Secondary 4 Mathematics Tuition: Why Do Return Bearings Keep Going Wrong?

The phrase “bearing of B from A” means stand at A and look toward B. The angle begins at the north direction at A and turns clockwise to the line from A to B.

The phrase “bearing of A from B” changes the observation point to B. It describes the opposite journey along the same segment.

A child can know the three-figure convention yet measure from the wrong north line. The arithmetic then looks sensible while answering a different question.

Before calculating, circle or underline the point after “from”. That point is the angle’s vertex and the journey’s start.

Draw a small directed arrow toward the destination. A line joining two points without an arrow may not protect the required direction.

Do not begin with the triangle’s most prominent angle. A bearing is defined by north and the destination ray, not by whichever angle is easiest to see.

Ask the student to say the journey aloud: “from A toward B”. Then ask where the north line belongs. This makes the reading decision explicit.

If the child measures correctly at A but the question asks from B, repair viewpoint selection first. Additional trigonometry will not fix that misunderstanding.

Keep the original diagram and markings. They show whether the mistake occurred in reading, drawing the reference direction, choosing clockwise rotation or performing arithmetic.

The first reliable habit is therefore a reading habit: start at “from”, not at the first point mentioned in the sentence.

Contents · Next chapter

A three-figure bearing in these school examples is measured clockwise from north. North is 000°, east 090°, south 180° and west 270°.

A direction slightly east of north has a small bearing. A direction slightly west of north has a bearing near 360°, not a small positive anticlockwise bearing.

For a ray thirty degrees west of north, the clockwise bearing is 330°. The thirty-degree angle shown beside north is a reference angle, not automatically the bearing.

For a ray forty degrees east of south, the bearing is 140°, because it lies forty degrees before south on the clockwise scale. For forty degrees west of south, the bearing is 220°.

The words east and west matter. Do not add forty to 180 merely because a south line is present; identify which side the destination lies on.

A bearing of 007° is seven degrees clockwise from north. Leading zeros communicate the three-figure format without changing the numerical angle.

The ordinary convention is to report a bearing from 000° up to, but not including, 360°. A complete clockwise turn returns to north, normally reported as 000°.

A protractor must be centred on the starting point and read from the north ray. On a diagram not drawn to scale, use stated angles and valid geometry rather than measuring the picture.

Ask the child to identify the expected quadrant before calculation. A point south-west of the observer should have a bearing between 180° and 270°.

This direction check does not prove the exact angle, but it catches many answers measured from east, anticlockwise or at the wrong point.

Contents · Previous chapter · Next chapter

When a parent sees several wrong answers, the natural question is whether the child needs more teaching, more practice or more time. The answer depends on where the reasoning first becomes unreliable.

A completed solution contains several decisions. The learner reads the task, chooses a representation, selects a method, carries out operations and reports a conclusion. A final error can originate at any of those stages.

Begin by comparing the question with the first meaningful line of working. Did the student identify the mathematical object being asked for? If not, later arithmetic may be irrelevant to the requested answer.

If the first line is sound, inspect the next transformation. A correct model or relationship can still be damaged by a sign, an omitted case or an invalid operation.

If the working is valid but the final conclusion changes its meaning, target reporting. The child may understand the calculation while confusing a boundary, a candidate or a direction with the required answer.

Keep those distinctions visible in discussion. “Needs help selecting the relationship” is more actionable than “does not understand the topic”. The narrower statement also acknowledges what the student can already do.

Choose one original attempt and one successful example. The comparison helps a teacher or tutor identify whether the gap is general or appears only when a condition changes.

Avoid making the child defend every mistake in a long conversation. Ask what they intended at one key line, then preserve the page for a focused lesson.

The original attempt is evidence, not a label. A learner can make a repeated error and still have useful knowledge nearby. Good support connects that knowledge to the missing decision.

For this topic, a suitable first check is: whether the observation point, north ray and clockwise direction match the requested bearing. That observation can guide the next example much more precisely than the total number of questions completed.

End the conversation with a teachable objective. The child might identify a condition, preserve a branch or choose a viewpoint without prompting. A small visible objective makes the next lesson easier to evaluate.

The purpose is to turn uncertainty into a practical teaching question. Parents do not need to solve the entire syllabus before asking for support; they need enough concrete evidence to start in the right place.

Contents · Previous chapter · Next chapter

For a straight segment in the ordinary plane model with parallel north lines, reversing the journey rotates its direction by 180°. That is the reason for the return-bearing rule.

