The purpose of this activity is for students to compare shapes to decide which is larger. Given their prior experiences with length, students may initially use length to reason about what it means for a shape to be larger than another shape. The Activity Synthesis should bring out the idea that length alone is not enough to compare two-dimensional shapes. Ideas around how much space the shapes cover should be emphasized. If students disagree about which shape is larger, encourage them to share their reasoning so that the class can consider multiple ideas and come to a resolution together (MP3).

• “Which shapes did you change your mind about as you discussed your ideas with your partner?” (In the last problem, I thought that the skinny rectangle was larger because it was taller. My partner showed me how to cut the rectangles to compare them.)
• “Are there shapes you still disagree about?”
• Have students share their justifications for any lingering disagreements.
• As students share, bring out the idea that the larger shape covers more space.  
• Consider asking:
  • “What questions do you have?”
  • “Do you agree with their reasoning?”
  • “Did you justify your choice in a different way?”

The purpose of this activity is for students to compare shapes by covering them with pattern blocks. Students experience tiling as a way to see which shape covers the most space. There are several ways to tile the shapes, but it may prove most useful to use the same units, such as triangles. The rectangle can be fully tiled only with square pattern blocks. To compare Shapes B and C, students need to notice that the rectangle and the parallelogram can be made the same length, but the square pattern blocks used to tile the rectangle are taller than the blocks used to tile the parallelogram.

The work here prepares students to tile figures with square tiles in the next lesson and to think of area in terms of square units.

• Ask selected students to share strategies for tiling each shape with pattern blocks and how the tiling helped them decide which shape covers the most space.
• “When we decide which shape covers the most space, we are talking about the area of a shape. We can think about the area as the amount of space covered by a shape.”
• “Which shape has the greatest area?” (Shape C takes up the most space, so it has the greatest area.)