3 tall. I write the formula: V = length × width × height.
I put in the numbers: V = 6 × 4 × 3.
First I multiply two of them: 6 × 4 = 24.
Then I multiply by the last one: 24 × 3 = 72.
So the volume is 72 cubic units. I use cubic units because volume fills space in 3 directions.

3Mathematical Word Bank

Volume with Whole-Number Edges (Volumen con aristas de números enteros) — The number of unit cubes inside a rectangular prism. Formula: V = l × w × h.
Volume (Volumen) — How much space is inside a solid shape.
Rectangular prism (Prisma rectangular) — A solid box shape with six flat rectangle sides.
Cubic units (Unidades cúbicas) — The units used to measure space inside, like cubic inches.
Length, width, height (Largo, ancho, altura) — How long, how wide, and how tall a box is.
Net (Plantilla (desarrollo plano)) — A flat shape that folds up into a solid.

4Watch out

A common mistake in Volume with Whole Number Edges is multiplying only two of the three edges and stopping there — for example, seeing a box that is 6 in long, 4 in wide, and 3 in tall, multiplying just 6 × 4 = 24, and calling that the volume, when 24 is only the area of the bottom face (in square inches), not the volume of the whole box. The height must also be multiplied in: V = 6 × 4 × 3 = 72 cubic inches. A second common mistake is adding the three edges instead of multiplying them (6 + 4 + 3 = 13 instead of 6 × 4 × 3 = 72 cubic inches). Volume always MULTIPLIES all three edges, and the answer is always labeled in cubic units (in³), never square units (in²) or plain units (in).

SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]

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

SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]

🗣️ 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