If the outward bearing is 065°, adding 180° gives 245°. Both describe the same line, but opposite directed rays.

If the outward bearing is 250°, adding 180° gives 430°. Subtract one full turn, 360°, to report 070°. Equivalently, subtract 180° directly from 250°.

For outward bearings below 180°, add 180°. For bearings at or above 180°, subtract 180°, using 000° for north when the result is zero.

Check the compass direction. An outward north-east direction must return south-west. An outward south-west direction must return north-east.

The return bearing is not generally 360° minus the outward bearing. That operation reflects the direction around the north line rather than reversing the segment.

For 065°, 360−65=295° points north-west, not back toward a point south-west of B. The correct return is 245°.

The rule applies to reversing the same directed segment. It does not find the final bearing home after two unequal legs in different directions without further geometry.

The school plane assumption also matters. This guide is about ordinary classroom diagrams, not long-distance great-circle navigation, where local north directions require more careful treatment.

Ask the child to draw both arrows on the same segment and state the approximate compass directions. The 180° calculation should agree with that visual reversal.

Contents · Previous chapter · Next chapter

North lines at different points in a plane school diagram are treated as parallel. Angle relationships with a joining segment can therefore connect the bearings at its two ends.

Suppose B lies north-east of A and the bearing of B from A is 040°. The segment AB makes forty degrees clockwise from the north line at A.

At B, the direction toward A is south-west. Relative to the north line at B, its clockwise bearing is 220°, the original direction plus 180°.

A diagram may label an acute angle between BA and the southward extension of the north line at B. That angle is forty degrees, but it is not the complete bearing from north.

The complete clockwise rotation includes the 180° from north to south plus the additional forty degrees toward west.

This is a common source of a forty-degree answer where 220° is required. The child has found a correct local angle but not the requested bearing.

Use corresponding or alternate-angle reasoning only where the relevant parallel lines and transversal have been identified. Do not name an angle rule merely because two north arrows appear on the page.

Ask the learner to distinguish the small angle they calculated from the full clockwise rotation they must report.

If the diagram rotates on the page, the north arrows still define the reference directions. Do not assume the top edge of the paper is north when an explicit arrow says otherwise.

The mathematical relationship should survive a redraw. The student’s answer depends on the labelled geometry, not the familiar orientation of one worksheet.

Contents · Previous chapter · Next chapter

A bearing is an oriented angle from north at one point. An interior triangle angle lies between two sides of the triangle. Sometimes they are numerically related, but they are not the same object.

Suppose B is on bearing 030° from A and C is on bearing 100° from A. The smaller angle BAC between the two rays is 100−30=70°.

That seventy-degree interior angle is not the bearing of either destination from A. Those bearings remain 030° and 100°.

Now consider bearings 350° and 020° from the same point. Direct subtraction gives 330°, but the smaller angle between the rays is thirty degrees across north.

The calculation can be written as ten degrees from 350° to north plus twenty degrees from north to 020°. The diagram prevents the wrong large interior angle.

The smaller angle between two rays is not always the angle a particular multi-point diagram asks for. Read the labelled region and the triangle’s actual vertices.

When using the triangle angle sum, ensure all three values are interior angles of that triangle. A 245° bearing is not an interior angle of an ordinary triangle.

Convert the bearing information into the appropriate local angle first. Then apply triangle rules and convert the result back to a bearing if the question asks for one.

A child who obtains a correct interior angle but reports it as a bearing needs a final interpretation repair, not necessarily a new trigonometric method.

Ask the student to label each angle by its job: bearing, reference angle or triangle interior angle. That makes the geometric relationships much easier to organise.

Contents · Previous chapter · Next chapter

A multi-leg journey introduces another angle: the change in travel direction at a waypoint. That turn is not automatically the triangle’s interior angle or the final bearing back to the start.

Suppose a traveller goes from A to B on bearing 060°, then from B to C on bearing 150°. The clockwise change from the forward heading AB to the heading BC is ninety degrees.

At B, the triangle’s ray toward A is BA, with bearing 240°. The ray toward C has bearing 150°. The smaller angle ABC between those rays is also ninety degrees in this particular example.

That agreement is coincidental to these numbers. If the second leg had bearing 120°, the forward-heading change would be sixty degrees, while the smaller angle between BA at 240° and BC at 120° would be 120°.

