6.GR.1 Lesson 5-2-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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5.2 Small Group · Group 1

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

Area of a Triangle · Base · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do we find the area of a triangle?
1Area of a triangle = ½ × base × height. A triangle is exactly half of a rectangle with the same base and height.
  • A triangle has three sides. The base is one side, and the height is the straight-up (perpendicular) distance from the base to the top corner. 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. My triangular garden has a base of 12 feet and a height of 8 feet.
  2. I write the formula: A = ½ × base × height.
  3. I put in the numbers: A = ½ × 12 × 8.
  4. I multiply base × height first: 12 × 8 = 96.
  5. I take half: ½ × 96 = 48. So the area is 48 square feet.
3Mathematical Word Bank
  • Area of a Triangle (Área de un triángulo) — The space inside a triangle. A triangle is half of a rectangle with the same base and height, so A = ½ × b × h.
  • Base (Base) — Any side of a triangle can be the base. Once you pick a base, the height must be measured perpendicular (at a 90° angle) to it.
  • Height (Altura) — The straight-up distance from the base to the top corner.
  • Area (Área) — How much space is inside a flat shape.
  • Perpendicular (Perpendicular) — Two lines that meet to make a square corner (90 degrees).
  • Composite figure (Figura compuesta) — A shape made by putting two or more simple shapes together.
4Watch out
  • A common mistake in Area of Triangles is forgetting the ½ — students multiply base × height like a rectangle and stop there, or they use the triangle's slanted side instead of the perpendicular height that's already given. Always check: did I take half, and did I use the straight-up height, not the slanted side?
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Use the formula A = ½ × b × h to find the area of each triangle.

    TriangleBaseHeightArea
    Sail A
    Sail B
    ✏️ Scratchpad / Reasoning
  2. 2 FILL TABLE

    Solve the mathematical problem. Show all of your work and reasoning.

    TriangleBaseHeightArea
    Garden A
    Garden B
    Garden C
    Garden D
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    What is the area of a triangle with base 10 cm and height 6 cm?

    1. A30 sq cm
    2. B60 sq cm
    3. C16 sq cm
    4. D30 cm
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  2. 4 MULTIPLE CHOICE

    A triangle has an area of 24 sq ft and a base of 8 ft. What is the height?

    1. A6 ft
    2. B3 ft
    3. C16 ft
    4. D12 ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  3. 5 MULTIPLE CHOICE

    Why do we divide by 2 when finding the area of a triangle?

    1. AA triangle is exactly half of a rectangle with the same base and height
    2. BTriangles have 2 equal sides
    3. CThe base is always twice the height
    4. DWe always divide area formulas by 2
    ✏️ Workspace & Solution Steps
  4. 6 MULTIPLE CHOICE

    What is the area of a triangle with base 14 ft and height 6 ft?

    1. A42 sq ft
    2. B84 sq ft
    3. C20 sq ft
    4. D42 ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
🗣️ 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