<p>In this lesson, students will review the concept of a line of symmetry through drawing and paper folding with objects such as alphabet letters, polygons, and polygon-based designs. The goal of this activity is to help students comprehend that a reflection about a line is an action that produces a new figure that is congruent to the original figure or object being reflected. This differs from a line of symmetry, which exists or does not exist in figures and objects. Students will:&nbsp;<br>- identify the lines of symmetry in a figure or design.&nbsp;<br>- explain why some figures have no line of symmetry.&nbsp;<br>- describe which types of figures have an infinite number of lines of symmetry.<br>- draw the missing pieces of a symmetric figure.&nbsp;<br>- identify the lines of reflection.&nbsp;<br>- recognize reflection about a line as an action that produces a new figure that is congruent to the original figure or object being reflected.&nbsp;<br>- understand reflection on a line that is not a line of symmetry for the shape.&nbsp;<br>- draw the reflection of a figure or design over a specified line of reflection.</p>

<p>- What strategies might we use to verify symmetry and congruency?&nbsp;<br>- What strategies may we take to continue a sequence?</p>

<p>- Line of Reflection: A line midway between something (a pre-image) and its mirror reflection.&nbsp;<br>- Line of Symmetry: A line that divides a figure into two halves that are mirror images of each other.&nbsp;<br>- Patterns: Regularities in situations such as those in nature, events, shapes, designs and sets of numbers (e.g., spirals on pineapples or geometric designs in quilts).&nbsp;<br>- Reflection: A transformation that produces the mirror image of a figure.&nbsp;<br>- Symmetry: A line of symmetry separates a figure into two congruent halves, each of which is a reflection of the other.&nbsp;<br>- Congruence: Having the exact same size and shape.</p>

<p>- paper cutouts of various regular polygons (large, 4 to 8 inches across), one for each student&nbsp;<br>- student copies of Vocabulary Journal pages (M-5-7-1_Vocabulary Journal)&nbsp;<br>- student copies of Alphabet Symmetry and a transparency (M-5-7-1_Alphabet Symmetry.doc and KEY)&nbsp;<br>- single-sided student copies of grid paper with vertical divider and one transparency (M-5-7-1_Grid Paper Vertical)&nbsp;<br>- back-to-back student copies of grid paper with vertical divider (M-5-7-1_Grid Paper Vertical)&nbsp;<br>- set of pattern blocks or paper pattern cutouts for each student (M-5-7-1_Pattern Cutouts 1 and M-5-7-1_Pattern Cutouts 2 or pattern blocks at EAI catalog site (http://www.eaieducation.com/category.aspx?categoryID=71 )&nbsp;<br>- a bag or envelope for each student to store pattern blocks or paper pattern cutouts&nbsp;<br>- back-to-back student copies of grid paper with diagonal divider and one transparency (M-5-7-1_Grid Paper Diagonal)&nbsp;<br>- student copies of Quick Quiz (M-5-7-1_Quick Quiz.doc and KEY)&nbsp;<br>- posterboard for each student (approximately 9 x 12 to 12 x 18 inches)&nbsp;<br>- student copies of Symmetry Sort Mat (M-5-7-1_Symmetry Sort Mat)&nbsp;<br>- student copies of Symmetry Sort Figures (M-5-7-1_Symmetry Sort Figures and M-5-7-1_Symmetry Sort Figures KEY)&nbsp;<br>- variety of colored markers for student use&nbsp;<br>- ruler&nbsp;<br>- optional: miras for student use (see miras EAI catalog site <a href="http://www.eaieducation.com/category.aspx?categoryID=82">http://www.eaieducation.com/category.aspx?categoryID=82</a>)</p>

<p>- When introducing vocabulary, use the Think-Pair-Share strategy to assess students' baseline grasp of the concepts.&nbsp;<br>- During the Alphabet Symmetry Activity, assess students' comprehension of the concepts through discussion and observation (M-5-7-1_Alphabet Symmetry and KEY).&nbsp;<br>- Observation and evaluation of Partner Reflection Design will help in determining the level of student proficiency.&nbsp;<br>- Use the Quick Quiz (M-5-7-1_Quick Quiz and KEY) for more evaluation.&nbsp;</p>

<p>Scaffolding, Active Engagement, Modeling, and Explicit Instruction<br>W: Begin the lesson by instructing students to identify lines of symmetry and reflection in various figures. Provide shapes for students to practice making reflections at their desks and to fold in half in order to find any lines of symmetry.<br>H: Folding letters of the alphabet in half to find lines of symmetry. Some may have only one line of symmetry, while others may have more than once, or some may have none. Experiment with different shapes to practice reflection lines. Point out that any shape can be reflected, the result will look like a mirror image of the original shape.&nbsp;<br>E: Using graph paper, instruct students to print their name along a vertical fold in the paper and draw the reflection of their name on the other side of the line. Students should use pattern blocks to create a design along a vertical line and then trade with a partner to draw the reflection.<br>R: Circulate around the room while students work on the reflections. Assist any pairs as needed, and make sure they're drawing reflections rather than translations. Review with individual students as needed.&nbsp;<br>E: To assess students' grasp of symmetry and reflection, have them complete the Quick Quiz (M-5-7-1_Quick Quiz and KEY).&nbsp;<br>T: Ensure that students are using suitable vocabulary for symmetry and reflection. Use the Symmetry Sort activity to get more practice finding lines of symmetry (M-5-7-1_Symmetry Sort Mat, M-5-7-1_Symmetry Sort Figures.doc, and M-5-7-1_Symmetry Sort Figures KEY). There are several different symmetry and reflection activities available for use in this lesson.<br>O: The class is organized in a discovery format, with students learning about properties of reflection and symmetry through experimentation.</p>