The interior angle uses the backward ray toward the previous point, not the previous forward heading carried mentally through B.

To find the bearing of A from C after two legs, you need the net geometry. Reversing the second leg only gives the bearing of B from C.

If BC has bearing 120°, its reverse CB has bearing 300°. That does not establish the bearing of A from C unless A lies in that same direction from C.

Lengths matter in a general two-leg problem. Different leg lengths can change the final position and therefore the bearing home.

Ask the child what each line actually joins before using the return rule. The endpoints must be the same pair in reverse order.

This protects an important boundary: the simple 180° rule reverses one segment; it does not solve every journey containing the word return.

Contents · Previous chapter · Next chapter

A bearings question may eventually require trigonometry, but the trigonometric method depends on the triangle that has actually been established.

For a right-angled triangle, use the appropriate ratio based on the known sides and required angle or length. A bearing diagram does not automatically contain a right angle.

For a non-right-angled triangle, use only methods included in the learner’s course, such as the sine or cosine rule when their conditions are met.

Suppose A to B is due east, B to C is due north, and the lengths are three and four units respectively. The displacement from A to C has east component three and north component four.

The angle east of north is arctan(3/4), approximately 36.87°. Therefore the bearing of C from A is approximately 036.9° if that accuracy is requested, or 037° to the nearest degree.

The return bearing of A from C is approximately 216.87°, or 217° to the nearest degree. Reverse the net segment AC, not only the final northward leg.

The distance AC is five units by Pythagoras. The five-unit displacement length differs from the seven-unit path length along the two legs.

The ratio for the angle from north uses east displacement over north displacement. Measuring an angle from east first would produce the complementary angle, which must then be converted.

State the required accuracy and use the calculator in degree mode for degree-bearing questions. Retain unrounded values until the final reporting step.

The conceptual order is geometry, trigonometry and final bearing interpretation. A calculator cannot choose the correct reference ray for the student.

Contents · Previous chapter · Next chapter

Contents · Previous chapter · Next chapter

A final bearing should match the requested start and endpoint, lie within the chosen one-turn convention and point into the correct compass region.

For a destination north-east of the observer, expect a bearing between 000° and 090°. South-east lies between 090° and 180°, south-west between 180° and 270°, and north-west between 270° and 360°.

Boundary directions such as due east or due south need their exact compass bearings. Do not describe every point in the broad region as an acute bearing.

The region check is approximate. It cannot distinguish 215° from 225° if both point south-west, but it can catch 035° reported for a return that should point south-west.

Check the endpoints again after a long solution. A correct calculation for B from A is still not an answer to A from B.

If the answer exceeds 360° or is negative, convert it to the equivalent direction within one full turn. Then use the requested format and accuracy.

Do not round an intermediate triangle angle unnecessarily before combining it with a reference direction. Early rounding may shift the final answer.

A diagram not drawn to scale should still support qualitative direction reading when positions are indicated consistently, but exact values must come from stated information and valid geometry.

If the drawing and written conditions appear inconsistent, ask the teacher or tutor rather than forcing a measurement from the picture.

The final check is not cosmetic. It confirms that the algebra and trigonometry have returned to the actual question about direction.

Contents · Previous chapter · Next chapter

Use one outward bearing, 080°, and compare three proposed return answers. The correct opposite direction is 260°.

Method one repeats 080°. This keeps the same direction instead of reversing the segment. A destination east of the outward observer cannot remain east of the return observer along the same line.

Method two uses 360−80=280°. The arithmetic is correct, but the operation has reflected the ray around north rather than turned it through 180°.

Method three uses 180−80=100°. This may arise from calculating a supplementary angle beside a north line. One hundred degrees is a legitimate bearing, but it does not point back along the original segment.

Ask the student to place each proposed direction approximately on a compass. The correct return should point west and somewhat south, opposite the east-and-somewhat-north outward direction.

The approximate direction can rule out 080° and 100° immediately. Both 260° and 280° lie on the western side, so the exact reversal calculation is still needed.

This shows why a quadrant check and an exact calculation complement each other. Neither should be mistaken for the other.

Now use an outward bearing of 320°. The correct reverse is 140°. Repeating 320° fails direction; 360−320=40° reflects around north; 180−320=−140° is outside the usual reporting range and describes another direction when normalised.

The proper rule can be recorded as adding 180° and reducing by a full turn when needed, or using the simpler add-or-subtract cases.

