Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.15.1 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the area of a parallelogram using base × height, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 5.1. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Slanted sideSpanish: Lado inclinado A side that leans instead of going straight up and down. It is not the perpendicular height. In a leaning parallelogram, use the dashed 90° height—not the slanted side—in A = b × h.
ParallelogramSpanish: Paralelogramo A four-sided shape with two pairs of parallel sides. opposite sides never meet
ParallelSpanish: Paralelas Two lines or sides that stay the same distance apart and never meet. The top and bottom of a parallelogram never get closer together — matching arrowheads (›) mark one parallel pair, double arrowheads (››) mark the other.
BaseSpanish: 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. b in A = b × h
HeightSpanish: Altura The straight-up distance from the base to the top. h in A = b × h
PerpendicularSpanish: Perpendicular Two lines that meet to make a square corner (90 degrees). height ⟂ base

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Base 9 in., height 4 in., slanted side 5 in. Find the area.

  1. Base = 9 in., height = 4 in.
  2. Skip the 5 in. slanted side.
  3. A = 9 × 4 = 36

Answer: 36 in²

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A parallelogram has a base of 5 cm and a height of 4 cm. Find its area.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The base is and the perpendicular height is .
  • I know that measure is the height because .
  • Area = × = square units.
  • The slanted side is not used because .

Word bank parallelogrambaseheightperpendicularsquare cornerareaformulamultiplysquare unitsslanted siderectanglerearrange

Watch out!A common mistake

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.

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.15.1 Small Group · Group 2

Group 2Challenge practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the area of a parallelogram using base × height, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 5.1. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

  1. 1Complete each step, then write the final answer.
    120 ft²h = ?15 ft10 ft
    The height is the dashed line, not the 10 ft side.

    A parallelogram has an area of 120 square feet. Its base is 15 feet. Its slanted side is 10 feet. What is its height?

    1. 1Write the formula with the numbers you know.
    2. 2Divide the area by the base. What is the height?
    3. 3Check by multiplying.
    Final answer:
  2. 2Complete each step, then write the final answer.
    120 ft²h = ?10 ft
    A new base gets its own height, at a square corner.

    Use the same parallelogram. Now the 10-foot side is the base. What is the height to that base?

    1. 1The area does not change. Write the formula with the new base.
    2. 2What is the height to the 10-foot base?
    3. 3Why is this height longer than 8 feet?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A parallelogram has an area of 91 square centimeters. Its height is 7 cm. How long is its base?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Two parallelograms have the same area. One has a base of 18 inches and a height of 6 inches. The other has a base of 9 inches. What is its height?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A parking lot is shaped like a parallelogram. Its area is 2,400 square feet. Its base is 80 feet. How far is it from the base to the opposite side?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Ana multiplies the two side lengths of a parallelogram, 9 cm and 6 cm, and gets 54 square centimeters. The height to the 9 cm side is 4 cm. What is the real area?

    Show your work
    Final answer:

Explain your thinkingOne parallelogram has base 15 and height 8. Using a side of 10 as the base, the height is 12. How can both be right?

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help