<p><strong>Before students arrive, write the following terms on the board: line of symmetry, reflection, and symmetric. Cut one geometric figure for each student. Give each student a figure when he/she enter the classroom.&nbsp;</strong><br><br><strong>Think-Pair-Share:</strong> Provide each student with a half sheet of paper. Assign each term written on the board to one-fourth of the class. Ask students to come up with their own definitions and examples for their term. Give them about three minutes on their own. Next, ask them to turn to their partner and express their ideas. Allow students 1-2 minutes each to share. Select students at random to present their ideas to the class. Continue to choose students to explain until you have a good description of all four words. Clarify that symmetric (or symmetry) means that a figure or diagram can be divided into two congruent halves by a line of symmetry, whereas a line of reflection creates a new figure that is congruent to the original figure in the same relative position but on the opposite side of the line of reflection (it will be "flipped").&nbsp;<br><br>Have students place their pencils upright on their desktops, about halfway across the width of the desk. Ask students to place their geometric figure on the left side of their pencil, so it touches the pencil. <strong>"Your pencil is the line of reflection."</strong> Ask students to "flip" their figure over and place it on the right side of the pencil, still touching it but from the opposite side. This shows the reflection motion. If some students slide their figure rather than flip it, explain that the "slide" action is a different type of change (or transformation), known as a translation. Translation will be discussed further in Lesson 3.&nbsp;<br><br>Repeat the process once more time, but instruct students to leave a small space between their figure and the pencil (on the left side) and keep this space on the right side after they flip the figure.<br><br>After all students have successfully demonstrated the reflection motion, ask them to put the pencil away and try to fold their figure in half so that all parts of one half match the other half without overlapping. When they open the fold, they'll notice the reflection line.&nbsp;<br><br><strong>"Are all polygons (or shapes) symmetric?"</strong> (<i>no</i>)&nbsp;<br><br><strong>"Could I have two or three volunteers come up and draw an example of a non-symmetric figure?"</strong>&nbsp;<br><br><strong>"Can these figures still be reflected even though they are not symmetric?"</strong> (<i>yes</i>)<br><br>If the figures are not too complicated, draw a vertical or horizontal line of reflection for each and ask volunteers to reflect them, or show the reflection process yourself. Draw a simpler irregular polygon to show if the students' examples cannot be simply used for the demonstration.&nbsp;<br><br><strong>"Today's lesson will cover identifying lines of symmetry and reflection in various types of figures. We will also draw missing portions of symmetric figures and reflections.</strong><br><br><strong>"We'll start by looking for 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 hold it up to the light after folding to ensure that all parts match. This is frequently called mirror symmetry because, like a reflection in a mirror, a figure (or part of a figure) is 'flipped' but remains congruent when viewed in the mirror."</strong>&nbsp;<br><br>Distribute Alphabet Symmetry and KEY sheet (M-5-7-1_Alphabet Symmetry and KEY) to each student. Use the transparency to demonstrate drawing lines of symmetry on several letters and counting the number of lines of symmetry below the letters. Allow students 3–5 minutes to complete the alphabet. Ask for student volunteers to explain their answers on the overhead or whiteboard. Clarify any problem areas, such as N, S, and Z, which might appear to have symmetry even though they do not. Use this chance to discuss figures with infinite lines of symmetry. The "O" on this sheet is oblong, so it only has two lines of symmetry, whereas if it were totally round, it would have infinitely many lines of symmetry. Show how a square or circle can have many more lines of symmetry than an oval or rectangular shape. Fold a rectangle of paper to demonstrate 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 only a few lines of symmetry (vertical and horizontal), whereas round, square, and other regular shapes have many more or even infinitely many.&nbsp;<br><br><strong>"Next, we'll look at figures that are reflected over a line. 