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.

Why This Matters This is your challenge small group for Lesson 10.2. 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
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 out!A common mistake

Thinking a figure lacks bilateral symmetry just because its line of symmetry is not vertical

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.

Why This Matters This is your challenge small group for Lesson 10.2. 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.
    0−5−4−3−2−112345−11234(−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.
    0−5−4−3−2−1123456−6−5−4−3−2−1123456(−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.
    0−5−4−3−2−112345−1123456(−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.

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