How to Perform in PSLE | Learner’s Guide Vol 0919 | Science: Predict Shadow Size by Tracking the Light Source, Object and Screen

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1. Build the three-part model

Name the light source, the opaque object and the screen or surface receiving the shadow. A shadow is not a substance emitted by the object; it is a region receiving less light because the object blocks particular paths.

Use a four-step explanation. First identify light source opaque object and screen. Next establish boundary rays from the source past the object. Then connect the evidence to shadow size and edge sharpness observation. Finally audit changed distance controlled variables viewpoint source size and claim limits. This order prevents a familiar word or number from replacing the actual relationship.

The nearest misconception usually preserves one visible feature but drops a controlling condition. Repair it by naming what the tempting answer notices, what it ignores and why the ignored condition changes the conclusion. A correct answer should survive a small change of story while still responding to the decisive structure.

For independent control, rewrite the example with one decisive condition changed and predict whether the result stays or changes. Explain the boundary in a complete sentence. This contrast is more useful than repeating the original wording because it tests whether the mechanism can be transferred.

• Check light source opaque object and screen.
• Check boundary rays from the source past the object.
• Check shadow size and edge sharpness observation.
• Check changed distance controlled variables viewpoint source size and claim limits.

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CHAPTER 2 OF 12 · Back to contents

2. Trace boundary rays before memorising a direction

Draw straight rays from the source that just pass the object’s edges. Extend them to the screen. The distance between their arrival points estimates the full shadow width in a simple point-source model.

Use a four-step explanation. First identify light source opaque object and screen. Next establish boundary rays from the source past the object. Then connect the evidence to shadow size and edge sharpness observation. Finally audit changed distance controlled variables viewpoint source size and claim limits. This order prevents a familiar word or number from replacing the actual relationship.

The nearest misconception usually preserves one visible feature but drops a controlling condition. Repair it by naming what the tempting answer notices, what it ignores and why the ignored condition changes the conclusion. A correct answer should survive a small change of story while still responding to the decisive structure.

For independent control, rewrite the example with one decisive condition changed and predict whether the result stays or changes. Explain the boundary in a complete sentence. This contrast is more useful than repeating the original wording because it tests whether the mechanism can be transferred.

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CHAPTER 3 OF 12 · Back to contents

3. Move the object toward the source

With source and screen fixed, an object closer to the source blocks a wider cone of paths, so its shadow on the screen is generally larger. The comparison assumes the object’s size and orientation do not change.

Use a four-step explanation. First identify light source opaque object and screen. Next establish boundary rays from the source past the object. Then connect the evidence to shadow size and edge sharpness observation. Finally audit changed distance controlled variables viewpoint source size and claim limits. This order prevents a familiar word or number from replacing the actual relationship.

The nearest misconception usually preserves one visible feature but drops a controlling condition. Repair it by naming what the tempting answer notices, what it ignores and why the ignored condition changes the conclusion. A correct answer should survive a small change of story while still responding to the decisive structure.

For independent control, rewrite the example with one decisive condition changed and predict whether the result stays or changes. Explain the boundary in a complete sentence. This contrast is more useful than repeating the original wording because it tests whether the mechanism can be transferred.

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CHAPTER 4 OF 12 · Back to contents

4. Move the object toward the screen

With source and screen fixed, moving the object nearer the screen generally makes the shadow closer to the object’s actual size and therefore smaller than when the object was near the source.

Use a four-step explanation. First identify light source opaque object and screen. Next establish boundary rays from the source past the object. Then connect the evidence to shadow size and edge sharpness observation. Finally audit changed distance controlled variables viewpoint source size and claim limits. This order prevents a familiar word or number from replacing the actual relationship.

The nearest misconception usually preserves one visible feature but drops a controlling condition. Repair it by naming what the tempting answer notices, what it ignores and why the ignored condition changes the conclusion. A correct answer should survive a small change of story while still responding to the decisive structure.

For independent control, rewrite the example with one decisive condition changed and predict whether the result stays or changes. Explain the boundary in a complete sentence. This contrast is more useful than repeating the original wording because it tests whether the mechanism can be transferred.

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CHAPTER 5 OF 12 · Back to contents

5. Move the screen while other positions stay fixed

If the screen moves farther behind the object in a diverging beam, the boundary rays spread farther before reaching it and the projected shadow becomes larger. State what remains fixed.

