Geometry: Hide and Seek
||6 to 8|
||10 to 20 minutes|
This lesson was excerpted from the Afterschool Training Toolkit
under the promising practice: Math Games
This is an example of a Math Game that builds geometry skills. In this activity, students hide geometric shapes on coordinate grids while others try to find the vertices from hints.
- Use coordinate systems to specify locations
- Use coordinate geometry to represent and examine the properties of geometric shapes
- Use coordinate geometry to examine specific geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides
- Gather materials.
- Determine how you would like to generate the groups. Perhaps have students count off by threes, or assign them to a group of three.
What to Do:
- Group students into threes. One student hides and the other two seek geometric figures in a coordinate system.
- Provide the hider with one grid and the "seekers" with an identical grid. During play, the hider is back-to-back with the seekers.
- Have the hiders draw a geometric shape on the grid, making sure the vertices, the intersections of two or more lines of the geometric figure (for instance, a corner), have integer coordinates.
- After the hider draws the geometric shape, he or she begins the game by telling the seekers what type of geometric shape was drawn.
- The goal of the game is for the seekers to cooperatively locate the points corresponding to the vertices of the hidden shape. The hider provides clues after each guess that tells the seekers where the guess is relative to the shape. There are four clues that can be given during the game: (1) inside the shape; (2) outside the shape; (3) on an edge but not a vertex; or (4) a vertex. The seekers use the clues, their knowledge of a coordinate system, and their knowledge of the properties of geometric shapes to find the vertices in as few guesses as possible.
- Once the seekers have determined all the vertices of the shape, the students rotate positions so that each student has the opportunity to be the hider.
Students may have a question about how to start, and it may be helpful to talk with them about how the playing grid works and the vocabulary that relates to it: x-axis (the horizontal axis), y-axis (the vertical axis), ordered pair, (x-coordinate, y-coordinate), vertex, edge, and the names of common geometric shapes, from triangle through octagon.
Students may begin by using their own informal terms, which is fine, but be sure to check their understanding of the underlying concepts, and encourage them to order their points in an x,y sequence. For instance, even if they are using terms like "four points up" or "three to the right," ask them to put the horizontal direction first.
As students play, encourage the group seeking the figure to talk about how they will keep track of each guess, and which of the four conditions each guess met. The hider should tally the number of guesses.
The students' language to refer to the points may be ambiguous. Phrases like, "the point all the way at the left" or, "just below the last point" may come up. If you hear something like this, ask the seekers how the hider will know how to answer and whether there is a more concise, less ambiguous way to refer to a point. This way, students may see the value of the (x,y) ordered-pair approach, which does not depend on outside references and is less ambiguous.
If someone draws a circle, or another shape that is not a polygon, ask them to draw a regular polygon instead, but as time allows discuss circles or curves after the play.
Ask students to review their strategies. Were some figures harder to find than others? Why? How did they keep track of what they had discovered?
Evaluate (Outcomes to look for):
- Student engagement and participation
- Comments and answers that reflect students using properties of geometric shapes to help them find coordinates
- Comments and answers that reflect students using coordinate systems to specify locations
- Students working cooperatively and discussing strategies for selecting the next coordinate
Click this link to see additional learning goals, grade-level benchmarks, and standards covered in this lesson.