<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 understand 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 occurs or does not exist in figures and objects. Students will:&nbsp;<br>- identify the lines of symmetry in a figure or design.<br>- explain why certain figures lack a line of symmetry.<br>- describe the types of figures with an infinite number of lines of symmetry.&nbsp;<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 operation that creates a new figure that is congruent to the original figure or object being reflected.&nbsp;<br>- understand reflection on a line that is not symmetrical.&nbsp;<br>- reflect a figure or pattern over a given line of reflection.</p>

<p>- How do spatial relationships, such as shape and dimension, help to create, construct, model, and portray real-world scenarios or solve problems?&nbsp;<br>- How may geometric properties and theorems be applied to describe, model, and analyze problems?&nbsp;<br>- How can patterns be used to describe relationships in mathematical situations?&nbsp;<br>- How might recognizing repetition or regularity help to solve problems more efficiently?&nbsp;<br>- How might using geometric shape features help with mathematical reasoning and problem solving?&nbsp;</p>

<p>- Acute Angle: An angle measuring less than 90˚.&nbsp;<br>- Acute Triangle: A triangle made up of 3 acute angles.&nbsp;<br>- Angle: A geometric figure formed by two rays that share a common endpoint.&nbsp;<br>- Line: A straight path that extends infinitely in both directions.&nbsp;<br>- Line of Symmetry: A line of symmetry separates a figure into two congruent halves, each of which is a reflection of the other.&nbsp;<br>- Line Segment: A straight path with a finite length.&nbsp;<br>- Obtuse Angle: An angle measuring more than 90˚.&nbsp;<br>- Obtuse Triangle: A triangle made up of 1 obtuse angle and 2 acute angles.&nbsp;<br>- Point: A specific location in a geometric plane with no shape, size, or dimension.&nbsp;<br>- Ray: A straight path that begins at an endpoint and extends infinitely in 1 direction.&nbsp;<br>- Right Angle: An angle measuring exactly 90˚.&nbsp;<br>- Right Triangle: A triangle with 1 right angle and 2 acute angles.&nbsp;<br>- Symmetry: The equivalence, point for point, of a figure on opposite sides of a point, line, or plane.</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-4-5-3_Vocabulary Journal)&nbsp;<br>- student copies of Alphabet Symmetry and a transparency (M-4-5-3_Alphabet Symmetry and KEY)&nbsp;<br>- single-sided student copies of grid paper with vertical divider and one transparency (M-4-5-3_Grid Paper Vertical)&nbsp;<br>- back-to-back student copies of grid paper with vertical divider (M-4-5-3_Grid Paper Vertical)&nbsp;<br>- set of pattern blocks or paper pattern cutouts for each student (M-4-5-3_Pattern Cutouts 1 and M-4-5-3_Pattern Cutouts 2 or pattern blocks at EAI - -catalog site <a href="http://www.eaieducation.com/category.aspx?categoryID=71">http://www.eaieducation.com/category.aspx?categoryID=71</a> )&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-4-5-3_Grid Paper Diagonal)&nbsp;<br>- student copies of Quick Quiz (M-4-5-3_Quick Quiz and KEY)&nbsp;<br>- poster board for each student (approximately 9 x 12 inches to 12 x 18 inches)&nbsp;<br>- student copies of Symmetry Sort Mat (M-4-5-3_Symmetry Sort Mat)&nbsp;<br>- student copies of Symmetry Sort Figures (M-4-5-3_Symmetry Sort Figures and 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 technique to assess students' baseline grasp of the concepts.&nbsp;<br>- During the Alphabet Symmetry activity, assess students' comprehension of the ideas through discussion and observation (M-4-5-3_Alphabet Symmetry and KEY).&nbsp;<br>- Observation and evaluation during the Partner Reflection design will assist in determining the level of student proficiency.&nbsp;<br>- Use the Quick Quiz (M-4-5-3_Quick Quiz and KEY) to assess student mastery.&nbsp;</p>

<p>Scaffolding, Active Engagement, Metacognition, Modeling, Explicit Instruction, and Formative Assessment&nbsp;<br>W: Students will identify lines of symmetry and reflection in various figures. Provide shapes for students to practice reflecting at their desks and folding in half to find lines of symmetry.&nbsp;<br>H: Using letters of the alphabet, fold the letters in half to reveal lines of symmetry. Some may have only one line of symmetry, while others may have several, or none at all. Experiment with different shapes to practice reflection lines. Point out that any shape can be reflected, resulting in a mirror image of the original shape.&nbsp;<br>E: Have students print their name along a vertical fold in graph paper, then draw the reflection on the other side of the line. Students should use pattern blocks to build a vertical line design and then trade with a partner to draw the reflection.&nbsp;<br>R: Circulate around the room while students work on their reflections. Assist any pairs as needed, and make sure they're drawing reflections rather than translations. Review with individual student as needed.&nbsp;<br>E: Have students take the Quick Quiz to check their comprehension of symmetry and reflection. Use the Symmetry Sort task to get more practice finding lines of symmetry. There are several different symmetry and reflection activities available for use in this lesson.&nbsp;<br>T: Use the Extension option to customize the lesson to match the needs of the students. The Routine section describes opportunities to review instructional content throughout the year. The Small Group section is designed for students who might benefit from more learning or practice opportunities. The Expansion section presents a challenge that goes beyond the requirements of the standard.&nbsp;<br>O: The class follows a discovery structure, with students learning about reflection and symmetry via trial and experience.&nbsp;</p>