Use a four-step explanation. First identify light source opaque object and screen. Next establish boundary rays from the source past the object. Then connect the evidence to shadow size and edge sharpness observation. Finally audit changed distance controlled variables viewpoint source size and claim limits. This order prevents a familiar word or number from replacing the actual relationship.

The nearest misconception usually preserves one visible feature but drops a controlling condition. Repair it by naming what the tempting answer notices, what it ignores and why the ignored condition changes the conclusion. A correct answer should survive a small change of story while still responding to the decisive structure.

For independent control, rewrite the example with one decisive condition changed and predict whether the result stays or changes. Explain the boundary in a complete sentence. This contrast is more useful than repeating the original wording because it tests whether the mechanism can be transferred.

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CHAPTER 6 OF 12 · Back to contents

6. Separate size from sharpness

An extended light source sends light from many points and can create a partial-shadow region at the edge. Source size affects edge sharpness as well as geometry, so a blurred outline should not be treated as a new object size.

Use a four-step explanation. First identify light source opaque object and screen. Next establish boundary rays from the source past the object. Then connect the evidence to shadow size and edge sharpness observation. Finally audit changed distance controlled variables viewpoint source size and claim limits. This order prevents a familiar word or number from replacing the actual relationship.

The nearest misconception usually preserves one visible feature but drops a controlling condition. Repair it by naming what the tempting answer notices, what it ignores and why the ignored condition changes the conclusion. A correct answer should survive a small change of story while still responding to the decisive structure.

For independent control, rewrite the example with one decisive condition changed and predict whether the result stays or changes. Explain the boundary in a complete sentence. This contrast is more useful than repeating the original wording because it tests whether the mechanism can be transferred.

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CHAPTER 7 OF 12 · Back to contents

7. Design a fair comparison

Change only one distance, use the same source, object, orientation and screen, darken the surroundings consistently, and measure the shadow at the same defined boundary. Otherwise the result has more than one possible cause.

Use a four-step explanation. First identify light source opaque object and screen. Next establish boundary rays from the source past the object. Then connect the evidence to shadow size and edge sharpness observation. Finally audit changed distance controlled variables viewpoint source size and claim limits. This order prevents a familiar word or number from replacing the actual relationship.

The nearest misconception usually preserves one visible feature but drops a controlling condition. Repair it by naming what the tempting answer notices, what it ignores and why the ignored condition changes the conclusion. A correct answer should survive a small change of story while still responding to the decisive structure.

For independent control, rewrite the example with one decisive condition changed and predict whether the result stays or changes. Explain the boundary in a complete sentence. This contrast is more useful than repeating the original wording because it tests whether the mechanism can be transferred.

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CHAPTER 8 OF 12 · Back to contents

8. Control the examination explanation

State the manipulated distance, describe how the boundary rays spread or narrow and connect that geometry to measured shadow size. Avoid slogans such as nearer means bigger without naming nearer to what.

Use a four-step explanation. First identify light source opaque object and screen. Next establish boundary rays from the source past the object. Then connect the evidence to shadow size and edge sharpness observation. Finally audit changed distance controlled variables viewpoint source size and claim limits. This order prevents a familiar word or number from replacing the actual relationship.

The nearest misconception usually preserves one visible feature but drops a controlling condition. Repair it by naming what the tempting answer notices, what it ignores and why the ignored condition changes the conclusion. A correct answer should survive a small change of story while still responding to the decisive structure.

For independent control, rewrite the example with one decisive condition changed and predict whether the result stays or changes. Explain the boundary in a complete sentence. This contrast is more useful than repeating the original wording because it tests whether the mechanism can be transferred.

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CHAPTER 9 OF 12 · Back to contents

9. Worked examples

Worked case 1: With source and screen fixed, an object moves toward the source. What usually happens to the shadow?

Controlled answer. It becomes larger. The object intercepts a wider cone of diverging rays.

Mechanism. Begin with light source opaque object and screen, then use boundary rays from the source past the object to decide the operation or language choice. The answer is justified only when shadow size and edge sharpness observation is shown explicitly. Keep every unit, referent and condition attached to the quantity or clause it controls.

Misconception repair. A tempting answer may copy the nearest noun, visible number or remembered slogan. That shortcut is unsafe because it does not test changed distance controlled variables viewpoint source size and claim limits. State the missing condition and show how it affects the result instead of merely labelling the first answer wrong.

Transfer. Trace two boundary rays. Solve the altered case from the relationship, not from surface resemblance. If the conclusion changes, identify the exact changed condition; if it stays, explain why the mechanism is invariant.