Do not teach the incorrect methods as equally valid shortcuts. Their comparison is an error-analysis task designed to identify what each operation actually does.

A tutor can ask the learner to explain why one tempting operation is wrong before providing more numerical questions. That makes the repair resistant to superficial arithmetic fluency.

The key question remains: did the direction reverse along the same pair of endpoints?

If not, the final angle answers a different geometric question.

Contents · Previous chapter · Next chapter

Consider a fictional plane diagram. A traveller goes from A to B four units due north, then from B to C three units due east. North lines are parallel and the legs form a right angle.

Relative to A, C is four units north and three units east. The angle from north toward C satisfies tan θ=3/4, so θ is about 36.87°.

The bearing of C from A is therefore approximately 037° to the nearest degree. The bearing of A from C is approximately 217°.

The last leg B to C is due east, with bearing 090°. Its reverse C to B is 270°. That is not the bearing of A from C, because A lies south-west of C rather than directly west.

The distinction tests whether the child reverses the requested segment or merely the final printed leg. The word return does not make those segments identical.

The straight-line distance from A to C is five units, while the route length A to B to C is seven units. Those quantities also answer different questions.

Now double both leg lengths. C lies eight units north and six east of A. The direction remains the same because the ratio of east to north displacement remains three to four, while the distance doubles.

Change only the eastward leg to four units, keeping the northward leg four. The outward bearing becomes 045° and the return 225°.

These variations reveal what controls direction: the relative displacements, not the total path length alone. The method should be used only when the learner’s course includes the required right-triangle trigonometry.

Ask the student to state the destination’s compass region before touching the calculator. Then ask which side is opposite the angle measured from north.

Finally, retain the unrounded angle when calculating the return and round only to the requested final accuracy. A clear geometric setup makes the later calculator work far less fragile.

Contents · Previous chapter · Next chapter

A contrast pair changes one decisive feature while keeping much of the question familiar. It helps the learner see why a method applies instead of merely recognising a worksheet pattern.

The two questions should be close enough that the difference stands out. If every number, diagram and instruction changes simultaneously, the comparison may become another difficult problem rather than a clear explanation.

For this article, one useful contrast is B from A beside A from B, followed by a two-leg journey that asks for the direct bearing home. Ask what changed, what stayed the same and which part of the reasoning must respond.

Let the child make a prediction before completing the calculation. A prediction exposes the selected relationship, even if the later arithmetic is not fluent.

After solving, compare the checks. The answers may have different forms because the condition changed. They may occasionally coincide numerically without making the methods equivalent.

Include a near-miss where the familiar rule does not apply. That tests whether the student notices the condition or merely sees a familiar noun, symbol or diagram.

Do not describe the near-miss as a trap. It is a legitimate mathematical comparison designed to make a boundary visible. A learner should feel invited to examine it, not ambushed.

The tutor can model one pair, guide another and then offer a new pair without naming the method. Those stages provide different evidence about understanding and independence.

If the child fails the independent pair, return to the precise feature that was missed. Repeating the entire explanation may be unnecessary if one condition needs more attention.

A parent can keep the pair as a small revision resource. The useful reminder is not just two answers; it is the reason the answers or methods differ.

Later practice should vary the surface while preserving that decisive contrast. Change numbers, labels or wording so the child cannot rely on visual memory alone.

The goal is flexible recognition. The learner should be able to say, “This looks similar, but this condition has changed, so my earlier method needs this adjustment.” That is a stronger foundation than a fast answer obtained from a familiar layout.

Contents · Previous chapter · Next chapter

Not every checking method is equally useful for every failure. A student can carefully repeat the same incorrect reasoning and obtain the same wrong answer.

Choose a check that approaches the decision from another representation or tests a condition the original solution might have missed.

For this topic, the useful check is compare the compass region with the sketch and confirm that the requested segment has reversed by 180°. It should be short enough that the child can realistically use it when the corresponding uncertainty arises.

A check has a scope. It may verify that a candidate works, expose a wrong direction or confirm a constant relationship. It may not establish every part of a complete solution.

Teach the learner to state what the check has shown. This prevents a successful small check from being mistaken for proof of a much broader claim.

For example, one substituted value can reveal a contradiction, but agreement at that value may not prove a whole identity or solution set. A qualitative direction check can catch the wrong quadrant without determining the exact angle.

The checking method should therefore complement valid reasoning, not replace it. It is a safety net around a meaningful solution.

