Why can I not make a really thin angle?

Because the number is written inside its own wedge, and below about twenty degrees two labels sit on top of each other and a class cannot tell which number belongs to which angle. A drag that would squash one is refused rather than clamped, so nothing moves.

Do the numbers always add up exactly?

Yes, by construction. The rays are whole degrees, so the angles between them are whole numbers that add to exactly 180 or 360. The triangle's third angle is worked out as 180 take away the other two rather than measured on its own, so three rounded numbers can never come to 179.

Can the class find the missing angle without being shown?

That is what tapping an angle is for. It becomes a question mark, the sentence under the picture shows the subtraction with the answer left off, and Answer fills it in when you are ready.

Angle Facts

Shape & Space · Year 5–Year 6

Angles on a line, round a point and in a triangle, and they add up.

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About the angle facts

Three boards: angles on a straight line, angles round a point, and the angles in a triangle. Drag a ray, or a corner of the triangle, and the numbers change while the total does not. That is the whole objective, and it is something a class watches rather than something the board tells them.

The protractor tool measures one angle. This one is about a set of them adding up, which is the Year 5 and Year 6 fact: 180 on a straight line, 360 round a point, 180 in a triangle. A class that has only ever measured cannot answer “the other one is 55, how do you know”.

Tap an angle to turn it into the question. It becomes a question mark, and the sentence under the picture turns round from an addition into the subtraction a class has to do: 180 minus 125 equals what? The answer stays off the board until you press Answer, because a board that shows the thing it is asking for is not asking.

Everything is worked out from where the rays are, so the board can never print a set of angles that do not add up. The rays are whole degrees, so the numbers are exact rather than rounded. The triangle's third angle is 180 take away the other two, for the same reason: three angles each rounded on their own can come to 179, and a class would spot that immediately.

Press New for a fresh arrangement, and How many to split a line into two or three angles, or a point into three or four.

How to use it on your whiteboard

1Pick a board: straight line, round a point, or triangle.
2Drag a ray, or a corner of the triangle. Watch the numbers change and the total stay the same.
3Tap an angle to hide it. The sentence turns into the subtraction the class has to do.
4Press Answer when they have had a go, or tap the angle again to put it back.
5Press New for a fresh set, and How many to split it into more angles.

Questions

Why can I not make a really thin angle?: Because the number is written inside its own wedge, and below about twenty degrees two labels sit on top of each other and a class cannot tell which number belongs to which angle. A drag that would squash one is refused rather than clamped, so nothing moves.
Do the numbers always add up exactly?: Yes, by construction. The rays are whole degrees, so the angles between them are whole numbers that add to exactly 180 or 360. The triangle's third angle is worked out as 180 take away the other two rather than measured on its own, so three rounded numbers can never come to 179.
Can the class find the missing angle without being shown?: That is what tapping an angle is for. It becomes a question mark, the sentence under the picture shows the subtraction with the answer left off, and Answer fills it in when you are ready.