Is this a bearing?
A categorical atom from mrbartonmaths.com
What this sequence teaches
A bearing is an angle that starts at the North line and turns clockwise. Both parts matter: failing either one is enough to make an angle not a bearing. Everything else can vary freely — which way the other line points, how big the angle is (including over 180°), and whether other lines are drawn.
Both parts are taught in one sequence on purpose. A sequence about “from North” alone would have the rule “if it’s measured from North, it’s a bearing” — which is, word for word, the anticlockwise mistake.
The teaching sequence
Example 1 (not a bearing). A line just west of North, marked with the small anticlockwise angle. This is the commonest bearings error: “it’s 55° from North”.
Example 1 → Example 2. Same two lines. The arc shrinks back into the North line and comes out the other way.
Example 2 (bearing). The clockwise angle, the long way round. Only the direction of turn changed. The first bearing students see is over 180°, on purpose.
Example 2 → Example 3. The line swings back round past South and East, and the arc shrinks with it, its start pinned at North.
Example 3 (bearing). A tiny angle is a bearing too. This one matters straight after Example 2: “the bigger angle is the bearing” would otherwise explain the first two verdicts as well as the rule does.
Example 3 → Example 4. A clean fade: a new example, not a transformation.
Example 4 (bearing). A second line appears, as on a journey diagram, and the angle still starts at North. Students see that extra lines don’t matter before the last example relies on it.
Example 4 → Example 5. The arc’s end stays where it is; its start slides off North onto the other line.
Example 5 (not a bearing). It still turns clockwise, but it starts at the wrong line. This is the exam error — giving the angle between two legs of a journey — and it is the contrast students should leave with.
Why the sequence is shaped this way
- Two parts, two non-examples. The first non-example fails “clockwise”; the last fails “starts at the North line”. Each is one change from the bearing next to it.
- Every arc draws itself, from where it starts to where it ends. That movement is “turns clockwise from North”, so the direction of turn is something students watch rather than decode from an arrowhead. The arrowhead stays, for print.
- Every diagram has a North arrow with an N, as exam diagrams do, so “North” is read rather than judged by eye.
- The shaded wedge and the arc are always the same colour, whatever the verdict. The colour marks the angle being asked about, never the answer.
What this sequence doesn’t address
Which point the North line belongs at (“the bearing of B from A”), three-figure notation (045°) and numbers of any kind are later atoms. Here North always points up the page and the North line always sits at the angle’s corner.
Measuring from a horizontal line, and diagrams with no North line, are in the testing card. North–South lines, a tilted North and angles with no arrowhead are in the expansion card.
The rule and the script
The rule, exactly as the Show rule button displays it: For the following examples: if the angle starts at the North line and turns clockwise, it is a bearing.
The spoken justifications:
- Bearings — “This is a bearing. How do I know? Because it starts at the North line, and it turns clockwise.”
- The anticlockwise non-example — “This is not a bearing. How do I know? Because it starts at the North line — but it turns anticlockwise.”
- The wrong-start non-example — “This is not a bearing. How do I know? Because it turns clockwise — but it starts at the other line, not the North line.”
Whether students see the words is your call. For some classes the rule and the justifications help; for others the examples should do the talking. Nothing appears unless you click. Show rule puts the rule above the stage — you can turn it on before Example 1 — and it stays until you turn it off. Why? appears after each reveal: it shows the justification, and at the same moment the line the angle starts from pulses (with the N underlined when that line is North) and the arc replays its turn. On the fade into Example 4, where no animation has drawn the eye, it is worth asking “Where does it start? Which way does it turn?” before you click.
Where this atom sits
Before it: clockwise and anticlockwise, and seeing which side of a line an angle is on. No angle measurement is needed.
This atom: which angle a bearing is.
After it: the expansion card below; then “Is this the bearing of B from A?” (which point the North line belongs at) and three-figure bearings.
Running the sequence
Give students time to watch each arc draw itself, then pause before revealing. The pause is the prediction moment.