Begin with a tutor demonstrating why the check catches an incorrect worked answer. Then ask the student to select the check for a new example.

Avoid asking for every possible verification on every question. An exhaustive checklist can consume attention without protecting the relevant decision.

Where a calculator is permitted, it can support arithmetic verification. It cannot read the question’s viewpoint, decide a model’s assumptions or explain why a candidate has been excluded.

As the student becomes more fluent, the checking process may become compact. A short substitution, a labelled direction or a comparison of invariants may be sufficient.

If the same error survives the check, reconsider whether the check is genuinely independent of the original misconception. The learner may need a different representation.

The desired habit is specific and reusable: when this type of decision is uncertain, use this kind of evidence to test it. That is more helpful than the general instruction “check your work”, which leaves the child to invent the method under pressure.

Contents · Previous chapter · Next chapter

A correction is valuable when it changes a later independent attempt. Copying a correct solution can clarify the method, but it does not by itself demonstrate that the learner can select that method again.

Keep the original and corrected versions together. Mark the first changed decision, not only the final answer. This gives the correction an explanatory purpose.

Ask the child for a brief repair note. It should name the condition or operation that mattered. A note such as “read the starting point first” is easier to use than a long copied paragraph.

Then choose a new question with the same underlying decision and a changed surface. It should not be so different that a new prerequisite obscures the repair.

Let the student attempt it without the corrected example directly above. This checks whether the relevant decision is available rather than merely visible.

Record the support level honestly. A specific cue, a general prompt and an unprompted attempt represent different stages. Correct guided work is useful, but it should not be reported as unaided mastery.

Revisit the decision later with new numbers or wording. The delay need not be part of a rigid timetable; it can be a brief check when the topic next appears.

If the error returns, ask whether the original repair addressed the actual cause. Perhaps the child remembered the procedure but not its condition, or managed the simple example but not the wording in context.

Do not automatically respond by doubling the workload. A more revealing contrast may be the better next step.

The student should gradually take ownership of the repair note and check. They should know what to try when the same uncertainty appears in schoolwork.

Parents can ask, “What changed between the first attempt and this one?” That invites a concrete explanation without turning the correction into a judgment.

A useful correction has three parts: the original decision, the reason it failed and a later task showing whether the revised decision can be used independently. Neatness supports communication, but it is not the central measure of learning.

Contents · Previous chapter · Next chapter

Choosing Mathematics tuition is easier when the conversation begins with evidence rather than a broad description of confidence. Bring the actual question, first attempt and school scope to the provider.

Ask what they would observe before teaching. A thoughtful response should distinguish reading, conceptual selection, execution and final interpretation instead of assuming every wrong answer requires the same worksheet.

Ask how the lesson will make the central relationship visible. The answer might involve a number line, paired data, a graph or a directional sketch, depending on the learner’s gap.

Then ask how the student will move from watching to doing. A clear demonstration is helpful, but the learner needs a chance to select the method without a direct cue.

In a small group, ask how each child’s own attempt will be checked. A classmate’s spoken answer does not establish that every student made the same decision.

In an individual lesson, ask how prompting will be faded. Constant one-to-one help can make work look fluent while leaving the learner dependent on the tutor’s next instruction.

Neither arrangement is automatically better for every learner. The relevant question is whether the teaching process fits the child’s needs, current course and ability to participate.

Confirm current fees, timing, location, availability and class arrangements directly. An educational article cannot establish that a particular slot is open or that an older service detail remains current.

Avoid selecting a provider solely because they can solve the question quickly. The more useful evidence is whether they can explain the child’s misconception and design a revealing next attempt.

Ask what information the family will receive afterward. A short learning target and a focused practice suggestion may be enough; the format is less important than the clarity.

Be cautious with guaranteed-result language. A responsible conversation can describe teaching, feedback and assessment of progress without promising a particular mark.

The student should be included respectfully. Ask what makes the current task confusing and what support feels usable. Their explanation is not the whole diagnosis, but it is relevant evidence.

A good fit gives the family a plausible next teaching step and a way to see whether it worked. It should reduce uncertainty, not amplify ordinary topic difficulty into an emergency.

Contents · Previous chapter · Next chapter

The examples in this article are illustrations of mathematical relationships, not a declaration that every student in the same secondary year has an identical assessment scope.

Confirm the school’s current topic, subject level, notation and instructions before selecting a practice route. Secondary year alone does not provide all of that information.

