• Use the Think-Pair-Share strategy when introducing vocabulary to help determine students’ baseline understanding of the concepts. [IS.10 - All Students]
  

• Use discussion and observation during the Alphabet Symmetry Activity to determine the extent to which students understand the concepts (M-5-7-1_Alphabet Symmetry.doc and M-5-7-1_Alphabet Symmetry KEY.doc).

• Observation and evaluation of Partner Reflection Design will help to recognize the level of student proficiency.

• Use the Quick Quiz (M-5-7-1_Quick Quiz.doc and M-5-7-1_Quick Quiz KEY.doc) for further assessment.

[IS.9 - All Students]

[IS.3 - Struggling Learners] Prior to students arriving, place these terms on the board: line of symmetry, line of reflection, reflection, and symmetric. Cut out one geometric figure for each student. Hand each student a figure as he/she enters the classroom.

Think-Pair-Share: Provide a half sheet of paper to each student. Assign each term written on the board to one-fourth of the class. Ask students to think of a definition in their own words and an example for their term. Give them approximately 3 minutes on their own. Next, have them turn to a partner and share their ideas. Give students 1-2 minutes each to share. Select students randomly to explain their ideas to the class. Continue selecting students to explain until you have a good description of all four words. Clarify that symmetric (or symmetry) means a figure or diagram can be divided by a line of symmetry to create two congruent halves, while a line of reflection is used to create a new figure, congruent to the original figure in the same relative position but on the opposite side of the line of reflection (it will be “flipped”).

Have students place their pencil vertically on their desktop about halfway across the width of the desk. Ask students to place their geometric figure on the left side of their pencil, touching the pencil. “Your pencil is the line of reflection.” Ask students to “flip” their figure over and lay it down on the right side of the pencil, still touching the pencil but on the opposite side. This shows the reflection motion. If some students slide their figure instead of flip it, bring up that the “slide” motion is a different type of change (or transformation), called a translation. Translation will be discussed further in Lesson 3.

Repeat this process a second time, but have students leave a small space between their figure and the pencil (on the left side) and maintain this space on the right side after they flip the figure.

After all students have successfully shown the reflection motion, ask them to put the pencil away and try to fold their shape in half so that all parts of one half match the other half without overlapping. When they open the fold, they will be able to see the reflection line.

“Are all polygons (or shapes) symmetric?” (no)

“Could I have two or three volunteers come up and draw an example of a non-symmetric figure?” [IS.4 - All Students]

“Can these figures still be reflected even though they are not symmetric?” (yes)

If the figures are not too complex, draw a vertical or horizontal line of reflection for each and ask for volunteers to reflect them, or demonstrate the reflection process yourself. Draw a simpler irregular polygon to reflect if the students’ examples cannot be easily used for the demonstration.

“In today’s lesson, we will be identifying lines of symmetry and reflection in different types of figures. We will also be drawing missing portions of symmetric figures and reflections.”

“We will begin by identifying lines of symmetry in the letters of the alphabet. If a figure has a line of symmetry, you should be able to fold it along the line and have the two halves match like we did with our polygons. If it is a drawing rather than a cutout figure, you can check to see if all parts match by holding it up to the light after you fold it. This is sometimes called mirror symmetry because, like a reflection in the mirror, a figure (or part of a figure) is ‘flipped’ but still congruent when viewed in the mirror.”

Hand out Alphabet Symmetry sheets to each student (M-5-7-1_Alphabet Symmetry.doc and M-5-7-1_Alphabet Symmetry KEY.doc). Use the transparency to demonstrate drawing lines of symmetry on several letters and recording the number of lines of symmetry below the letters. Allow students 3–5 minutes to complete the alphabet. [IS.5 - All Students] Ask for student volunteers to explain their answers on the overhead or white board. Clarify any problem areas such as N, S, and Z, which can appear to have symmetry even though they do not. Also take this opportunity to discuss figures with infinite lines of symmetry. The “O” on this sheet is oblong so it only has two lines of symmetry, but if it were completely round, it would have an infinite number of lines of symmetry. Demonstrate how a square or circle can have many more lines of symmetry than an oval or rectangular figure. Fold a rectangular piece of paper to show that the vertical and horizontal folds work, while the diagonals do not. Draw a variety of additional figures to help students think about and verbalize the generalization that all oblong figures will have limited lines of symmetry (limited to vertical and horizontal), while round, square, and other regular shapes are more likely to have many more or even infinitely many.