Examination control. Write the decisive evidence before the conclusion. Reread the full prompt, check that the response answers the requested quantity or meaning, and verify that no unstated fact has been added. A concise answer is strong only when its reasoning remains inspectable.

Reverse construction. Invent a new prompt whose correct answer is “It becomes larger”, then create a near-nonexample by changing one condition. Explain the pair without reusing the original story. This reverse task checks genuine ownership of the method.

Worked case 2: The same object moves toward the screen. What usually happens?

Controlled answer. The shadow becomes smaller and closer to the object’s size. There is less distance for the boundary rays to spread after the object.

Mechanism. Begin with light source opaque object and screen, then use boundary rays from the source past the object to decide the operation or language choice. The answer is justified only when shadow size and edge sharpness observation is shown explicitly. Keep every unit, referent and condition attached to the quantity or clause it controls.

Misconception repair. A tempting answer may copy the nearest noun, visible number or remembered slogan. That shortcut is unsafe because it does not test changed distance controlled variables viewpoint source size and claim limits. State the missing condition and show how it affects the result instead of merely labelling the first answer wrong.

Transfer. Keep source and screen fixed. Solve the altered case from the relationship, not from surface resemblance. If the conclusion changes, identify the exact changed condition; if it stays, explain why the mechanism is invariant.

Examination control. Write the decisive evidence before the conclusion. Reread the full prompt, check that the response answers the requested quantity or meaning, and verify that no unstated fact has been added. A concise answer is strong only when its reasoning remains inspectable.

Reverse construction. Invent a new prompt whose correct answer is “The shadow becomes smaller and closer to the object’s size”, then create a near-nonexample by changing one condition. Explain the pair without reusing the original story. This reverse task checks genuine ownership of the method.

Worked case 3: The screen moves farther behind a fixed object. What happens in a diverging beam?

Controlled answer. The shadow becomes larger. Boundary rays spread farther before reaching the screen.

Mechanism. Begin with light source opaque object and screen, then use boundary rays from the source past the object to decide the operation or language choice. The answer is justified only when shadow size and edge sharpness observation is shown explicitly. Keep every unit, referent and condition attached to the quantity or clause it controls.

Misconception repair. A tempting answer may copy the nearest noun, visible number or remembered slogan. That shortcut is unsafe because it does not test changed distance controlled variables viewpoint source size and claim limits. State the missing condition and show how it affects the result instead of merely labelling the first answer wrong.

Transfer. State the fixed distances. Solve the altered case from the relationship, not from surface resemblance. If the conclusion changes, identify the exact changed condition; if it stays, explain why the mechanism is invariant.

Examination control. Write the decisive evidence before the conclusion. Reread the full prompt, check that the response answers the requested quantity or meaning, and verify that no unstated fact has been added. A concise answer is strong only when its reasoning remains inspectable.

Reverse construction. Invent a new prompt whose correct answer is “The shadow becomes larger”, then create a near-nonexample by changing one condition. Explain the pair without reusing the original story. This reverse task checks genuine ownership of the method.

Worked case 4: Why is an opaque object needed for a clear dark shadow?

Controlled answer. It blocks light paths. A transparent object transmits much of the light.

Mechanism. Begin with light source opaque object and screen, then use boundary rays from the source past the object to decide the operation or language choice. The answer is justified only when shadow size and edge sharpness observation is shown explicitly. Keep every unit, referent and condition attached to the quantity or clause it controls.

Misconception repair. A tempting answer may copy the nearest noun, visible number or remembered slogan. That shortcut is unsafe because it does not test changed distance controlled variables viewpoint source size and claim limits. State the missing condition and show how it affects the result instead of merely labelling the first answer wrong.

Transfer. Compare translucent material. Solve the altered case from the relationship, not from surface resemblance. If the conclusion changes, identify the exact changed condition; if it stays, explain why the mechanism is invariant.

Examination control. Write the decisive evidence before the conclusion. Reread the full prompt, check that the response answers the requested quantity or meaning, and verify that no unstated fact has been added. A concise answer is strong only when its reasoning remains inspectable.

Reverse construction. Invent a new prompt whose correct answer is “It blocks light paths”, then create a near-nonexample by changing one condition. Explain the pair without reusing the original story. This reverse task checks genuine ownership of the method.

Worked case 5: Does the object create darkness?

Controlled answer. No. The dark region receives less light because paths are blocked.

