The purpose of this activity is for students to explore area by making figures out of square tiles and ordering the figures from smallest to largest. Although students are prompted to create “shapes” in the activity directions, they may create figures that are not familiar polygons (see below). Students learn that they can use the term “figure” to describe a shape that doesn’t have a specific name.

Students may consider the size of the figures in a variety of ways. For example, they may see the first figure as larger than the second figure because the squares in the former are more spread out than in the latter, which is completely filled with tiles. In the Activity Synthesis, students learn that they can count the square tiles to determine the amount of space a figure covers.

Do not worry if students create figures that include gaps between tiles (as in the first figure above). Focus their conversation on describing the sizes of the figures. However, it may be necessary to encourage students not to stack the tiles on top of one another. Students will learn more about the importance of avoiding gaps and overlaps when measuring area in upcoming lesson activities.

• “Some of you created shapes that have names, such as 'square' or 'rectangle.' Some of you created shapes or designs that do not have names. We can call these shapes ‘figures’ as we talk about them. This word will be helpful in describing other shapes that don’t have names.”
• Invite previously selected students to share how they ordered their figures.
• As students share, consider asking, “How did you decide how much space each figure covered?”
• “It is common to use squares, such as the square tiles we used in this activity, to measure area. Each square tile is one square unit of area. If we count the number of tiles that make up a figure, we can find the area of the figure. For example, if a figure is covered by 12 square tiles, it has an area of 12 square units.”

The purpose of this activity is for students to use square tiles to measure area. Students are given square tiles and a variety of figures. Students cover the figures completely with square tiles and use the number of tiles to describe the area of the figure. In the Activity Synthesis, students share ideas about how to tile shapes in any way that makes sense to them. They also consider why it’s important to make sure they don’t leave gaps when they use square tiles to measure area (MP6).

There is an opportunity to ask students about the figures, the areas of which are the easiest to find. There is no right or wrong answer, but the question may elicit the idea that the structure of rectangles is helpful. This idea will be explored fully in future lessons.

• Display the first, fourth, and fifth figures.
• “How did you tile each figure?” (I filled the whole figure with tiles until I couldn’t fit any more. I started with the bottom row, then made the row above it until the figure was full.)
• “How did you determine the area of each figure?” (I counted the number of tiles it took to fill each figure completely.)
• Consider asking, “Which figures did you and your partner think had the easiest areas to find?” (The rectangle, because there were clear rows and columns. The third figure, because we could split it into 2 rectangles. All of them, because they could all be covered completely with square tiles and had no uncovered space.)
• “Why was it important not to leave any gaps as you tiled your figures?” (Because the whole figure needs to be completely covered. If there are gaps between tiles or around the edge, then the whole figure isn’t covered.)