“Next we are going to consider figures which are reflected over a line. [IS.6 - All Students] The line of reflection is similar to the line of symmetry in that what is on one side is congruent, but ‘flipped’ when compared to the other side. The difference is that we will have a complete figure on one side of the line of reflection and draw another complete figure which is its reflection on the other side of the line. We end up with two congruent figures rather than one figure split in half by a line of symmetry. There can be no space, a small space, or a large space between the two figures depending on how close the original figure is to the line of reflection. Think about when you placed your own polygon touching your pencil (line of reflection), the first time you reflected it, and the second time you reflected it away from your pencil. Let’s consider these examples.”

Display the figures below for students to see.

“Raise your hand if you can tell which of these lines is a line of symmetry, [IS.7 - All Students] and which is also a line of reflection.” (Line 1 is both a line of symmetry and reflection, while line 2 is a line of reflection only.) Make sure students are clear on the distinction.

Call on one or more students to explain.

“When working with lines of reflection, you will often be asked to draw the reflection over a specific line. It will be ‘flipped’ and must be placed in the same relative position. Like with lines of symmetry, an easy test is to fold along the line of reflection or place a mirror or mira on the line of reflection to see if the figure and its image match exactly in shape and location.”

Demonstrate by drawing a vertical line and a diagonal line on the board or use the grid transparencies (M-5-7-1_Grid Paper Vertical.doc and M-5-7-1_Grid Paper Diagonal.doc). Cut out two sets of matching paper figures that are not regular, such as the ones below. Tape one of each near the lines on the board or overhead. One figure at a time, hold the second congruent figure overlapping the original taped figure (do not tape the second one). Demonstrate reflecting (flipping) the figure toward the line and moving it across the line an equal distance from the line so it is reflected. Trace the figure to show its reflection.

Name Reflection Activity

Provide each student with one sheet of grid paper with a vertical dividing line down the center (single-sided copies, M-5-7-1_Grid Paper Vertical.doc). Ask students to write their name in capital letters going down vertically on the right side of the paper touching the vertical dividing line with each letter. Explain that students will reflect each letter of their name across the vertical line to the left side of the line. Demonstrate the activity with your name or initials on the board or overhead. The example of the initials EK is shown below.

 

Walk around the room to check for understanding and accuracy before moving on to the partner activity. Watch for students who may be translating (sliding) instead of reflecting (flipping) their letters.

Optional challenge for students: An option is to have students turn another sheet of grid paper so the line of reflection is horizontal. In this position, students will write their name above the line and reflect it below the line.

Partner Block Reflection Activity

Group the class into pairs of students. Provide each student with a double-sided sheet of grid paper with a straight line drawn vertically down the center on both sides (M-5-7-1_Grid Paper Vertical.doc). Also provide each student with a bag or envelope of pattern blocks or paper pattern cutouts (M-5-7-1_Pattern Cutouts 1.doc and M-5-7-1_Pattern Cutouts 2.doc). Instruct each student to create a design on one side of the vertical line on their own grid paper, using a total of five to eight blocks or paper pattern cutouts and a variety of shapes. Each student’s design should touch the line in some way.

Once both students have created a design, ask them to make the mirror image of their partner’s design on the other side of the line on their partner’s page. It might be helpful to have students change seats when they begin to create their partner’s reflection. This will avoid the need to move and disturb the sheets with pattern blocks or paper cutouts on them. When students are finished creating the reflections, they should each check their partner’s reflection for accuracy. Once the partners believe their reflections are represented correctly, students should raise their hands to have you check the designs. [IS.8 - All Students] If time permits, have students repeat the process using a design that does not touch the line of reflection. If time is running too short for you to check all of the reflection designs during class time, students can trace outlines of the pieces on both sides of the line of reflection for you to check at a later time or to continue working on during a different class period.

Optional: Students may use a mira, if they are available, to check their work. Students would place the mira on the line of reflection and look into it from the side of the original design. With the mira in place, they should see exactly the same image as they see when they lift the mira.