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 its reflection on the other side of the line. Instead of splitting one figure in half by a symmetry line, we get two congruent figures. The distance between the two figures can be no space, a small space, or a large space, depending on how close the original figure is to the line of reflection. Think about when your own polygon touch your pencil (line of reflection), reflecting it the first time, and then reflecting it away from your pencil the second time. Let's consider these examples."</strong><br><br>Display the following figures for students to see.<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_42.png" width="485" height="166"><br><br><strong>"Raise your hand if you can tell which of these lines is a line of symmetry, and which is also a line of reflection."</strong> (<i>Line 1 is both a line of symmetry and reflection, whereas Line 2 is only a line of reflection.</i>) Make sure students understand the difference.&nbsp;<br><br>Call on one or more students to explain.<br><br><strong>"When working with lines of reflection, you are often asked to draw the reflection over a specific line. It will be 'flipped' and must remain in the same relative position. As with lines of symmetry, one simple 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."</strong><br><br>To demonstrate, draw a vertical and diagonal line on the board or use the grid transparencies (M-5-7-1_Grid Paper Vertical and M-5-7-1_Grid Paper Diagonal). Cut out two sets of matching paper figures that are not regular, like the ones seen below. Tape one of each near the lines on the board or overhead. One figure at a time, hold the second congruent figure while overlying 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 away from the line to reflect it. Trace the figure to show the reflection.<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_43.png" width="358" height="211"><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_44.png" width="242" height="253"></p><p><strong>Name Reflection Activity</strong><br><br>Give each student one sheet of grid paper with a vertical dividing line down the center (single-sided copies, M-5-7-1_Grid Paper Vertical). Ask students to write their name in capital letters going down vertically on the right side of the paper, touching the vertical dividing line between each letter. Explain to students that each letter of their name will be reflected across the vertical line to the left. Show the activity with your name or initials on the board or overhead. An example of the initials EK is provided below.<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_45.png" width="174" height="148"><br><br>Before beginning the partner activity, walk around the room to check for understanding and accuracy. Look for students who are translating (sliding) instead of reflecting (flipping) their letters.<br><br><i><u>Optional task for students:</u></i> An option is to have them turn another sheet of grid paper so that the line of reflection is horizontal. In this position, students will write their name above the line and reflect it below the line.<br><br><strong>Partner Block Reflection Activity</strong><br><br>Divide the class into pairs of students. Give each student a double-sided piece of grid paper with a straight line drawn vertically down the center on both sides (M-5-7-1_Grid Paper Vertical). Also, give each student a bag or envelope containing pattern blocks or paper pattern cutouts (M-5-7-1_Pattern Cutouts 1 and M-5-7-1_Pattern Cutouts 2). Instruct each student to draw a design on one side of the vertical line on their own grid paper, using five to eight blocks or paper pattern cutouts and a variety of shapes. Each student's design should touch the line in some way.<br><br>Once both students have completed a design, instruct them to make a mirror image of their partner's design on the other side of the line on their partner's page. It may be helpful to have students switch seats as they begin to create their partner's reflection. This eliminates the need to move or disturb sheets containing pattern blocks or paper cutouts. When students have completed the reflections, they should individually check their partner's reflection for accuracy. Once the partners believe their reflections are accurately represented, students should raise their hands for you to review the designs. If time allows, instruct students to repeat the process with a design that does not touch the line of reflection. If you don't have enough time in class to examine all of the reflection designs, students can trace the outlines of the pieces on both sides of the line of reflection for you to check later or continue working on during another class period.&nbsp;<br><br><i>Optional:</i> If miras are available, students may use them to check their work. Students would place the mira on the line of reflection and look through it from the original design's side. With the mira in place, they should see the same image as they see when they lift the mira.<br><br>You should move around the room and observe while students are working on making reflections of their partner's designs. Make recommendations or ask guiding questions to help students who require additional practice or who are attempting to translate rather than reflect the figures. Also, when pairs ask you to review their final reflections, encourage them to make necessary changes.