Sorting Shapes

Est. Class Sessions: 2–3

Developing the Lesson

Sort Shapes Built with Triangles. Using the shapes built from triangles in Lesson 4, students will sort shapes into categories based on properties of the shapes. Display the Shapes from Triangles chart you prepared. See Materials Preparation. Tell students that you have sorted all the shapes the students made in Lesson 4 into four groups.

Give students a few minutes to examine shapes in each group and ask:

What property did I use to sort the shapes into each group? What is the same about all the shapes in each group? (Possible response: The shapes are sorted by the number of sides and angles. The shapes in Group 1 have three sides and three angles. The shapes in Group 2 have four sides and four angles. The shapes in Group 3 have five sides and five angles. The shapes in Group 4 have six sides and six angles.)
What are the names of the shapes in each group? (Possible responses: triangles, quadrilaterals, pentagons, hexagons)
Choose a group. Draw an additional shape that belongs in that group.

Students will probably easily name the triangles in Group 1. Quadrilaterals have four sides; pentagons have five sides, and hexagons six. Label each group of shapes with the appropriate names. Distribute one self-adhesive note to each student. Ask them to choose one of the four groups and to draw a new shape that would go in that group. Then ask students to add their shapes to the display.

Display and discuss Questions 1–3 in the Student Guide to analyze the properties of groups of shapes. These questions show other ways to sort the shapes into two groups. In Question 1, the shapes in Group 1 have at least one right angle and the shapes in Group 2 do not have any right angles. In Question 2 students are asked to examine the shapes using a property: opposite sides the same length. They are also asked to add a shape and to think critically about another shape added to the group. Display the groups in Question 2 and ask several students to share the shapes they added to each group (Question 2B).

Discuss Question 2C further by asking:

What shape did Natasha draw? (rhombus)
All the shapes you have been sorting are shapes made from the small right triangle tangram pieces (isosceles right triangles). Do you think this shape could be built from these right triangles? (No, the rhombus could not be made with the small triangles because the sides of the rhombus have to be the same length. If the long sides of the right triangles are put together, a square is built. If the short sides are put together, the resulting parallelogram has two sides longer than the other two sides.)

Attempt to build a rhombus using the small right triangles from a set of tangram pieces and discuss the differences in side length.

Display the groups in Question 3 to discuss how students are analyzing the shapes. Use Question 3C to introduce the concept of parallel sides. Parallel sides are the same distance apart.

Ask:

Look around the room. Can you find other shapes in the room that have parallel sides? (Possible response: the sides of the doorway, the top and bottom of the board, the top and the bottom of a wall, the sides of a bookcase)

Play Shape Finder. Ask students to refer to the shapes on the cards they prepared from the Quadrilateral Sort Cards in the Student Activity Book. Note that the shapes are quadrilaterals made from the small right triangles except for the last shape in the last row. This shape is the rhombus that Natasha added to the sort in Question 2 in the Student Guide. Display the Shape Finder chart you prepared and tell students the rules of the game.

Ask:

I will name a property of a shape. A property is an attribute or characteristic of a shape that helps you identify it. For example, I might say, “Find a shape with four sides” or “Find a shape with a right angle.”
Be ready to show or tell how you made your choice.

Have students find at least one shape that has each property and prepare to explain their choices. The table in Figure 2 provides a list of properties, examples of shapes, and lists one possible explanation for identifying each property. Others are possible. It is not necessary for the class to find every shape that has a given property.

At this point in students' development it is not necessary for them to give a rigorous geometric proof to justify their choices of shapes. For example, they do not yet have the tools to prove that opposite sides of a given shape are parallel. It is enough for them to visually identify the parallel sides and show that they understand what it means for lines to be parallel. However, they should be clear in their explanations and be able to point to the parts of the shapes they discuss.

As the class discusses each property, build a Shape Finder Chart of the properties with examples of the shapes from several copies of the Quadrilateral Sort Cards Master you prepared. This will compile a record of the properties and corresponding shapes that students can use during the remainder of the lesson. See Figure 3 for the beginning of a sample chart.

After playing Shape Finder, ask students to discuss the shapes and their properties.

Ask:

Are there shapes that have some of the same properties?
Which properties show a rectangle? (Possible response: four sides, at least one right angle, all right angles, at least one pair of parallel sides, two pairs of parallel sides, opposite sides are the same length, and all sides are equal.)
Which properties show a square? (all sides are equal, four sides, at least one right angle, all right angles, at least one pair of parallel sides, two pairs of parallel sides, opposite sides are the same length, and all sides are equal)
What is the difference between a rectangle and a square then? (A square is a rectangle, but a square has sides that are all the same length.)

Play Mystery Sort with Quadrilaterals. Display a two-column table. Label one column “Yes” and the other “No.” Use the display set of the Quadrilateral Sort Cards Master you prepared to demonstrate how to play Mystery Sort.

Ask:

Watch carefully as I sort some of the shapes into two groups, one shape at a time. If a shape has the mystery property, I will put it in the “Yes” column. If a shape does not have the mystery property, I will put it in the “No” column.
Do not guess out loud. Sometimes I will use all the possible shapes that belong together in the “Yes” column, and sometimes I will not. When you think you know the property, raise your hand and I will call on someone to place a remaining shape in the correct column. If you think a shape has been incorrectly placed in a column you may move it. When all shapes have been placed in one of the columns, we will name the property.

Use the list of properties on the Shape Finder chart to sort the shapes. This sorting activity will be used to classify quadrilaterals: rectangles, squares, rhombuses, parallelograms, and trapezoids. Following are some sample sorts and the related discussions:

Play Mystery Sort by placing all shapes with only one set of parallel sides in the “Yes” column and all other shapes in the “No” column. See Figure 4.

Ask:

What is true about all the shapes in the “Yes” column? (They all have only one set of parallel sides.)
Draw another shape that would fit in the “Yes” column. (See Figure 4.)
Draw another shape that would fit in the “No” column. (See Figure 4.)

Play Mystery Sort by placing all 12 sort cards in the “Yes” column.

Ask:

What is the same about all of these shapes? (All of these shapes have 4 sides.)
What are these shapes called? (quadrilaterals)

Play Mystery Sort by placing the shapes with two sets of parallel sides in the “Yes” column and shapes that do not in the “No” column. See Figure 5.

Ask:

What is true about all the shapes in the “Yes” column? (They all have two sets of parallel sides and opposite sides are the same length.)
Draw another shape in the “Yes” column. (See Figure 5.)
Draw another shape in the “No” column. (See Figure 5.)

Ask students to play Mystery Sort with a partner using the directions on the Mystery Sort: Quadrilaterals page in the Student Activity Book. For now ask students to use only the category cards with shape properties. These category cards do not have stars. Students will play with these other categories during Summarizing the Lesson.

Observe students as they play Mystery Sort to assess students' abilities to describe [E1] and classify [E4] twodimensional shapes using their properties.

Student Guide: 310 311

Answers