While students are working on creating the reflections of their partner’s design, observe as you circulate about the room. Make suggestions or ask guiding questions to assist any students who need more practice or those who are attempting to translate rather than reflect the figures. Also, when pairs ask you to check their final reflections, they should be encouraged to make appropriate adjustments.

Quick Quiz: Each student or pair of students should complete the Quick Quiz at the end of the lesson (see M-5-7-1_Quick Quiz and M-5-7-1_Quick Quiz KEY in the Resources folder).

Extension: Use these suggestions to tailor this lesson to meet the needs of your students during the unit and throughout the year.

• Routine: Discuss the importance of understanding and using the correct vocabulary words to communicate mathematical ideas clearly. During this lesson, the following terms should be entered into students’ Vocabulary Journals (M-5-7-1_Vocabulary Journal.doc): line of reflection, line of symmetry, reflection, and mirror (or line) symmetry. Keep a supply of Vocabulary Journal pages on hand so students can add pages as needed. Bring up instances of reflection and symmetry as they are seen throughout the school year in math examples and other content areas such as art or science. Ask students to bring in examples that they see in magazines or newspaper ads and describe the use of symmetry in that particular context.

• Small Group: Symmetry-Sort Activity

Use this activity for students who are having difficulty with the concept of multiple lines of symmetry within the same figure. Provide students with the Symmetry Sort Figures and Symmetry Sort Mat (M-5-7-1_Symmetry Sort Figures.doc, M-5-7-1_Symmetry Sort Mat.doc, and M-5-7-1_Symmetry Sort Figures KEY.doc). Students will need to carefully cut out the figures first (or have them cut out prior to the lesson and store them in a bag or envelope). Figures can be cut along the outlines of each or just cut into rectangular cards. Instruct students to determine the number of lines of symmetry each figure has and place it on the sorting mat in the space marked with the number. It may be helpful for students to try folding or drawing on some of the figures to make their determination. Students can work individually or with a partner.

• Expansion or Station:Name Card Activity

This activity is appropriate for students who have shown proficiency at reflecting their name or initials vertically and/or horizontally. Ask student to create an artistic name plate (card) for their desk or locker. Direct them to use first name only, last name only, or first name and last name initial. Ask students to design a lettering style of their own to use. The designs should be colorful and include some sort of detail or pattern. Also direct students to draw a symbol or sketch at the beginning and end of their name of something that helps describe them such as a football or music note. Each student’s name design needs to be reflected over a line, including the pattern designs and symbols, using the same colors. Allow students to choose a vertical, horizontal, or diagonal representation for their project. Provide materials such as poster board and colorful markers, which allow the name plate to be used on a locker, in the classroom, or at home. Students will also need rulers.

Note to teacher: These may be good items to display for parents to find students' desks or lockers during an open house or conferences.

• Expansion or Station 1:Partner Patterns Activity (Diagonal)

Provide each pair of students two sheets of grid paper with a straight line drawn diagonally (45^◦) through each page, using diagonal grid paper (M-5-7-1_Grid Paper Diagonal.doc). Also provide each student a bag or envelope of pattern blocks or paper pattern cutouts (M-5-7-1_Pattern Cutouts 1.doc and M-5-7-1_Pattern Cutouts 2.doc). Instruct each student to create a design on one side of the line, using a total of five to eight blocks or paper pattern cutouts, and a variety of shapes. Each student’s design should touch the line in some way. The task is for each student to make the mirror image of their partner’s design on the opposite side of the line. When students are finished, they should have their partner check for accuracy on the reflection first, and then raise their hand to have you check it. If time permits, have students repeat the process using a design that does not touch the diagonal line of reflection.

Optional: Students may use a mira, if they are available, to check their work. They would place the mira on the line of reflection and look into it from the side of the original design. With the mira in place, they should see exactly the same image as they see when they lift the mira.

• Technology Connection: Color Me Symmetric Challenge

If computers are available, have students visit the following website with a partner:

http://www.adrianbruce.com/Symmetry/game/whiteboard-activity4.html

Each pair will be challenged to color the two sides of a sketch to create a symmetric picture. The first student will color one side of the picture using multiple colors. The second student is challenged to color the other side the same way to create symmetry. This activity also works well using an interactive whiteboard.

Students may also do a similar activity without using the web link. Using draw tools or a word processing program on the computer, each student should create a design using lines, figures, and color. When students are finished they should each be assigned to create the reflection of one other student’s design and color it.