Mechanism. Begin with light source opaque object and screen, then use boundary rays from the source past the object to decide the operation or language choice. The answer is justified only when shadow size and edge sharpness observation is shown explicitly. Keep every unit, referent and condition attached to the quantity or clause it controls.

Misconception repair. A tempting answer may copy the nearest noun, visible number or remembered slogan. That shortcut is unsafe because it does not test changed distance controlled variables viewpoint source size and claim limits. State the missing condition and show how it affects the result instead of merely labelling the first answer wrong.

Transfer. Name the source of surrounding illumination. Solve the altered case from the relationship, not from surface resemblance. If the conclusion changes, identify the exact changed condition; if it stays, explain why the mechanism is invariant.

Examination control. Write the decisive evidence before the conclusion. Reread the full prompt, check that the response answers the requested quantity or meaning, and verify that no unstated fact has been added. A concise answer is strong only when its reasoning remains inspectable.

Reverse construction. Invent a new prompt whose correct answer is “No”, then create a near-nonexample by changing one condition. Explain the pair without reusing the original story. This reverse task checks genuine ownership of the method.

Worked case 6: What are boundary rays?

Controlled answer. Rays that just pass the object’s edges and mark the shadow limits. They connect geometry to the observed outline.

Mechanism. Begin with light source opaque object and screen, then use boundary rays from the source past the object to decide the operation or language choice. The answer is justified only when shadow size and edge sharpness observation is shown explicitly. Keep every unit, referent and condition attached to the quantity or clause it controls.

Misconception repair. A tempting answer may copy the nearest noun, visible number or remembered slogan. That shortcut is unsafe because it does not test changed distance controlled variables viewpoint source size and claim limits. State the missing condition and show how it affects the result instead of merely labelling the first answer wrong.

Transfer. Draw arrows in the direction of travel. Solve the altered case from the relationship, not from surface resemblance. If the conclusion changes, identify the exact changed condition; if it stays, explain why the mechanism is invariant.

Examination control. Write the decisive evidence before the conclusion. Reread the full prompt, check that the response answers the requested quantity or meaning, and verify that no unstated fact has been added. A concise answer is strong only when its reasoning remains inspectable.

Reverse construction. Invent a new prompt whose correct answer is “Rays that just pass the object’s edges and mark the shadow limits”, then create a near-nonexample by changing one condition. Explain the pair without reusing the original story. This reverse task checks genuine ownership of the method.

Worked case 7: Why must nearer be followed by a reference point?

Controlled answer. Nearer to the source and nearer to the screen predict different changes. Distance language is relational.

Mechanism. Begin with light source opaque object and screen, then use boundary rays from the source past the object to decide the operation or language choice. The answer is justified only when shadow size and edge sharpness observation is shown explicitly. Keep every unit, referent and condition attached to the quantity or clause it controls.

Misconception repair. A tempting answer may copy the nearest noun, visible number or remembered slogan. That shortcut is unsafe because it does not test changed distance controlled variables viewpoint source size and claim limits. State the missing condition and show how it affects the result instead of merely labelling the first answer wrong.

Transfer. Rewrite an ambiguous conclusion. Solve the altered case from the relationship, not from surface resemblance. If the conclusion changes, identify the exact changed condition; if it stays, explain why the mechanism is invariant.

Examination control. Write the decisive evidence before the conclusion. Reread the full prompt, check that the response answers the requested quantity or meaning, and verify that no unstated fact has been added. A concise answer is strong only when its reasoning remains inspectable.

Reverse construction. Invent a new prompt whose correct answer is “Nearer to the source and nearer to the screen predict different changes”, then create a near-nonexample by changing one condition. Explain the pair without reusing the original story. This reverse task checks genuine ownership of the method.

Worked case 8: What changes if the source becomes larger?

Controlled answer. The edge may become less sharp and the partial-shadow region wider. Light arrives from more source points.

Mechanism. Begin with light source opaque object and screen, then use boundary rays from the source past the object to decide the operation or language choice. The answer is justified only when shadow size and edge sharpness observation is shown explicitly. Keep every unit, referent and condition attached to the quantity or clause it controls.

Misconception repair. A tempting answer may copy the nearest noun, visible number or remembered slogan. That shortcut is unsafe because it does not test changed distance controlled variables viewpoint source size and claim limits. State the missing condition and show how it affects the result instead of merely labelling the first answer wrong.

