Take a turn with your body

Look at a wall. Spin around until you’re looking at the back wall: you’ve made a u-turn. Another half turn takes you back to the start. Now try to do the same spin in four equal parts. Each part is a quarter turn.

A lap can be split in several ways. Two halves and four quarters complete the same lap:

$$\frac12+\frac12=1,\qquad \frac14+\frac14+\frac14+\frac14=1.$$

Here the number 1 represents a full turn. We are not measuring the length of the path your feet travel, but the turn of your direction.

Why do two quarters make a half?

Draw a circle and fold it into four equal parts. Paint two neighboring parts. The painted region occupies half of the disk. That’s why:

$$\frac14+\frac14=\frac24=\frac12.$$

This is a demonstration by apportionment: the same parts can be counted in quarters or in halves.

A name for the measure

Adults often say that a turn has $360°$, read as “360 degrees”. Then:

$$360°\div2=180°,\qquad360°\div4=90°.$$

It is not necessary to memorize numbers before recognizing the spin. Make a full turn, a half and a quarter; only then associate the names with the measurements.

In everyday life

  • United order. At school and in the army, “turn around, turn around!” he says turn half a turn, and “right, turn!”, a quarter turn.
  • Steering wheel and tap. Opening a tap “a quarter of a turn” or turning a steering wheel “half a turn” are measurements of turning.
  • Clock. In 15 minutes the large hand makes a quarter turn; in 30 minutes, half a turn.
On the clock, 15 minutes are a quarter turn of the large hand and 30 minutes are half a turn.

Activity

Make a marker with an arrow on a disk. Start from the top position and advance a quarter of a turn at a time. You will visit four directions before returning to the start. At each stage, say how much you have turned: one quarter, two quarters, three quarters and one turn.

Exercises with resolution

1. You have turned three-quarters of a turn. How long does it take to complete the lap?

Check resolution 1

One quarter left: $\frac34+\frac14=1$.

2. Do two half-turns lead to the initial direction?

Check resolution 2

Yes. $\frac12+\frac12=1$ comes back. The rotation carried out exists, even if the final direction is the same as the initial one.

Correspondence with source material

Preparatory activity on angles and triangles, adapted for this stage. General formulas appear in the following tracks.

The text of this class is a didactic rewrite. The page transcription preserves the sequence of exercises and other items from the original; it still has OCR snippets pending review.

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