Teaching Angles

We are surprised every year (re-surprised?) at the most common mistakes fifth graders make around angles.

What’s NOT surprising:

  • The difficulty of choosing WHICH of the 2 numbers you encounter on the protractor… Is is 60º or 120º?

What IS surprisingIMG_2138

  • Measuring an angle that isn’t there…



  • Measuring the LENGTH instead of the angle:






  • IMG_2140.jpgLooking for AREA …






How to correct misunderstandings and build the concept of what an angle is:

  1. Spaghetti to the rescue, again. By holding down one of the angle legs, and moving the other, we can TALK through the opening and narrowing of an angle, COUNTING as the angle grows and shrinks. The counting helps students know what the size is – for example 60 not 120 degrees. It helps them internalize the idea of what an angle is; the gradual opening (like a fan) of the 2 angle legs.  Note – some students have to do this MULTIPLE, multiple, multiple times before it becomes intuitive. Whenever they’re confused, have spaghetti around!

2. If you have Geometer’s Sketchpad software, it functions similarly. Students can drag one leg of an angle to demonstrate different angle sizes and pairs. Students created videos similar to the one below.

3. Finally, give LOTS of opportunity for review. Here’s a game we played — we’re trying to offer a couple levels of challenge in each slide. CW angles

Game Rules: Half the class sits in a circle in IMG_2143

the middle of the room, at their desks.

The other half sit INSIDE that circle, where they

work in teams (7 teams for example, at right).

After every slide, the students on the inside rotate to the next table. This decreases competition and yet keeps the groups conspiratorially quiet and motivated. (You can keep score by team number, but it doesn’t mean a lot because of the rotation.) Smaller groups than 4 are even better.

Final note: The LEARNING going on in this unit should be the visual concept of what angles are — by size, by pairs, in triangles. Vocabulary should be a useful acquisition, but a secondary one. The goal is the solving of complex angle puzzles – an activity most children enjoy naturally. More on that next posting!





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