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

Lesson 10.210.2 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can use bilateral symmetry to describe structure in nature and in human creations — one step at a time, with support.

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 butterfly is drawn on a grid. Its line of symmetry is the y-axis. One wing tip is at (−4, 3). Where is the matching wing tip?

  1. Find the line of symmetry: line of symmetry: y-axis
  2. Count how far the tip is from the line: (−4, 3) → 4 units left
  3. Count the same distance on the other side: 4 units right → (4, 3)
  4. The matching wing tip is at (4, 3).

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? Where is the line of symmetry in one layer?

Answer:

Say it and write itSentence starters

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

  • I have seen symmetry in .
  • The two sides .

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 1

Group 1Supported practice

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

Learning target With my small group, I can use bilateral symmetry to describe structure in nature and in human creations — one step at a time, with support.

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    A shape has points at (−3, 1) and (3, 2). Lin says they are mirror points across the y-axis. Which statement is correct?

    1. ALin is wrong. The mirror of (−3, 1) is (3, 1).
    2. BLin is right. Both points are 3 units from the y-axis.
    3. CLin is right. One point is on the left and one is on the right.

    Hint Mirror points are the same distance from the line. What else must stay the same?

    Show your work
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.
    −5−4−3−2−112345−1123456(−3, 4)
    The y-axis splits the leaf into mirror halves.

    A leaf is drawn on a grid. Its line of symmetry is the y-axis. One edge point is at (−3, 4). Where is the matching point on the other half?

    1. 1How many units is (−3, 4) from the y-axis?
    2. 2Count the same distance on the other side. What is the new x-coordinate?
    3. 3Does the y-coordinate change? Write the matching point.
    Final answer:
  2. 3Complete each step, then write the final answer.
    −6−5−4−3−2−1123456−11234(2, 1)(5, 3)
    The right wing. The left wing is its mirror image.

    A butterfly is symmetric across the y-axis. Its right wing has points at (2, 1) and (5, 3). Find the matching points on the left wing.

    1. 1Mirror (2, 1) across the y-axis. What is its new x-coordinate?
    2. 2Mirror (5, 3) across the y-axis. Write the new point.
    3. 3What changes, and what stays the same?
    Final answer:
  3. 4Complete each step, then write the final answer.

    The y-axis is a line of symmetry. A point is at (−2, 5). Its mirror point is at (?, 5). What is the missing number?

    Show your work

    Hint The point is 2 units left of the y-axis. Count 2 units to the right.

    Final answer:
  4. 5Complete each step, then write the final answer.

    A butterfly is symmetric across the y-axis. One wing spot is at (4, −2). Its mirror spot is at (?, −2). What is the missing number?

    Show your work

    Hint The spot is 4 units right of the y-axis. Count 4 units to the left.

    Final answer:
  5. 6Complete each step, then write the final answer.

    A plant grows in layers. Each layer has 2 leaves that are mirror images. The plant has 7 layers. How many leaves does it have?

    Show your work

    Hint How many leaves are in one layer? Multiply by the number of layers.

    Final answer:

Explain your thinkingHow do you find a mirror point across the y-axis? Use Lin's mistake to explain what changes and what stays the same.

Sentence starter The x-coordinate ___. · The y-coordinate stays the same because ___.

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