Fold to 'Unfold' Symmetry

 

Resource Overview  Quantile® Measure: 

580Q  Identify and make figures with line symmetry. 

Skill or Concept: 

(QT‐G‐85) 

Identify the number of lines of symmetry in a  figure.  (QT‐G‐615)    

Excerpted from: 

Gourmet Learning  1937 IH 35 North Suite 105   New Braunfels, TX 78130  www.gourmetlearning.com  © Gourmet Learning   

 

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Unit 2 – Lesson 3

Geometry

Student Expectation: Students will identify lines of symmetry in two-dimensional geometric figures

Reteach Symmetry “Fold to ‘Unfold’ Symmetry”

K C Ap

Teacher note: Lines of symmetry are imaginary lines. Difficulty with identifying lines of symmetry are usually experienced by students who cannot visualize the lines. These students need to “see” the lines. In this activity, students fold and unfold designs to “see” the different lines of symmetry. Group size: whole group Materials: definitions, page 4; Instructional Strategy, pages 34-35; figures, pages 36-40; scissors; answer key, page 51 Before class: Copy the figures, pages 36-40, for each student. Make an additional copy of page 36 for demonstration. Directions: • Review the definitions of “symmetry,” “lines of symmetry,” “asymmetrical,” “horizontal,” “vertical,” and “diagonal” from page 4. • Explain how folding figures can help determine symmetry. Distribute figure #1 to each student. Cut out the figure to demonstrate, and follow the Instructional Strategy below to guide students.

Questioning Technique Instructional Strategy Cut out figure #1 while students do the same. Say: We want to know if this figure is symmetrical. By folding it in different ways, we will be able to determine this. Demonstrate by folding figure #1 vertically. Then have students fold their figures in the same manner. Be sure students line up the edges. Ask: When I folded this figure, the sides lined up perfectly. What does that mean? (Both sides of the figure are the same.) Ask: What does it mean when both sides of a figure are the same? (They are symmetrical.) Ask: What does this folded line represent? (the line of symmetry) Ask: Sometimes figures have more than one line of symmetry. How could we find out if this figure has more than one line of symmetry? (by folding it in a different direction) Demonstrate folding figure #1 horizontally. Students will do the same. Ask: What did you discover when you folded it horizontally? (The edges don’t line up.) Ask: What does that mean? (The figure is not symmetrical when folded horizontally.)

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Gourmet Curriculum Press, Inc.©

Unit 2 – Lesson 3

Geometry

Student Expectation: Students will identify lines of symmetry in two-dimensional geometric figures

Reteach Symmetry “Fold to ‘Unfold’ Symmetry” Questioning Technique Instructional Strategy Ask: What is the other line of symmetry besides vertical and horizontal? (diagonal) Say: Let’s find out if this figure is symmetrical diagonally by folding it. Demonstrate how to fold the figure diagonally. Ask: Is it symmetrical diagonally? (No.) How do you know? (The edges do not line up.) Ask: Who can summarize what we know about figure #1 now? (Figure #1 has one line of symmetry that is vertical.) Distribute figures #2-#5 to students. Instruct students to cut out figure #2. Ask: How can you find out if this figure is symmetrical? (by folding it) Say: Try folding it vertically first. Monitor students as they fold the figure vertically and assist as needed. Ask: Is this figure vertically symmetrical? (No.) Why not? (When it is folded, the edges do not line up.) Ask: What other ways can you fold it to check for symmetry? (horizontally and diagonally) Have students fold figure #2 horizontal. Monitor and assist students. Ask: What did you discover when you folded it horizontally? (The edges don’t line up, so it is not horizontally symmetrical either.) Finally, have students fold the figure diagonally. Ask: What happens when you fold it diagonally? (The edges still don’t line up.) Ask: What can you say about figure #2? (It is not symmetrical in any direction.) What is another way of saying this? (It is asymmetrical.) Follow the same procedure for the remaining figures. If students are still struggling with identifying the line(s) of symmetry, have them fold the figure and then cut along the fold. Students can hold the 2 halves back-to-back to verify symmetry.

Gourmet Curriculum Press, Inc.©

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Unit 2 – Lesson 3

Geometry

Student Expectation: Students will identify lines of symmetry in two-dimensional geometric figures

Reteach—Figure #1 Symmetry “Fold to ‘Unfold’ Symmetry”

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Gourmet Curriculum Press, Inc.©

Unit 2 – Lesson 3

Geometry

Student Expectation: Students will identify lines of symmetry in two-dimensional geometric figures

Reteach—Figure #2 Symmetry “Fold to ‘Unfold’ Symmetry”

Gourmet Curriculum Press, Inc.©

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Unit 2 – Lesson 3

Geometry

Student Expectation: Students will identify lines of symmetry in two-dimensional geometric figures