Transfer. Keep shadow size and sharpness separate. Solve the altered case from the relationship, not from surface resemblance. If the conclusion changes, identify the exact changed condition; if it stays, explain why the mechanism is invariant.

Examination control. Write the decisive evidence before the conclusion. Reread the full prompt, check that the response answers the requested quantity or meaning, and verify that no unstated fact has been added. A concise answer is strong only when its reasoning remains inspectable.

Reverse construction. Invent a new prompt whose correct answer is “The edge may become less sharp and the partial-shadow region wider”, then create a near-nonexample by changing one condition. Explain the pair without reusing the original story. This reverse task checks genuine ownership of the method.

Worked case 9: Can a shadow form without a screen?

Controlled answer. Light is still blocked, but a visible outline needs a receiving surface or particles. The screen makes the reduced illumination observable.

Mechanism. Begin with light source opaque object and screen, then use boundary rays from the source past the object to decide the operation or language choice. The answer is justified only when shadow size and edge sharpness observation is shown explicitly. Keep every unit, referent and condition attached to the quantity or clause it controls.

Misconception repair. A tempting answer may copy the nearest noun, visible number or remembered slogan. That shortcut is unsafe because it does not test changed distance controlled variables viewpoint source size and claim limits. State the missing condition and show how it affects the result instead of merely labelling the first answer wrong.

Transfer. Distinguish path region from displayed image. Solve the altered case from the relationship, not from surface resemblance. If the conclusion changes, identify the exact changed condition; if it stays, explain why the mechanism is invariant.

Examination control. Write the decisive evidence before the conclusion. Reread the full prompt, check that the response answers the requested quantity or meaning, and verify that no unstated fact has been added. A concise answer is strong only when its reasoning remains inspectable.

Reverse construction. Invent a new prompt whose correct answer is “Light is still blocked, but a visible outline needs a receiving surface or particles”, then create a near-nonexample by changing one condition. Explain the pair without reusing the original story. This reverse task checks genuine ownership of the method.

Worked case 10: Why keep object orientation fixed?

Controlled answer. Turning the object changes its projected outline and width. Orientation would be a second manipulated variable.

Mechanism. Begin with light source opaque object and screen, then use boundary rays from the source past the object to decide the operation or language choice. The answer is justified only when shadow size and edge sharpness observation is shown explicitly. Keep every unit, referent and condition attached to the quantity or clause it controls.

Misconception repair. A tempting answer may copy the nearest noun, visible number or remembered slogan. That shortcut is unsafe because it does not test changed distance controlled variables viewpoint source size and claim limits. State the missing condition and show how it affects the result instead of merely labelling the first answer wrong.

Transfer. Design a fair test. Solve the altered case from the relationship, not from surface resemblance. If the conclusion changes, identify the exact changed condition; if it stays, explain why the mechanism is invariant.

Examination control. Write the decisive evidence before the conclusion. Reread the full prompt, check that the response answers the requested quantity or meaning, and verify that no unstated fact has been added. A concise answer is strong only when its reasoning remains inspectable.

Reverse construction. Invent a new prompt whose correct answer is “Turning the object changes its projected outline and width”, then create a near-nonexample by changing one condition. Explain the pair without reusing the original story. This reverse task checks genuine ownership of the method.

Worked case 11: A learner measures from different edge thresholds each time. Is the test reliable?

Controlled answer. No. Blurred edges require one consistent measurement rule.

Mechanism. Begin with light source opaque object and screen, then use boundary rays from the source past the object to decide the operation or language choice. The answer is justified only when shadow size and edge sharpness observation is shown explicitly. Keep every unit, referent and condition attached to the quantity or clause it controls.

Misconception repair. A tempting answer may copy the nearest noun, visible number or remembered slogan. That shortcut is unsafe because it does not test changed distance controlled variables viewpoint source size and claim limits. State the missing condition and show how it affects the result instead of merely labelling the first answer wrong.

Transfer. Define the boundary before collecting data. Solve the altered case from the relationship, not from surface resemblance. If the conclusion changes, identify the exact changed condition; if it stays, explain why the mechanism is invariant.

Examination control. Write the decisive evidence before the conclusion. Reread the full prompt, check that the response answers the requested quantity or meaning, and verify that no unstated fact has been added. A concise answer is strong only when its reasoning remains inspectable.

Reverse construction. Invent a new prompt whose correct answer is “No”, then create a near-nonexample by changing one condition. Explain the pair without reusing the original story. This reverse task checks genuine ownership of the method.

Worked case 12: What travels from source to screen?