The Replay button appears on Examples 2, 3 and 5, where a single change is the lesson. It doesn’t appear on Example 4: that is a new example, not a transformation.
If a class struggles with Example 5, go back to Example 4 and replay the change: “What stayed the same? What moved?”
About the testing sequence
Ten items in a new random order each time: five bearings, five not. The rule decides every one. There is no Show rule button here — students apply the rule without it on screen. Why? works as in the teaching sequence, after each answer.
The items animate. Each arc draws itself as it arrives, exactly as in teaching, and the answer buttons wait until it has landed. That’s a deliberate departure from static testing: the turn is the visual language for a bearing, and a static arc would test a different reading from the one taught. There’s no Replay.
What each item is diagnosing
The anticlockwise habit. A small anticlockwise angle just west of North (the plain form), and an anticlockwise angle just under 180° (the harder form: “pick the one under 180°” makes the wrong direction feel right). A bearing due west, where anticlockwise would be a tidy 90°, catches the same habit from the other side.
The wrong start line. An angle measured from a horizontal line (the protractor habit); an angle from the previous leg of a journey (the exam error); and a diagram with no North line at all.
“A bearing is the smaller angle.” Three bearings over 180°, one of them a sliver short of a full turn.
Range and context. A bearing a sliver past North, and a journey diagram with two lines whose angle still starts at North.
Common confusions
- Rejecting large bearings, especially the near-full turn.
- Accepting any clockwise angle once two lines are drawn.
- Reading which side the wedge is on but not which way it turns.
Discussion prompts
- “Say the rule, then use it on this one.”
- “Which part of the rule does this one fail?”
- “Where does this angle start? Which way does it turn?”
- “What would you move to make it a bearing?”
Reading the summary
The ✓ or ✗ in the corner is what the item is; the green or red tint is whether the answer was right. A red tint on a ✓ over 180° is the “smaller angle” belief. A red tint on the previous-leg ✗ is the journey error.
About the expansion sequence
Six items just outside what was taught, to see how far understanding travels — not to grade. It works exactly like the testing sequence: random order, Bearing or Not a bearing, feedback, Why?, and a summary.
The rule began “For the following examples”. In those examples North always pointed up the page, the North line stopped at the corner, and every arc had an arrowhead. This card changes each of those.
Two kinds of item
The rule still works on an unfamiliar surface. A North–South line with the angle starting at the North end; North not pointing up the page; and an angle with no arrowhead on the anticlockwise side of North.
The rule’s words, used blindly, give the wrong answer.
- A North–South line with the angle starting at the South end. “It starts on the North line” says yes; it isn’t a bearing.
- An angle starting at the line that points up the page, when North is tilted. “Up is North” says yes; it isn’t a bearing.
- An angle with no arrowhead on the clockwise side of North. “Nothing shows it turning” says no; it is a bearing.
The last one matters most. Exam diagrams rarely draw arrowheads, and students have to read the marked angle as the clockwise turn from North themselves.
The two angles with no arrowhead fade in rather than draw themselves, since the drawing would give away a direction.
Who it’s for
Anyone secure on the testing card. The tilted-North items suit students who have met maps that aren’t north-up.
The justifications
Each one extends the template by naming what’s new, for example: “…The line carries on through the point, but the angle starts from the end pointing North.” “…North doesn’t point up the page here — the arrow with the N shows where it is.” “There’s no arrow, so read it from the North line: it starts at the North line and turns clockwise round to the other line.”
On the two angles with no arrowhead, Why? does the reading for the student: North pulses, then a clockwise turn is drawn from it. On the anticlockwise one, that turn goes round the other side, dashed, which is exactly what the justification says.
Discussion prompts
- “The rule said ‘for the following examples’. What’s different here?”
- “Where is North in this one?”
- “With no arrow, how would you read it?”
Reading the summary
As on the testing card. Errors on the three blind-rule items are expected and informative: they show a student using the rule’s words rather than what they mean.