<p>Before the students arrive, write the following terms on the board: <i>line of symmetry, line of reflection, reflection,</i> and <i>symmetric</i>. Cut out one geometric figure for each student, and distribute them when they enter the classroom.<br><br><strong>Think-Pair-Share:</strong> Provide each student with a half sheet of paper. Assign each phrase written on the board to one-fourth of the class. Ask students to come up with their own definitions and examples for their term. Allow them around 3 minutes to work independently on this. 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 thoughts to the class. Continue to choose students to explain until you have a thorough description of all four words. To clarify, 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").<br><br>Place students' 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 illustrates the reflection motion. If some students slide their figure rather than flip it, explain that the "slide" action is a separate type of change (or transformation), known as a <i>translation</i>.<br><br>Repeat the technique, but instruct students to leave a little space between their figure and the pencil (on the left side) and keep this space on the right side after flipping the figure.<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_46.png" width="368" height="230"><br>After all students have successfully demonstrated the reflection action, instruct them to put the pencil away and attempt to fold their figure in half so that all parts of one half match the other without overlapping. When they open the fold, they'll notice the reflection line.<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_47.png" width="304" height="156"><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?"&nbsp;</strong><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 invite volunteers to reflect them, or show the reflection process yourself. Draw a simpler irregular polygon to show that 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 parts 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 such that the two halves match, like we did with our polygons. If it is a drawing rather than a cutout figure, hold it up to the light after folding to ensure that all sections 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><br><br>Distribute Alphabet Symmetry sheets to each student (M-4-5-3_Alphabet Symmetry and KEY). 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 clarify their answers on the overhead or whiteboard. Clarify any problem areas, such as N, S, and Z, which may look to have symmetry but 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 far more lines of symmetry than an oval or rectangular shape. Fold a rectangle of paper to demonstrate that the vertical and horizontal folds work but the diagonals do not. Draw a variety of additional figures to help students think about and verbalize the generalization that all oblong figures have only a few lines of symmetry (vertical and horizontal), whereas round, square, and other regular shapes have many more, if not infinitely many.<br><br><strong>"Next, we'll look at figures reflected across a line. The line of reflection, like the line of symmetry, is congruent on one side but 'flipped' on the other. The difference is that we will draw a complete figure on one side of the line of reflection and its reflection on the other side. Instead of splitting one figure in half by a symmetry line, we get two congruent figures. The distance between the two figures can be zero, small, or enormous, depending on how close the original figure is to the line of reflection. Consider placing your own polygon near your pencil </strong>(line of reflection)<strong>, reflecting it the first time, and then reflecting it away from your pencil the second time. Let us consider these examples."&nbsp;</strong><br><br>Display the following figures for students to see.</p><p><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_48.png" width="588" height="250"><br><br>[Note: Lines of reflection can be identified within a shape (Line 1) or used to reflect the complete shape (Line 2).]&nbsp;<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 only.</i>) Make sure students understand the distinction.<br><br>Call on one or more students to explain.<br><br><strong>"When working with lines of reflection, you will frequently be requested to draw the reflection over a particular 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 observe 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-4-5-3_Grid Paper Vertical and M-4-5-3_Grid Paper Diagonal). Cut out two sets of non-standard matching paper figures, like the ones seen below. Tape one to each line on the board or overhead. Hold the second congruent figure while overlying the original taped figure. 