Find the missing angle on a straight line

What this sequence teaches

The whole routine for finding a missing angle on a straight line, one step per click. It assumes students have met each step on its own: Are these angles on a straight line?, Recall the angles on a straight line fact and Write the calculation for the missing angle. None of those names appears on screen, so say as much or as little as you like. The fact itself does appear, at step 2, because saying it is part of the routine.

The steps

1. Decide. Which angles are on a straight line with x? Nothing is highlighted, so students have to choose. On the click the straight line lights up, the point pulses, and an orange line runs round each of those angles in turn. Angles that are not on the line with x are left as they were.
2. Say the fact. Before you click, ask students to say it, or write it: “Angles on a straight line add up to 180°.” The click then shows the sentence. It appears instantly, with no fade, so there is no glimpse of it beforehand. This step is easy to skip, and it is the one that usually stays hidden: knowing which angles to use is not the same as knowing what they add up to.
3. Write the calculation. 180 arrives first. Then each angle students know lights in turn and its number moves from the diagram into the calculation. Nothing is worked out yet.
4. Work it out. The answer appears. This step is optional. If you don’t want students to do the arithmetic, stop on the calculation; if you want calculators out, this is the moment. It has no page of its own.

The two examples

Example 1 — 47°, x and 68° on one side of the line, 124° on the other. x = 180 − 47 − 68, so x = 65°. The 124° meets the others at the same point, but it is on the other side of the line, so it is never marked and never used.

Example 2 — x moves to the other side. One thing changes: where x is. Now the 124° is the only angle on a straight line with it, so x = 180 − 124 = 56°. On Next the old working fades first, the stage pauses, and only then does x move, so nobody misses it. While you work through it, the previous answer (x = 65°) stays at the bottom of the stage, dimmed and labelled, so you can ask students to predict whether the answer will change. It is replaced only when the new answer is shown.

Running the sequence

• Nothing moves between steps until you click, so you can talk or check boards for as long as you want.
• Replay shows the last thing again. Why? gives the reason for the step on screen.

About the testing sequence

Six diagrams in a fixed order. Students write every line on their whiteboards: the fact, the calculation and, if you want it, the answer. There is no scoring; the whiteboards are the data. Early on you might check boards after each step. Later, ask for all the working at once and click through to compare.

What each item catches

1. x, 58° and 73°, with 116° on the other side → x = 180 − 58 − 73 = 49°. A board with 116 on it means every number on the diagram was used. 360 − … means the wrong fact. 58 + 73 means no 180.
2. The same diagram, with x on the other side → x = 180 − 116 = 64°. The previous answer stays on screen, dimmed. A board that still has 58 and 73 on it means the student copied the last calculation without looking at where x is.
3. x and 112° on a sloping line → x = 180 − 112 = 68°. 112 − 180, or a blank, means the student thinks two numbers are needed.
4. 31°, 44°, x and 38° on an upright line, with 78° on the other side → x = 180 − 31 − 44 − 38 = 67°. Only two angles taken away means the student stopped early.
5. 53°, x and 46°, with 71° at a second point on the line → x = 180 − 53 − 46 = 81°. A board with 71 on it means the student used an angle that doesn’t meet the others at one point.
6. x and 118°, with 137° and 43° on the other side → x = 180 − 118 = 62°. Both sides of the line are full of numbers. Only one of them is on a straight line with x.

Reading the boards

• The wrong angles in the calculation: go back to “Are these angles on a straight line?”
• 360, or no 180 at all: rehearse the fact.
• The right angles and 180, but added, or the wrong way round: go back to writing the calculation.
• The calculation is right but the answer is wrong: it is an arithmetic slip, and nothing about angles needs reteaching.

About the expansion sequence

Three diagrams with no new teaching. Each adds one thing, and the routine still works.

1. A right angle shown only by its square corner → x = 180 − 90 − 36 = 54°. The 90 is not written on the diagram, but it is still taken away. Check beforehand that students know a square corner means 90°.
2. Four angles known → x = 180 − 27 − 43 − 35 − 46 = 29°. The 128° on the other side is not used.
3. Two angles are both x → 2x = 180 − 40. This one stops at the line of working, because what comes next is solving an equation, which is a different routine. A student who writes x = 180 − 40 has missed that there are two of them.