Grade 6 Mathematics · Unit 10: Math Is...Standard MPP.7

Lesson 10.210.2 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can use bilateral symmetry to describe structure in nature and in human creations, explain how I can tell, and judge a case I have not seen before.

Start hereWords for this lesson

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

WordWhat it meansExample
symmetricSpanish: simétrico Having two halves that match — one side is a mirror image of the other. A butterfly: the left wing is the mirror of the right.
mirror imageSpanish: imagen reflejada A copy of a figure flipped across a line, so the two halves face each other. Fold the layer down the middle: each leaf lands on its partner.
bilateral symmetrySpanish: simetría bilateral Reflective symmetry in plants and animals — the two sides of the body mirror each other. All 17,000+ butterfly species have it — two sides, one mirror line.
line of symmetrySpanish: eje de simetría The line you can draw through a figure so each side is a reflection of the other. The line straight down the butterfly's body.
balanceSpanish: equilibrio An even, steady arrangement — neither side feels heavier than the other. Two matching halves — neither side feels heavier than the other.

How it worksWorked example

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

A shape has corners at (−3, 0), (3, 0), (2, 4), and (−1, 4). Mia says the y-axis is a line of symmetry. Is she right?

  1. Test the two bottom corners: (−3, 0) and (3, 0)
  2. Find the mirror point of (2, 4): (2, 4) → (−2, 4)
  3. Look for that point on the shape: (−2, 4) is not a corner
  4. No. The corner (2, 4) has no mirror corner at (−2, 4), so the y-axis is not a line of symmetry.

Now you trySame steps, your turn

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

A plant grows in layers. Each layer has 2 leaves. How many leaves are in 3 layers? Is each layer symmetric?

Answer:

Say it and write itSentence starters

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

Word bank symmetricmirror imagebilateral symmetryline of symmetrybalance

Watch outA common mistake

Thinking a figure lacks bilateral symmetry just because its line of symmetry is not vertical — the mirror line can run in any direction, and the test is whether the two sides match across it.

Grade 6 Mathematics · Unit 10: Math Is...Standard MPP.7

Lesson 10.210.2 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can use bilateral symmetry to describe structure in nature and in human creations, explain how I can tell, and judge a case I have not seen before.

  1. 1Complete each step, then write the final answer.
    −5−4−3−2−112345−11234(−4, 0)(4, 0)(3, 3)(−3, 3)
    Check each corner for a mirror corner.

    A shape has corners at (−4, 0), (4, 0), (3, 3) and (−3, 3). Is the y-axis a line of symmetry?

    1. 1Are (−4, 0) and (4, 0) mirror points? Why?
    2. 2Mirror (3, 3) across the y-axis. What is the new x-coordinate?
    3. 3Is (−3, 3) a corner of the shape?
    Final answer:
  2. 2Complete each step, then write the final answer.
    −5−4−3−2−1123456−6−5−4−3−2−1123456(−4, 0)(−2, 3)(1, 5)(3, 2)(5, 0)
    The top half. The x-axis is the line of symmetry.

    A shape is symmetric across the x-axis. Its top half has corners at (−4, 0), (−2, 3), (1, 5), (3, 2) and (5, 0). How many corners does the whole shape have?

    1. 1Across the x-axis, what is the mirror point of (−2, 3)?
    2. 2Which corners are on the x-axis?
    3. 3How many corners does the whole shape have?
    4. 4Why do (−4, 0) and (5, 0) not get new mirror points?
    Final answer:
  3. 3Complete each step, then write the final answer.

    The x-axis is a line of symmetry. A point is at (5, −3). Its mirror point is at (5, ?). What is the missing number?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    −5−4−3−2−112345−1123456(−2, 1)(2, 1)(4, 5)(−3, 5)

    A shape has corners at (−2, 1), (2, 1), (4, 5) and (−3, 5). Is the y-axis a line of symmetry? Type yes or no.

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

    An artist makes a dot design that is symmetric across a line. One half has 9 dots, and 3 of those dots sit on the line. How many dots does the whole design have?

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

    A shape is symmetric across the line x = 2. One corner is at (5, 4). Its mirror corner is at (?, 4). What is the missing number?

    Show your work
    Final answer:

Explain your thinkingA shape can look balanced but still not be symmetric. How do you test a line of symmetry? What does one unmatched corner tell you?

ChallengeWrite your own problem

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

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help