Lesson plan

Half-to-Half Symmetry

Where's the other half? In this lesson, young mathematicians learn the relationship between halves and symmetry through a fun scavenger hunt. Your students will have a blast figuring out what makes a shape symmetrical.
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Students will understand the concept of symmetry and be able to identify lines of symmetry.

(5 minutes)
  • Hold up a piece of paper and fold in half.
  • Ask students for "help" on how to make a heart.
  • Guide students toward the idea that you need to make half of a heart, then unfold it.
  • Think aloud as you cut half of a heart about how both sides will match and be symmetrical since you folded the paper evenly.
  • Open up and display the two halves that made a whole heart.
  • Point to the middle and draw an invisible line from the top to the bottom. Explain that this invisible line, where the fold was, is the line that divides in half two sides that match. Add that his line is called a line of symmetry.
(10 minutes)
  • Draw a face on the board, with ears. Draw a line in down the middle of the face and explain that our faces are symmetrical; we have two eyes and two ears, with one of each on each side.
  • Tell students we will now draw an invisible line from the top of our heads to our shoes.
  • Direct students to put their hands together directly in front of the middle of their bodies, as though they were in the middle of clapping.
  • Demonstrate "drawing" a line of symmetry down the middle of your face. Complete the body line of symmetry by moving your hands down to between your shoes.
  • Direct students to do the same.
  • Explain that we just created an invisible line of symmetry down the middle between the left and right sides of ourselves. Add that we can do this with shapes.
  • Hold up the heart from the Symmetrical Shapes sheet and ask students to remember what happened the to heart cutout from the Introduction. Ask them to think about where the line of symmetry would be.
  • Fold the heart shape in half, on the line and emphasize only the vertical line works to show matching half.
  • Fold the heart shape horizontally to demonstrate that this does not cut the shape in half, nor does it create matching halves.
  • Repeat the above procedure with the triangle, demonstrating that the line of symmetry only works when it’s folded horizontally.
  • Hold up the square and show how it works both horizontally and vertically. Ask students why this is. Make sure they understand the importance of the fact that a square has four equal sides.
(15 minutes)
  • Pass out sheets of white paper.
  • Ask students to each draw a symmetrical shape and cut it out.
  • Direct students to fold the shape they cut out down the middle to create a line of symmetry.
  • Direct the students to cut the shape in half down the line of symmetry.
  • Gather the half shapes and mix them together in a bowl or other container.
  • Gather students together to begin a short game.
  • Have each student pull a shape half out of the container.
  • When all students have a half, have them use clues to try to find their other halves. For example, a student may say, "My half has a curve."
(15 minutes)
  • Distribute the Complete the Shape worksheet and explain its directions.
  • Have students complete it independently.
  • Circulate the room to monitor for understanding.
  • Enrichment: Challenge advanced students to combine multiple shape halves to make symmetrical shapes. For example, four triangles can be symmetrical if you arrange them properly.
  • Support: Give struggling students one-on-one support. Walk them through what makes a shape symmetrical.
(5 minutes)
  • Name a shape and ask students to say "yes" if it's symmetrical and "no" if it's not.
  • Assess students' understanding of the lesson content based on how they respond.
(10 minutes)
  • Review the meanings of "half," "symmetrical," and "line of symmetry."

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