Reteach—Figure #3 Symmetry “Fold to ‘Unfold’ Symmetry”

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Gourmet Curriculum Press, Inc.©

Unit 2 – Lesson 3

Geometry

Student Expectation: Students will identify lines of symmetry in two-dimensional geometric figures

Reteach—Figure #4 Symmetry “Fold to ‘Unfold’ Symmetry”

Gourmet Curriculum Press, Inc.©

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Unit 2 – Lesson 3

Geometry

Student Expectation: Students will identify lines of symmetry in two-dimensional geometric figures

Reteach—Figure #5 Symmetry “Fold to ‘Unfold’ Symmetry”

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Gourmet Curriculum Press, Inc.©

Unit 2 – Practice #3

Geometry

Directions: Read each problem carefully. Decide which answer best completes the question. Show your work.

Problem #1

Problem #3

Which of the following figures has a line of symmetry? Draw the line of symmetry through your choice.

Marco and Alexander were playing a game with a spinner. Marco’s dog ate half of the spinner. Since the boys knew that the spinner was symmetric, they were able to make a new one just like the old one. If the part the dog didn’t eat looked like this, then what did the entire spinner look like?

A

B

C

D

green

red Problem #2 Look at the quilt Tanya’s grandma made. Which statement is true about this quilt?

blue

A

B

G

G Y

R

F

D

It has multiple lines of symmetry.

G It has one horizontal line of symmetry.

G

G

G R

R

H It has one vertical line of symmetry. J

R B

B

C

B

R

B

R B

It has no lines of symmetry. Gourmet Curriculum Press, Inc.©

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Unit 2 – Practice #3

Geometry

Directions: Read each problem carefully. Decide which answer best completes the question. Show your work.

Problem #4

Problem #6

Native Americans often used symmetry in making their rugs. Describe the symmetry you see in the picture below.

Explain why your hand is NOT symmetrical.

Problem #7 The following are four flags flown throughout the world. Which one does not have a line of symmetry?

Problem #5 Mark the line of symmetry on each of these bugs. If it does not have a line of symmetry, simply write “none” below it.

A

B

C

What inference can you make about insects?

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D

Gourmet Curriculum Press, Inc.©

Unit 2 – Practice #3

Geometry

Directions: Read each problem carefully. Decide which answer best completes the question. Show your work.

Problem #8

Problem #10

Which of the following letters are symmetric?

Which of the following is the best definition of symmetry?

F G H J

G S H Z

F

two figures that look the same but are different colors

G a picture whose two halves are an exact reflection H two of any one thing – like two animals or two vegetables J

Problem #9 Color the butterfly to show a symmetric design.

an object that has two of everything

Problem #11 Which of the asymmetrical?

following

is

A

B

C

D

Gourmet Curriculum Press, Inc.©

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Unit 2 – Application #3

Geometry

Directions: Read each problem carefully. Decide which answer best completes the question. Show your work. Problem #1

Problem #3

Each of the following pictures shows a part of a holiday celebrated by people in America. Which of these symbols does not have a line of symmetry?

Draw a symmetrical jack-o’-lantern face on this pumpkin.

Problem #2 Mark the line of symmetry on each of these hats. If it does not have a line of symmetry, simply write “none” below it.

Problem #4 Which of the following words are not symmetric? MOM COO HOOD TOOTH Copy one of the symmetrical words below, and draw the line or lines of symmetry through it.

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Gourmet Curriculum Press, Inc.©

Unit 2 – Application #3

Geometry

Directions: Read each problem carefully. Decide which answer best completes the question. Show your work. Problem #5

Problem #7

Architects use symmetry when designing buildings. Describe the symmetry you see in this building.

Are all squares symmetrical? Explain your reasoning. Make a drawing below to help prove your reasoning.

Problem #6 The following are all shapes commonly seen as street signs.

Problem #8

What is true about all of these shapes?

What is true about Keisha’s roll?

None of them symmetry.

has

a

line

of

They all have exactly one line of symmetry. Only the circle and rectangle have more than one line of symmetry. They all have more than 1 line of symmetry.

Kendra and Keisha were playing a board game. Keisha rolled this on the number cubes.

Neither number cube has a line of symmetry. They both have exactly one line of symmetry. Only the 6 has more than one line of symmetry. They both have more than one line of symmetry. Justify your answer by drawing the line(s) of symmetry.

Gourmet Curriculum Press, Inc.©

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Unit 2 – Application #3

Geometry

Directions: Read each problem carefully. Decide which answer best completes the question. Show your work. Problem #9

Problem #11

The following are four flags flown throughout the world. Which one has a line of symmetry?

The following are cave art drawings made by a tribe of Native Americans. Which one is asymmetrical?

Problem #10 Which of the following has more than one line of symmetry?

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Gourmet Curriculum Press, Inc.©