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# Estimating Angles

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### Clock Hands

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Estimating Angles is an engaging game that enables students to improve their familiarity with angles of different sizes. By setting this activity up as a game with a target to beat, students are likely to persevere and engage for longer than they might with a more traditional angles exercise.

The interactive provides instant feedback and in 2 player mode students can challenge a friend to beat their score.

Start the lesson by asking students what they know about angles, and collect together ideas such as names of angles (acute, obtuse, reflex, right-angled) and landmark angles (90 degrees, 180 degrees, 270 degrees, 360 degrees).

Draw acute, obtuse and reflex angles on the board and ask students to estimate their size. Encourage justification for estimates.

Draw another five angles on the board and challenge the class to make better estimates than you can. Invite students to estimate each angle, and then estimate the angles yourself. Then measure each angle with a protractor. The closest estimate gains a point.

You may wish to use the GeoGebra applet below - move the dot to change the angle, and tick/untick the box to show/hide its measurement.

Demonstrate the interactivity at Level 1 or 2 before setting the group off to work in pairs. The challenge is to score more than 50 points in 10 turns.

Keep a record of the highest score on the board. How close to 100 points can any pair get? Can anyone get an average of more than 8 after more than 10 turns? These could be long-term challenges, with students taking a screenshot when they get their average above a certain target.

Pairs could move on to Level 3 or 4 when appropriate.

Which angles are easy to estimate?

What strategies can you use to improve your estimates?

Paper Plate Angles are a great way to get students to engage with angle terminology. This YouTube Video shows how to construct them. Numberless protractors are also a valuable resource: NumberlessProtractor180.pdf and NumberlessProtractor360.pdf.

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?