• Individual Technology: 20-a-Day

If computers are available for student use, this activity could be used for extra practice. Use this activity for students who are having difficulty grasping the concepts of symmetry and reflection, or for any student who needs practice or review. If you have the ability to project to a classroom screen from a single computer, these problems could be used as practice or review for the class or in a class game. Practice problems are can be found at:

http://www.ixl.com/math/practice/grade-4-lines-of-symmetry

This siteallows students to practice 20 problems per day related to lines of symmetry. Note to teacher: Users are limited to 20 questions per day. Additional problems are only available to members.

• Station 2 Option: Partner Building Activity

Students will work in pairs for this activity. One will be a designer and the other will be a builder. The designer and builder will face each other but will need a divider placed between them so that the “builder” cannot see the pattern being designed. If a divider is not available, partners may sit back-to-back instead. Provide students with pattern blocks or pattern cutouts made on a variety of colors of paper (M-5-7-1_Pattern Cutouts 1.doc and/or M-5-7-1_Pattern Cutouts 2.doc).

Instruct the designer to create a square design using pattern blocks. The designer of the square will give directions to the builder, so the builder can re-create a reflection of the design without seeing the original. When the builder is finished, he/she will explain to the designer what the design looks like. Finally, the two designs are compared visually to see if the builder did actually create the reflection. If a mira is available, allow students to compare designs by sliding their designs closer together and placing the mira centered between the two squares (on what they believe to be the line of reflection). Adjustments to the reflected design may need to be made. When the designer and builder agree that the design square and reflection are complete and accurate, together the partners will record answers to questions such as:

• What words or phrases helped you re-create the design?

• What words or phrases confused you? Why?

• Can you think of better ways to explain the directions for making the design?

If time permits, the activity can be repeated with the partners switching roles. Follow the activity with a classroom or small group discussion that emphasizes the geometric vocabulary used by students.

This activity can be modified by altering the number of blocks used and by varying the types of questions students are allowed to ask while the reflection is being created. Encourage students to not use color to identify a block but rather to use its name or talk about its characteristics. Tailor the activity to different ability levels by using more/less difficult shapes.

Note to teacher: The activity will likely be most successful if students are paired homogeneously by ability in both verbal and spatial skills.

 

• Station 3 Option: Mira Activity

This optional activity requires the use of miras and should only be considered if miras are available.

Provide 4 pattern blocks or pattern cutouts, a sheet of plain paper, and a mira (M-5-7-1_Pattern Cutouts 1.doc and/or M-5-7-1_Pattern Cutouts 2.doc). Instruct students to place the four pattern blocks together on the paper to create a simple design or have them draw four figures on their paper. Next, ask students to place the mira on a line touching the edge of the design. Explain and/or demonstrate to students how to look into the design side of the mira at the image being reflected. Ask them to draw the reflection they see on their paper.

Keeping the same design in place, ask them to place the mira on one corner (or vertex) of the design, but without touching an entire edge of the design or of any figure. Again, ask them to draw what they see on the mira.

Last, have students turn their paper over and re-create the same design. Instruct them to try two or three different placements of the mira so it is not touching the design at all and not touching any vertex of the design. Guide them to try placements that are not just vertical or horizontal. Students should draw on their paper what they observe in the mira as it changes positions. They should be comparing how moving the line of reflection (the mira) changes the reflection outcome. Encourage students to verbalize what they are seeing as the line of reflection is moved.

To close this activity, draw several small designs and their reflections on the board or a transparency which have unique (not all vertical or horizontal) lines of reflection. Call on student volunteers to draw in the line of reflection. Allow students to check their answer using the mira.

The lesson is organized in a discovery format with students learning about properties of reflections and lines of symmetry through experimentation. Vocabulary terms were introduced first and emphasized throughout the lesson. Students identified the difference between reflection and mirror symmetry. They were asked to create symmetry and reflection in designs as well as identify the location and number of lines of symmetry and reflection. The lesson concluded with a short assessment intended to allow students to show proficiency in each of these areas. Several remediation, extra practice, and extension activities were suggested to help deepen student understanding of these concepts. Lessons 2 and 3 will scaffold on the ideas presented in this lesson by using similar activities and strategies.