&nbsp;<br><br><strong>Quick Quiz:</strong> At the end of the class, each student or pair of students should take the Quick Quiz (see M-5-7-1_Quick Quiz and KEY in the Resources folder).&nbsp;<br><br><strong>Extension:</strong> Use these suggestions to personalize this lesson to your students' needs throughout the unit and the year.<br><br><strong>Routine:</strong> Discuss the significance of understanding and using the appropriate vocabulary phrases to convey mathematical ideas clearly. During this lesson, students should record the following terms in their Vocabulary Journals (M-5-7-1_Vocabulary Journal): line of reflection, line of symmetry, reflection, and mirror (or line) symmetry. Keep a supply of Vocabulary Journal pages on hand so that students can add them as needed. Bring up examples of reflection and symmetry as they are seen throughout the school year, including math and other content areas such as art and science. Ask students to bring in examples from magazines or newspaper ads and explain how symmetry is used in that particular context.<br><br><strong>Small Group: Symmetry-Sort Activity</strong><br><br>Use this activity with students who are struggling with the concept of multiple lines of symmetry inside a single figure. Give students the Symmetry Sort Figures and Symmetry Sort Mat (M-5-7-1_Symmetry Sort Figures, M-5-7-1_Symmetry Sort Mat, and M-5-7-1_Symmetry Sort Figures KEY). Students will need to carefully cut out the figures first. Figures can be cut along the outlines or just cut into rectangular cards. Instruct students to count the number of lines of symmetry in each figure and place it on the sorting mat in the space marked with that number. Students may find it helpful to fold or draw on some of the figures to make their decision. Students can work independently or with a partner.<br><br><strong>Expansion or Station: Name Card Activity</strong><br><br>This activity is suitable for students who have shown proficiency at reflecting their name or initials vertically and/or horizontally. Ask students to design an artistic name plate (card) for their desk or locker. Tell them to use first name only, last name only, or first name and last name initials. Ask students to create their own lettering style to use. The designs should be colorful and contain some kind of detail or pattern. Instruct students to draw a symbol or sketch at the beginning and end of their name of something that describes them, such as a football or a music note. Each student's name design must be reflected over a line, including pattern designs and symbols, in the same colors. Allow students to choose between vertical, horizontal, and diagonal representation for their project. Provide materials such as poster board and colorful markers so that the name plate can be used on a locker, in class, or at home. Students will also need rulers.&nbsp;<br><br><i>Note to teacher:</i> These could be useful objects to display to help parents find students' desks or lockers during an open house or conferences.<br><br><strong>Expansion or Station 1: Partner Patterns Activity (Diagonal)</strong><br><br>Give 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). Also, provide each student a bag or envelope with pattern blocks or paper pattern cutouts (M-5-7-1_Pattern Cutouts 1 and M-5-7-1_Pattern Cutouts 2). Instruct each student to make a design on one side of the line using a total of five to eight blocks or paper pattern cutouts and various shapes. Each student's design should touch the line in some way. The task is for each student to create 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 the accuracy of the reflection first, and then raise their hand for you to check it. If time allows, instruct students to repeat the process with a design that does not touch the diagonal line of reflection.&nbsp;<br><br><i>Optional:</i> If miras are available, students may use them to check their work. They would place the mira on the line of reflection and look through it from the original design's side. With the mira in place, they should see the same image as when they lift it.<br><br><strong>Technology Connection: Color Me Symmetric Challenge</strong><br><br>If computers are available, students should visit the following website with a partner:<br><br><a href="http://www.adrianbruce.com/Symmetry/game/whiteboard-activity4.html">http://www.adrianbruce.com/Symmetry/game/whiteboard-activity4.html</a>&nbsp;<br><br>Each pair will be asked to color both sides of a sketch to create a symmetric picture. The first student will color one side of the picture with several colors. The second student is challenged to color the opposite side in the same way to create symmetry. This activity works well with an interactive whiteboard.&nbsp;<br><br>Students may also engage in a similar activity without using the web link. Each student should use draw tools or a word processing program on the computer to develop a design with lines, figures, and color. When students are finished, they should be asked to create and color a reflection of one of the other students' designs.