6.GR.1 Lesson 5-1-part2 Apply Day · Practice
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.1 · Part II

Application Practice for Today's Problem

Area of Parallelograms · Slanted side

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 5.1 · Part II
1Area of Parallelograms & Rhombuses
2Strategy Model — step by step
  1. Identify the base (any side)
  2. Identify the perpendicular height (height must be perpendicular to base, not slanted)
  3. Multiply base times height; label with square units (e.g. cm², in²)
3Mathematical Word Bank
  • Area of Parallelograms (Área de paralelogramos) — The space inside a parallelogram. Formula: A = b × h, using the perpendicular height.
  • Slanted side (Lado inclinado) — A side that leans instead of going straight up and down. It is not the perpendicular height.
  • Parallelogram (Paralelogramo) — A four-sided shape with two pairs of parallel sides.
  • Parallel (Paralelas) — Two lines or sides that stay the same distance apart and never meet.
  • Base (Base) — Any side of a parallelogram 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.
4Watch out
  • The most common mistake in Area of Parallelograms is multiplying the base by the slanted side instead of the perpendicular height. For a parallelogram with a base of 16 ft, a perpendicular height of 9 ft, and a slanted side of 11 ft, students compute 16 × 11 = 176 square feet instead of the correct 16 × 9 = 144 square feet. The height must be the straight-up (perpendicular) distance between the base and its opposite side, not the length of the slanted side, even though the slanted side is often the number that 'looks' like it belongs in the formula.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Which measurement is the height of a parallelogram?

    1. AThe perpendicular distance between the base and the opposite side
    2. BThe length of the slanted side
    3. CThe perimeter divided by 4
    4. DThe longest side
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Cut the slanted end off a parallelogram and slide it to the other side. What shape forms, and why does that show A = base × height?

    1. AA rectangle with the same base and height, so its area equals base x height
    2. BA bigger parallelogram, so the area gets larger
    3. CA triangle, so the area is cut in half
    4. DA square, so all four sides must be equal
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    A blueprint parallelogram has a base of 8 ft, a height of 5 ft, and a slanted side of 7 ft. What is its area?

    1. A40 sq ft
    2. B56 sq ft
    3. C35 sq ft
    4. D26 sq 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?
  4. 4 MULTIPLE CHOICE

    Two parallelograms both have base 10 ft and height 6 ft. N is more tilted (slant 9 ft). Compare their areas.

    1. AEqual: both are 10 x 6 = 60 sq ft because area depends on base and height, not the slant
    2. BBlueprint N is larger because its slanted side is 9 ft
    3. CBlueprint M is larger because it is less tilted
    4. DYou cannot compare them without the slanted side of M
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 OPEN RESPONSE

    A parallelogram has a base of 12 cm. If you double the height, the area doubles too. Explain why this happens using the formula, and give a specific example with numbers.

    💬 Sentence Starter: When the height doubles from ___ to ___, the area changes from ___ to ___ because in the formula A = b × h, the base stays at ___ and ___.
    ✏️ Mathematical Justification & Response
📐 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