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 reveal the reflection.<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_49.png" width="460" height="225"><br><br><strong>Name Reflection Activity</strong><br><br>Give each student one sheet of grid paper with a vertical dividing line in the center (single-sided copies, M-4-5-3_Grid Paper Vertical). Ask students to write their names 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. Instruct students to "self-check" by folding their paper down the line and checking if the letters match. Show the action 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_50.png" width="186" height="260"><br>Before beginning the partner exercise, walk around the room to ensure that everyone understands and is accurate. Look for kids who are translating (sliding) rather than reflecting (flipping) their letters.&nbsp;<br><br><i>Optional task for students:</i> Have them turn another sheet of grid paper so that the line of reflection is horizontal. In this position, students will write their names above the line and reflect them below it.<br><br><strong>Partner Block Reflection Activity</strong><br><br>Divide the class into pairs of students. Give each student a double-sided sheet of grid paper with a vertical line drawn along the center of both sides (M-4-5-3_Grid Paper Vertical). Also, give each student a bag or envelope containing pattern blocks or paper pattern cutouts (M-4-5-3_Pattern Cutouts 1 and M-4-5-3_Pattern Cutouts 2). Instruct students to construct one side of the vertical line on their own grid paper with five to eight blocks or paper pattern cuts and a variety of forms. Each student's design should intersect the line in some way.<br><br>Once both students have completed a design, instruct them to construct a mirror image of their partner's design on the other side of the line on their partner's sheet. It may be beneficial to have students switch seats as they begin to develop their partner's reflection. This eliminates the need to shift or disturb sheets containing pattern blocks or paper cutouts. When students have completed their reflections, they should individually review their partner's reflection for accuracy. Once the partners are satisfied that their reflections are accurately depicted, students should raise their hands for you to review the drawings. If time allows, instruct students to repeat the process with a design that does not touch the line of reflection.<br><br>If you don't have enough time in class to examine all of the reflection designs, students can trace the outlines of the parts 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> Students may verify their work using a mira if one is accessible. Students would lay 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>While students are working on making reflections of their partner's designs, observe as you move around the room. Make recommendations or ask guiding questions to aid students who require additional practice or who are attempting to translate rather than reflect the statistics. Also, when pairs ask you to review their final reflections, encourage them to make necessary changes.&nbsp;<br><br>At the end of the lesson, assign each student or pair of students to complete the Quick Quiz (M-4-5-3_Quick Quiz and KEY).<br><br><strong>Extension:</strong> Use these suggestions to personalize the lesson to the students' requirements 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-4-5-3_Vocabulary Journal): <i>line of reflection, line of symmetry, reflection,</i> and <i>mirror</i> (or <i>line</i>) <i>symmetry</i>. Keep a supply of Vocabulary Journal pages on hand so that students can add them as needed. Bring up examples of reflection and symmetry from throughout the school year, including math and other curriculum areas such as art and science. Ask students to bring in samples from magazines or newspaper ads and explain how symmetry is used in that setting.</p><p><strong>Small Group: Symmetry Sort Activity:</strong> Use this practice with students who are struggling with the notion of several lines of symmetry inside a single figure. Give students the Symmetry Sort Figures and Symmetry Sort Mat (M-4-5-3_Symmetry Sort Figures and KEY and M-4-5-3_Symmetry Sort Mat). Students will need to carefully cut out the figures first. Figures can be cut following their outlines or as 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 alone or with a partner.</p><p><strong>Expansion or Station: Name Card Activity:</strong> This activity is suited for students who have demonstrated competency in reflecting their name or initials vertically and/or horizontally. Ask them 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 utilize. The designs should be vibrant and contain some kind of detail or pattern. Also, instruct students to draw a symbol or sketch at the beginning and end of their name that helps describe them, such as a football or a music note. Each student's name design should be reflected across a line, together with the pattern designs and symbols, in the same colors. Allow students to choose between vertical, horizontal, and diagonal representations for their project. Provide tools such as poster board and bright markers so that the name plate can be used on a locker, in class, or at home. Students will also need rulers.