Controlled answer. Light. The shadow is the result of missing or reduced light, not a travelling material.

Mechanism. Begin with light source opaque object and screen, then use boundary rays from the source past the object to decide the operation or language choice. The answer is justified only when shadow size and edge sharpness observation is shown explicitly. Keep every unit, referent and condition attached to the quantity or clause it controls.

Misconception repair. A tempting answer may copy the nearest noun, visible number or remembered slogan. That shortcut is unsafe because it does not test changed distance controlled variables viewpoint source size and claim limits. State the missing condition and show how it affects the result instead of merely labelling the first answer wrong.

Transfer. Correct the direction arrows. Solve the altered case from the relationship, not from surface resemblance. If the conclusion changes, identify the exact changed condition; if it stays, explain why the mechanism is invariant.

Examination control. Write the decisive evidence before the conclusion. Reread the full prompt, check that the response answers the requested quantity or meaning, and verify that no unstated fact has been added. A concise answer is strong only when its reasoning remains inspectable.

Reverse construction. Invent a new prompt whose correct answer is “Light”, then create a near-nonexample by changing one condition. Explain the pair without reusing the original story. This reverse task checks genuine ownership of the method.

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CHAPTER 10 OF 12 · Back to contents

10. Independent practice

Practice 1: Why can a small object cast a large shadow?

Explained answer. Projection geometry can magnify the blocked region when the object is near a diverging source. Shadow size need not equal object size.

Reasoning route. Identify light source opaque object and screen, determine boundary rays from the source past the object, apply shadow size and edge sharpness observation and audit changed distance controlled variables viewpoint source size and claim limits. Do not reveal the answer first when practising; reconstruct this chain from the prompt.

Delayed transfer. Trace the ray cone. Return after two days and solve without the headings. Then compare the new reasoning with this explanation and mark the first step that was missing or uncertain.

Boundary test. Change one decisive condition while leaving the remaining story intact. Predict the effect before calculating or editing. A useful near-nonexample differs in only one important way, so the reason for the changed answer remains visible.

Independent proof. Restate the conclusion in your own words and give one relevant fact that would still be insufficient by itself. This separates proof from association and prevents a topic label from standing in for a mechanism.

Self-check. Confirm the target, evidence, operation or grammar, units or referents, and claim strength. If the answer relies on a hidden assumption, state it. If the prompt does not justify that assumption, narrow the claim.

Practice 2: If source rays were parallel, would moving the screen enlarge the ideal shadow?

Explained answer. Not in the same way. Parallel boundary rays do not spread with distance in the ideal model.

Reasoning route. Identify light source opaque object and screen, determine boundary rays from the source past the object, apply shadow size and edge sharpness observation and audit changed distance controlled variables viewpoint source size and claim limits. Do not reveal the answer first when practising; reconstruct this chain from the prompt.

Delayed transfer. State the model assumption. Return after two days and solve without the headings. Then compare the new reasoning with this explanation and mark the first step that was missing or uncertain.

Boundary test. Change one decisive condition while leaving the remaining story intact. Predict the effect before calculating or editing. A useful near-nonexample differs in only one important way, so the reason for the changed answer remains visible.

Independent proof. Restate the conclusion in your own words and give one relevant fact that would still be insufficient by itself. This separates proof from association and prevents a topic label from standing in for a mechanism.

Self-check. Confirm the target, evidence, operation or grammar, units or referents, and claim strength. If the answer relies on a hidden assumption, state it. If the prompt does not justify that assumption, narrow the claim.

Practice 3: What direct observation supports a size claim?

Explained answer. A measured increase in shadow width or area on the same screen. Words such as looked bigger should be operationalised.

Reasoning route. Identify light source opaque object and screen, determine boundary rays from the source past the object, apply shadow size and edge sharpness observation and audit changed distance controlled variables viewpoint source size and claim limits. Do not reveal the answer first when practising; reconstruct this chain from the prompt.

Delayed transfer. Choose one measurement. Return after two days and solve without the headings. Then compare the new reasoning with this explanation and mark the first step that was missing or uncertain.

Boundary test. Change one decisive condition while leaving the remaining story intact. Predict the effect before calculating or editing. A useful near-nonexample differs in only one important way, so the reason for the changed answer remains visible.

Independent proof. Restate the conclusion in your own words and give one relevant fact that would still be insufficient by itself. This separates proof from association and prevents a topic label from standing in for a mechanism.

Self-check. