This activity uses the idea of folding to introduce students to line symmetry. Students analyze examples of figures that have a line of symmetry and those that don’t, and use their observations to formulate a definition of line of symmetry, which they then refine with their peers (MP6). Students later identify and draw lines of symmetry in various figures.

Some students may wish to use tools to help them define and find lines of symmetry. Provide access to patty paper, rulers, protractors, scissors, and copies of the figures (provided in the blackline master), if requested.

This activity uses MLR1 Stronger and Clearer Each Time. Advances: Reading, Writing.

• Ask groups to share their definitions of line of symmetry and record key phrases. Invite the class to comment.
• Discuss responses to the last two questions. Ask students to share the lines of symmetry they drew.
• “¿Cómo podemos comprobar que la línea que dibujamos es una línea de simetría? ¿Cómo podemos saber si las dos mitades que parecen ser idénticas en realidad lo son?” // “How might we check that the line we drew is a line of symmetry? How can we tell if the two halves that appear to be identical are indeed the same?” (Some ways:
  • Cut out the figure and fold it along the line we drew.
  • Trace one half of the figure on patty paper and turn it over to see if it matches the other half.
  • Measure the segments and angles.)
• “Si una figura se puede doblar por una línea para formar dos partes que son un reflejo de espejo la una de la otra y que coinciden exactamente, decimos que la figura es simétrica o que es simétrica con respecto a una línea” // “If a figure can be folded along a line to create two parts that are a mirror reflection of one another and would match up exactly, we say that the figure has symmetry or has line symmetry.”
• “La línea que divide la figura en dos partes que son un reflejo la una de la otra y que coinciden exactamente se llama una línea de simetría” // “The line that splits a figure into two mirroring and matching parts is called a line of symmetry.”

In this activity, students practice identifying two-dimensional figures with line symmetry. They sort a set of figures based on the number of lines of symmetry that the figures have.

Continue to provide access to patty paper, rulers, and protractors. Students who use these tools to show that a figure has or does not have a line of symmetry use tools strategically (MP5). Consider allowing students to fold the cards, if needed.

• “¿Cómo decidieron si una figura tenía una línea de simetría? ¿Qué buscaron?” // “How did you decide if a figure had a line of symmetry? What did you look for?” (Look for matching parts on opposite sides of a figure—parts that have the same size and mirror each other.)
• “¿Supieron inmediatamente que algunas figuras no tenían líneas de simetría? ¿Qué característica de las figuras hizo que eso fuera evidente?” // “Were there figures that you could immediately tell had no lines of symmetry? What was it about the figures that made it clear?” (The parts are different from one another. No folding lines could make two parts mirror each other.)

This optional activity gives students an opportunity to reason about lines of symmetry. Students see that some figures can be folded in half again and again. Some students may notice that certain shapes, like a square, can be divided into two equal halves in perpetuity (MP8). Each new half created by a line of symmetry will continue to be line-symmetric.

• “Las figuras A, B y C tienen más de una línea de simetría. ¿La línea por la que empezamos a doblar influye en el número de veces que se puede doblar la figura hasta que ya no tenga líneas de simetría?” // “A, B, and C have more than one line of symmetry. Does the folding line we start with affect how many times the figure could be folded before there is no more line symmetry?” (In these figures, the starting fold doesn’t determine how many folds can be made afterward.)
• 1 minute: quiet think time
• “¿Cómo pueden saber cuándo una figura doblada ya no tiene líneas de simetría?” // “How can you tell when a folded figure no longer has line symmetry?” (No segments are the same length and no angles are the same size.)
• “¿Qué ideas nuevas sobre las líneas de simetría aprendieron?” // “What new ideas about lines of symmetry did you learn?” (Folding a figure along a line of symmetry may create new figures that also have lines of symmetry. These lines may create more figures with symmetry. For some figures, this process could go on even if we cannot physically fold the paper any longer.)