&nbsp;<br>[Note: 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:</strong> <strong>Partner Patterns Activity (Diagonal):</strong> Give each pair of students two pieces of grid paper with a straight line drawn diagonally (45°) through each page (M-4-5-3_Grid Paper Diagonal). Also, provide each student a bag or envelope with pattern blocks or paper pattern cutouts (M-4-5-3_Pattern Cutouts 1 and/or M-4-5-3_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 cuts and different shapes. Each student's design should intersect the line in some way. The assignment is for students to create the mirror image of their partner's work 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><i>Optional:</i> Students may verify their work using a mira if one is accessible. They would lay 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>Individual Technology: 20-a-Day:</strong> If computers are accessible for student usage, this activity could serve as extra practice or review. If you have the capacity to project on a classroom screen from a single computer, these tasks could be used as class practice or review, as well as in a classroom game. Practice problems can be found at:<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.&nbsp;<br><br>[Note: Users are restricted to 20 questions each day. Additional issues are only accessible to members.]<br><br><strong>Station 2 Option: Partner Building Activity:</strong> This task 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 divider will be placed between them so that the "builder" does not see the pattern being created. An open folder serves well as a divider. If a divider is not present, partners can sit back to back instead. Provide students with pattern blocks or pattern cutouts produced from various colors of paper (M-4-5-3_Pattern Cutouts 1 and/or M-4-5-3_Pattern Cutouts 2).&nbsp;</p><p>Instruct the designer to construct a square design with pattern blocks. The square's designer will provide guidance to the builder, allowing the builder to recreate a mirror of the design without seeing the original.&nbsp;<br>The builder will show the designer what the final design will look like. Finally, the two designs are compared visually to determine whether the builder truly created the reflection. If a mira is provided, students can compare designs by sliding them closer together and centering the mira between the two squares. 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:<br><br>Which words or phrases helped you recreate the design?&nbsp;<br>What words or phrases did you find confusing? Why?&nbsp;<br>Can you think of better ways to describe how to make the design?&nbsp;<br>If time allows, the activity can be repeated with the partners switching roles. Following the assignment, hold a classroom or small group discussion focusing on the students' geometric vocabulary.&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 qualities rather than their color. Customize the activity for different skill levels by using more/less challenging shapes.<br><br>[Note: The activity is most likely to be successful if students are paired similarly in terms of verbal and spatial skills.]<br><br><strong>Station 3 Option: Mira Activity:</strong> This optional activity uses miras and should only be considered if miras are accessible.&nbsp;<br>Provide four design blocks or pattern cutouts, a sheet of plain paper, and a mira (M-4-5-3_Pattern Cutouts 1 and/or M-4-5-3_Pattern Cutouts 2). Instruct students to arrange the four pattern blocks on the paper to form a basic design, or have them draw four figures on the paper. Next, instruct students to position 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 paper.</p><p>Keeping the same design in place, instruct them to place the mira in one corner (or vertex) of the design, but not on the full edge of the design or any figure. Again, have them draw what they see on the mira.</p><p>Finally, have students turn their paper over and recreate the same design. Instruct them to attempt two or three different mira positions so that it does not touch the design or any of its vertex. Encourage them to try locations that aren't just vertical or horizontal. Students should draw on paper what they see in the mira as it changes positions. They should compare how changing the line of reflection (the mira) affects the reflection result. Encourage students to describe what they are seeing as the line of reflection moves.</p><p>To conclude this project, draw several little designs and their reflections on a board or a transparency with distinct (not all vertical or horizontal) lines of reflection. Call for volunteers to draw the line of reflection. Allow students to check their answers with the mira.</p><p>The class follows a discovery structure, with students learning about reflection qualities and lines of symmetry through experimentation. Vocabulary terms were introduced first, then emphasized throughout the lecture. Students understood the distinction between reflection and mirror symmetry. They were asked to create symmetry and reflection in their designs, as well as determining the placement and amount of lines of both. The class closed with a short assessment designed to allow students to demonstrate their mastery in each of these areas. Several remediation, extra practice, and expansion exercises were proposed to help students better understand these concepts.</p>