<br><br><strong>Individual Technology: 20-a-Day</strong><br><br>If computers are available for student use, this activity could be used as additional practice. This activity is appropriate for students who are struggling to understand the concepts of symmetry and reflection, as well as 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 class practice or review, as well as in a classroom game. Practice problems are can be found at:<br><br><a href="http://www.ixl.com/math/practice/grade-4-lines-of-symmetry">http://www.ixl.com/math/practice/grade-4-lines-of-symmetry</a>&nbsp;<br><br>This website allows students to practice 20 problems with lines of symmetry each day. Note to teacher: Users are limited to 20 questions each day. Additional problems are only available to members.<br><br><strong>Station 2 Option: Partner Building Activity</strong><br><br>This activity requires students to work in pairs. One will be a designer, while the other will be a builder. The designer and builder will face each other, but a partition will be placed between them so that the "builder" does not see the pattern being created. If a partition is not present, partners can sit back to back instead. Provide students with pattern blocks or pattern cutouts made from various colors of paper (M-5-7-1_Pattern Cutouts 1 and/or M-5-7-1_Pattern Cutouts 2).<br><br>Direct the designer to create a square design using pattern blocks. The square's designer will provide direction to the builder, allowing the builder to recreate a reflection of the design without seeing the original. Finally, the two designs are compared visually to determine whether the builder truly created the reflection. If a mira is available, students can compare designs by sliding them closer together and putting the mira between the two squares (on what they believe to be the line of reflection). Adjustments to the reflected design may be required. When the designer and builder agree that the design square and reflection are complete and accurate, the partners will record answers to questions such as:&nbsp;<br><br>What words or phrases helped you recreate the design?&nbsp;<br><br>What words or phrases did you find confusing? Why?&nbsp;<br><br>Can you think of better ways to describe how to make the design?<br>If time allows, the activity can be repeated with the partners switching roles. Following the activity, hold a classroom or small group discussion focusing on the geometric vocabulary used by students.&nbsp;<br><br>This activity can be customized by changing the number of blocks used and the types of questions students may ask while creating the reflection. Encourage students to identify blocks by their names or talk about their characteristics rather than their color. Customize the activity for different skill levels by using more/less difficult shapes.&nbsp;<br><br><i>Note to teacher:</i> The activity will most likely be successful if students are paired based on their verbal and spatial abilities.<br><br><strong>Station 3 Option: Mira Activity</strong><br><br>This optional activity requires the use of miras and should only be considered if they are available.&nbsp;<br><br>Provide 4 pattern blocks or pattern cutouts, a sheet of plain paper, and a mira (M-5-7-1_Pattern Cutouts 1 and/or M-5-7-1_Pattern Cutouts 2). Instruct students to place the four pattern blocks on the paper to create a simple design, or have them draw four figures on their paper. Next, instruct students to place the mira along a line that touches the design's edge. Explain and/or illustrate to students how to look at the image reflected in the mira from the design side. Ask them to draw the reflection they see on their paper.<br><br>Keeping the same design in place, ask them to place the mira in one corner (or vertex) of the design, but without touching the full edge of the design or any figure. Again, have them draw what they see on the mira.&nbsp;<br><br>Finally, have students turn their paper over and recreate the same design. Instruct them to attempt two or three different mira placements so that it does not touch the design at all or any vertex of the design. Encourage them to try placements that are not just vertical or horizontal. Students should draw on paper what they see in the mira as it changes positions. They should compare how moving the line of reflection (the mira) affects the reflection result. Encourage students to express what they are seeing as the line of reflection is moved.&nbsp;<br><br>To conclude this activity, draw several little designs and their reflections on a board or a transparency which have unique (not all vertical or horizontal) lines of reflection. Call on student volunteers to draw the line of reflection. Allow students to check their answers with the mira.<br><br>The lesson follows a discovery structure, with students learning about properties of reflections and lines of symmetry through experimentation. Vocabulary terms were introduced first, then emphasized throughout the lesson. Students identified the difference between reflection and mirror symmetry. They were asked to create symmetry and reflection in their designs, as well as determining the location and number of lines of both symmetry and reflection. The lesson ended with a short assessment that allowed students to show proficiency in each of these areas. Several remediation, extra practice, and extension exercises were proposed to help students better understand these concepts. Lessons 2 and 3 will build on the ideas taught in this lesson using similar activities and strategies.</p>