• Assess student knowledge of triangles using the Lesson 2 Entrance Ticket (M-4-5-2_Lesson 2 Entrance Ticket and KEY.docx).
• Students may be evaluated based on their completion of the Categorizing Shapes worksheet (M-4-5-2_Categorizing Shapes and KEY.docx).
• Students may also be assessed based on performance on the Triangle Classifications sheet (M-4-5-2_Triangle Classifications and KEY.docx).

Activity 1

Draw a square on the board. “What shape is this?” Most students should identify it as a square. “How do you know it’s a square?” Students may identify that all four sides are the same. Record that information on the board. “What can you tell me about the angles in the square?” Students should be able to identify them as right angles; if not, take a moment to review the three kinds of angles covered in Lesson 1. Record on the board that a square has 4 right angles.

Then, highlight two opposite sides of the square. “What can you tell me about these line segments? If they were lines and kept going forever, would they ever cross?” (no) Then, highlight the other two sides of the square and ask the same question. Record that a square has 2 sets of parallel sides.

“All of these things—that the sides are all the same length, that there are 4 right angles, and that there are 2 sets of parallel sides—are all properties of a square. Any time you draw a square, it must have all these properties.”

Now, draw a rectangle on the board. Make sure it is clearly a rectangle and not just a square,
i.e., the length is much longer than the width.

“Is this a square?” (no) “Why not?” Students should point out that all 4 sides are not the same length. Ask about the other properties that were assigned to a square: “Are there four right angles?” (yes) “Are there two sets of parallel sides?” (yes) “What do we call this shape?” (rectangle) Record that it is a rectangle and record its two attributes.

“So it’s almost the same as a square. A rectangle just has to have two sets of parallel sides and four right angles. That’s what makes it a rectangle; as long as any shape has these two properties.” Discuss whether a square has the two properties required to be a rectangle. Talk about the fact that a square is really a special kind of rectangle, but that a rectangle is not a square because it doesn’t have all the properties noted for a square.

Then, draw a parallelogram. “Is this a square?” (No.) “Is this a rectangle?” (No.) “Why not?” Students will note that it doesn’t have four right angles. “Does it share any properties with a rectangle?” Students should note that it does have two sets of parallel sides. Label the figure parallelogram and record its only property: that it has two sets of parallel sides. Point out that the word parallel is right in the name parallelogram and that’s the only property you have to remember for determining whether something is a parallelogram.

“Is a rectangle a parallelogram?” If students aren’t sure, rephrase it as, “Does a rectangle have two sets of parallel sides?” (yes) “Then it is a parallelogram.”

“Is a square a parallelogram?” (Yes.)

Point out that a square is also a rectangle and a parallelogram.

Finally, draw a trapezoid on the board. “Is this a parallelogram?” (No.) “Why not?” (Because it doesn’t have two sets of parallel sides.) Point out one set of parallel sides (the bases), but demonstrate that the other two sides are, indeed, not parallel by extending them until it is clear they’ll intersect one another. “So, if it’s not a parallelogram, can it be a rectangle?” (No.) “And can it be a square?” (No.)

“So this shape is kind of all by itself. It doesn’t fit in with the other shapes we’ve learned about so far. It’s called a trapezoid and has just one property.” Write the word trapezoid and write its property: Exactly one set of parallel sides.

Activity 2

“The previous activity was about categorizing shapes with four sides. They have all sorts of names: square, rectangle, parallelogram, trapezoid, and there are some we didn’t learn about. Polygons with three sides are a little easier. First, what do we call a shape with three sides?” (Triangle.)

Draw a right triangle on the board. “Describe the angles in this triangle.” Students should note that there are 2 acute angles and 1 right angle. “Because there is one right angle, we call this triangle a right triangle. It doesn’t make a difference what the other angles look like. As long as it has a right angle, it’s a right triangle.” Write the term right angle under the picture and write has 1 right angle.

Have a volunteer come to the board. “Draw a triangle that is not a right triangle. Your triangle should not have a right angle in it.” Depending on what kind of triangle is drawn, employ the discussion below about acute or obtuse triangles.

After that discussion, ask for a volunteer to come up and draw a triangle that does not fit either of the two descriptions so far.

For acute triangles:

“Describe the three angles in this triangle.” Students should identify all of them as acute angles. “Because this has three acute angles, we call it an acute triangle.” Write the term and the definition next to the picture. “Notice that our right triangle had two acute angles. That’s not enough to make it an acute triangle. Acute triangles have to have three acute angles.”

For obtuse triangles:

“Describe the three angles in this triangle.” Students should identify two acute angles and one obtuse angle. “Because this has one obtuse angle, we call it an obtuse triangle.” Write the term and definition next to the picture. “Like our right triangle, we only care that it has one obtuse angle. We don’t really care about the other two angles.”

Ask for a volunteer to come up and draw a triangle that doesn’t fit any of the three descriptions so far. (This is an impossible task.) If students think they have one, let them come up and draw it, and then guide the class through the categorization process (or note why the figure is not a triangle at all, i.e., it has curved sides, isn’t closed, or has more than three sides).

Point out that every triangle falls into one of these three classifications.

Have students work in pairs to complete Categorizing Shapes worksheet (M-4-5-2_Categorizing Shapes and KEY.docx).

Students may be given the Triangle Classifications sheet (M-4-5-2_Triangle Classifications and KEY.docx) to complete if time allows, or for homework to help them further explore this skill.

This lesson scaffolded on previous learning about geometric shapes and attributes of geometric shapes. Students learned to classify quadrilaterals and triangles based on their attributes and definitions. Students should now understand that some figures will fit into several categories,
i.e. a square is a quadrilateral and a rectangle and a parallelogram.

Extension:

• Routine: To help students remember what they learned about triangles, have students redo the lesson activity by drawing more triangles. Begin by handing out blank papers and saying, “Please divide the sheet of paper into four quadrants like so.” On the board draw a rectangle to represent the paper and then a horizontal and vertical line through the middle (creating quadrants). Then say, “Now number them one through four in the upper left-hand corner of each quadrant. In the first quadrant please draw 3 triangles that are right triangles.” Give students under a minute to do this. Then say, “In the second quadrant draw 3 acute triangles.” Give them under a minute to do this. Then say, “In the third quadrant draw 3 obtuse triangles.” Give them under a minute to do this. Then say, “In the last quadrant, draw 1 triangle of each type and label each of them correctly.”

Many opportunities for refreshing definitions of geometric figures and categorizing shapes by attributes will present themselves during the course of the year as students continue their geometry studies.

• Small Group: Some students may benefit from additional practice or discussion of lesson concepts in small groups. Each group will be in charge of designing a “Type of Triangle” poster. Each poster must be titled with the type of triangle, include the written definition (in their own words), and display a “large” drawing of the triangle to model the definition. Students can also complete a similar activity for the four types of quadrilaterals discussed.
• Expansion:The lesson can be expanded in the following ways:
  • Students can explore classification of triangles based on side length rather than angle measure (scalene, isosceles, equilateral) and can then classify triangles based on both types of classification (i.e., isosceles right triangles).
  • Students can explore additional quadrilaterals (kites and rhombuses) and also create a Venn diagram showing the relationship between various types of quadrilaterals.
  • Students can explore convex and concave quadrilaterals.
  • Students may also practice recognition of geometric shapes using the game at the Web site: http://www.bbc.co.uk/bitesize/ks2/maths/shape_space/2d_shapes/play/.