Start here

Use the model to solve the first problem. Then try these quick review questions from earlier lessons.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it:

   1. A plant grows in layers. Each layer has 2 leaves. How many leaves are in 3 layers? Is each layer symmetric?
   2. How many leaves are in 3 layers? (3 × 2 = 6 leaves)
   3. Where is the line of symmetry for one layer? (Down the middle of the layer, along the stem, between the two leaves.)
   4. Are the two leaves exactly mirror images? (No. Real leaves are close, but never exactly identical.)
   5. Why do we still say the layer has bilateral symmetry? (Symmetry is a math model. The leaves are close enough to mirror images that the model is useful.)

   Show your work
2. 2

   Quick reviewA rectangular garden is 8 ft by 5 ft. What is its area?

   1. A13 square feet
   2. B26 square feet
   3. C40 square feet
   4. D40 cubic feet

   How do you know?
3. 3

   Quick reviewA box measures 3 by 4 by 2 units. What is its volume?

   1. A9 cubic units
   2. B12 cubic units
   3. C24 cubic units
   4. D24 square units

   How do you know?
4. 4

   Quick reviewA recipe makes 4 servings using 2 cups of rice. How much rice is in one serving?

   1. A1/2 cup
   2. B2 cups
   3. C4 cups
   4. D8 cups

   How do you know?

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughA butterfly's two wings look like mirror images of each other across a line down the center of its body. What is this type of symmetry called?

   1. ARotational symmetry
   2. BRadial symmetry
   3. CBilateral symmetry
   4. DPoint symmetry

   Why is that the answer?
2. 6

   Think it throughTo test whether a flower has bilateral symmetry, what should you do first?

   1. ACount the number of petals
   2. BDraw a line through the center and compare the two sides
   3. CMeasure the flower's height
   4. DCompare the flower to a different type of flower

   How do you know? Give a second reason as well.
3. 7

   Think it throughYour friend says only one of two flowers has bilateral symmetry. You test both by drawing a line through each flower's center and find both sides match on both flowers. What is most likely true?

   1. AThe friend is right — only one flower truly has symmetry
   2. BBoth flowers have bilateral symmetry, but the second flower's line of symmetry likely runs in a direction the friend didn't try
   3. CSymmetry cannot be tested in flowers
   4. DThe two flowers must be identical in shape to both be symmetric

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelThe butterfly's two wings are mirror images across a line down the middle of its body. Why does drawing that line matter for proving the butterfly is symmetric?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• A butterfly with wings spread open
• A human face seen from the front
• A dragonfly seen from above
• A layer of two leaves that are mirror images
• A ladybug seen from above
• The letter F
• A spiral snail shell
• The letter R

Use the words

Fill each blank with a word from the bank.

• Having two halves that match as mirror images is being ___.
• A copy of a figure flipped across a line is its ___ ___.
• Reflective symmetry in plants and animals is called ___ ___.
• The line you draw so each side reflects the other is the ___ ___ ___.

Explain the thinking

1. 9

   Find the mistakeRead the mistake. Explain what went wrong, then show the correct step.

   The 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.
2. 10

   Say moreWhen you sorted cards into 'has bilateral symmetry' and 'no bilateral symmetry,' why did the letter R end up in the 'no' column while a ladybug seen from above ended up in the 'yes' column?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A butterfly rests on a leaf with its wings spread wide open. The pattern of spots and colors on the left wing repeats on the right wing.

   Show your work

Last check

These two come from Lesson 10.1. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Which statement best shows what this lesson means by 'math is beauty'?

   1. AOnly things made by mathematicians can be beautiful
   2. BButterflies are the only living things with symmetry
   3. CBeauty and math are opposites — one is feeling and one is numbers
   4. DMath creates beautiful designs like bilateral symmetry, found in nature and used in human art, music, and architecture

   Explain your choice.
2. 13

   From Lesson 10.1Explain your thinking — Which statement best shows what this lesson means by 'math is everywhere'?

   1. AMath only appears in jobs that involve money
   2. BPeople use math every day in their professions and hobbies, and it solves problems around the house too
   3. CMath is a school subject with little relevance to life outside the classroom
   4. DOnly trained professionals like chefs are able to use math

   How do you know?
3. 14

   From Lesson 10.1Leaving the water running while brushing wastes an average of 4 gallons compared to turning the water on only to rinse. If one person brushes twice a day for a year (365 days), how many gallons would they save by turning the water off?

   1. A730 gallons
   2. B1,460 gallons
   3. C2,920 gallons
   4. D5,840 gallons

   How do you know?

Check your progress

Choose the box that best describes how you feel about each skill.