Math Background

Lesson: Plane Shapes and Solid Shapes
Developing the Concept

Review the ideas taught in Introducing the Concept. Explain to children that they will be using pictures and models to learn more about shapes and their attributes.

Materials: sets of shape cards, blank construction paper, tracing paper, dot paper, dot-paper transparency, scissors, pencils, solid-shape manipulatives in the shapes of cubes, pyramids, rectangular prisms, cones, cylinders, and spheres. Have 2 to 3 manipulatives for each shape.

Preparation: Create a set of shape cards that includes varying sizes of rectangles, squares, circles, and triangles. Make at least enough cards for each child to get one shape. Make a sign for each of the plane and solid shapes, writing the name of the shape on the sign. Create a dot-paper transparency with several different plane shapes on it. Using a sheet of construction paper folded in half, cut out an irregular shape that has a line of symmetry along the fold. Spread manipulatives out on a table or desk. Hand out sheets of construction paper and dot paper to each child, along with a pair of scissors.

Prerequisite Skills and Concepts: Children should be familiar with the names and attributes of plane and solid shapes. They should have experience in drawing and labeling shapes and in working with manipulatives.

  • Show children a rectangle shape card.
  • Say: Let's talk about this shape. How many sides does it have? How many vertices does it have? Have children volunteer the answers to these questions. What is the name of this shape? Have a child come to the board and write the name of the shape. (rectangle)

    Hand one shape card to each child. Using the signs you made, designate separate stations for each plane shape on one side of the room (for triangles, squares, circles, and rectangles) and stations for each solid shape on the opposite side of the room.

  • Say: Each of you has one shape card. Take a few minutes now to write down the number of sides and vertices your shape has.
    Give children enough time to write their answers, and then allow them to share with the class. Now take your shape and go to the station where your shape belongs. Make sure each child is at the correct station.
  • Ask: How did you know where to take your shape? (If you know the number of sides and vertices, you can usually tell what the shape is.)

    Ask children to return to their seats with their shapes. Hand out one solid shape or solid-shaped object to each child. Then hold up a rectangular prism. Point to a face of the shape.

  • Say: Look at this shape. It is a solid, rather than a plane shape. I am pointing to one of the faces of the shape. How many faces does this shape have? Have children volunteer the answer to this question. (6) What is a good way to describe the face of a solid shape? (the flat surface)

    Now run your finger along one edge of the rectangular prism.

  • Say: Now I am pointing to one of the edges of the shape. How many edges does this shape have? Have children volunteer to count to answer the question. (12) What is a good way to describe the edge of a solid shape? (the place where two faces meet)
  • Say: Each of you has one solid shape. Take a few minutes now to write down the number of faces and edges your shape has.
    Give children enough time to write their answers, then allow them to share with the class. Then have them repeat the sorting exercise they did with the plane shapes. Make sure each child is at the correct station.
  • Ask: How did you know where to take your shape? (Knowing the number of faces and edges helps you tell what the shape is.)

    Ask children to return to their seats and take out their plane shape cards again.

  • Say: Here's another idea about shapes. You know that congruent shapes are shapes that are the same size and shape. Tell me how you can draw a shape that is congruent to the shape card you have.
    Discuss the children's suggestions. Guide them to see that they can use tracing paper to trace the shape. Both shapes will be the same size and shape.

    Have each child trace the shape and check for congruency. Then have children draw a shape of their own on a sheet of paper. The shape does not have to be a regular plane shape. Then have them trade papers with a partner. Have children draw a shape that is congruent to their partner's shape. Allow them time to share their drawings and their thinking with the class.

  • Ask: How do you know the shape you drew is congruent to your partner's shape? (I put the traced shape on top of the drawing and it matches exactly.)

    Now hold up the shape you cut from construction paper.

  • Say: Shapes can be described as having or not having a line of symmetry. This shape has a line of symmetry. Make sure all children can see the shape clearly.
  • Ask: What is the line of symmetry in this shape? How can you tell? Encourage children to point out that the line of symmetry is the fold line. (If you refolded the paper, the two halves of the shape would match exactly.)

    Have each child draw a shape with at least one line of symmetry on dot paper and cut out the shape. Allow children to decorate their shapes if they wish. Have children share the shapes they have created with the class and encourage them to describe the line(s) of symmetry in each shape. If children wish, allow them to display their shapes around the room.

Wrap-Up and Assessment Hints
Children will need practice working with shapes to become familiar with their names and attributes. Take the opportunity each day to draw their attention to different shapes around the classroom or other places you frequent, such as the library. Encourage them to identify the names and attributes of the shapes. Ask them to point out pairs or groups of shapes that are congruent and shapes that have one or more lines of symmetry.

Houghton Mifflin Math Grade 2