# Zigzag vs Acute and Obtuse Angles

Integration of Math in Physical Education

For many years I have taught my students the term pathways.  In kindergarten through 2nd grade they learn about curvy pathways, zigzag pathways and straight pathways.  Primarily in relationship to the pathways they travel.  I describe this as: “if you had paint on your feet, and we were following the pathway you left.  Would it be zigzag, curvy or straight?.”

Students go on to practice moving in different pathways at different levels, and then apply the concept of pathways in chasing games.  I have found this very valuable as it seems few children intuitively understand to cut back and forth (zigzag pathway) to avoid a tagger.  This teaching extends to 3-5th grades when they are avoiding a defender.  In addition students learn the concept of  “open and closed pathways” in relationship to passing lanes.  Students learn “to get open” means to create an open pathway for an object to travel so it doesn’t get intercepted by an opponent.

However in mathematics teachers are not teaching curved, zigzag and straight lines past first grade.  Instead students are learning concepts relating directly to geometry.  A few of the math related common core standards for fourth graders reads:

• CCSS.Math.Content.4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
• CCSS.Math.Content.4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
• CCSS.Math.Content.4.G.A.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

I’m now asking myself ” Why have I been teaching curvy, zigzag and straight lines when clearly this doesn’t transfer to other learnings?”

With a simple change of terms I can easily integrate math terms, extending learning beyond the gym!

Curvy lines =Linked Arc Segments       I always have lines drawn on the white board to define what I am talking about, now with math terminology!

Zigzag lines= Angles (acute, obtuse, right)  Again I alway have lines drawn on white board, then have the students draw with their fingers, then we make the pathways with our feet.  I might use zigzag to describe  a line segment with acute angles, but no longer just as a zigzag line!

When I am teaching the pathway of an object in the air, such as volleyball, imagine the possible discussions that can be had around the trajectory arc of the ball!  Probably similar conversations to we had around the pathway of the ball but potential of  overarching themes between math and physical education get me excited!

My students start next week, so what brought on all this thought around math integration.  I have been thinking about how great quick 1-1 tag games are for teaching students dodging, or moving in acute angles.  I used to have many students, despite my great instruction, who still struggled with avoiding a defender.  These are the same students who when they are chased run straight away.  I realized that although I taught the skills, students didn’t use the skill in a game situation.

In the activity 1-1 tag students start by determining their playing space, which must not be larger than the basketball key.  Within these tight space constraints, students get the practice they need to embed “cutting” or moving in acute and obtuse angles to avoid a chaser or defender.