Some chapters include extensions. They are useful for a learner whose course requires them, but they should not become evidence that another child is behind simply because they have not been taught yet.

Distinguish Mathematics from Additional Mathematics where relevant. Connected ideas may appear at different depths, and a method appropriate to one course should not be imposed automatically on another.

Use the student’s actual materials to choose examples. Start with the decision that currently blocks schoolwork, then add the next connection when the prerequisites are stable.

For an assessment, follow the relevant school or official examination instructions for that cohort. Accuracy, notation, permitted tools and topics should come from those documents rather than a remembered rule from a different paper.

The guide’s worked examples can support understanding, but they do not replace that assessment contract. A tutor should help connect the two, not erase the distinction.

If a learner has changed course or subject level, ask which knowledge transfers and which demands are new. The answer should refer to actual work and requirements.

Do not confuse breadth with urgency. A child may benefit from understanding a linked idea later without needing to master it during tonight’s homework.

Likewise, do not avoid a necessary foundation because it appeared in an earlier year. A prerequisite repair can be worthwhile when it removes a current bottleneck.

The appropriate depth is therefore determined by the learner’s task and readiness. Good support can be ambitious while remaining well sequenced.

Parents can ask one practical question: “Which part is needed for the current course, and which part is an optional extension?” That makes the practice plan clearer and prevents unnecessary comparisons with another student’s timetable.

The aim is a coherent route through the actual learning problem. It is not a race to collect every connected technique before the child understands the relationship that makes the first one work.

Contents · Previous chapter · Next chapter

Speed becomes useful when the selected method is reliable. A faster version of the same misconception is not the progress the family is seeking.

Look first at the child’s initial decision. Can they identify the condition, choose the relevant representation and state what the answer must mean?

Then observe whether they preserve that meaning through the calculation. Signs, units, domains and viewpoints can be lost even after a sound beginning.

Finally, notice the check. Does the learner use it independently, and can they explain what it verifies?

This is stronger evidence than a corrected page completed with constant reminders.

Use comparable questions when judging change. A simpler later task may show a helpful starting point without proving that the original difficulty has been resolved.

A more complex task may introduce a new reading or arithmetic demand. Failure there does not automatically cancel progress in the repaired decision.

Keep the description specific. “Chooses the correct model but still needs help rearranging the equation” is both encouraging and useful. It identifies what has improved and what remains.

A total assessment mark is another piece of evidence, but it combines many skills. It should not be expected to reveal every small improvement or diagnose every remaining gap.

The child’s willingness to explain uncertainty also matters to the teaching process. A question such as “which north line do I use?” gives a tutor a clearer route than silent guessing.

Do not require the learner to sound confident before they have evidence. A careful explanation with one honest uncertainty can be more valuable than a fluent claim unsupported by the working.

End with a manageable action. Revisit one contrast, bring one original attempt to the next lesson or ask the school teacher about one instruction.

For this topic, the next independent target is identify the correct starting point and distinguish the reverse of one segment from the bearing home after several legs. Keep it visible and small enough to assess fairly.

The promise is not that Mathematics will become effortless. It is that repeated errors can become more understandable, and therefore more teachable, when the family and tutor attend to the decision that actually needs repair.

Contents · Previous chapter · Next chapter

Should my child always subtract the bearing from 360°?

No. That generally reflects the direction around north. Reversing the same segment changes the direction by 180°.

Why can a return bearing be larger than 180°?

It may point into the southern half of the clockwise scale. A bearing is not restricted to a triangle’s interior-angle range.

Where should the north line be drawn?

At the point from which the bearing is measured. The word after “from” identifies the observation point.

Does the rule work for a journey with two legs?

It reverses a specified segment. Finding the bearing home after several legs requires the net geometry, not just the last leg’s reverse bearing.

Can my child measure the worksheet with a protractor?

Only when the task permits measurement and the diagram is intended for it. A diagram not drawn to scale needs calculation from the stated information.

Are bearings always whole numbers?

No. The requested accuracy may allow decimal degrees. The three-figure convention for whole-degree bearings should not be confused with a universal three-significant-figure rule.

Should the tutor teach more trigonometry first?

If the error is choosing the observer or reference ray, repair that decision first. The later method depends on it.

What counts as progress?

The child identifies the correct viewpoint, computes a changed return direction and distinguishes a bearing from an interior angle in a new diagram.

Contents · Previous chapter · Mathematics learning hub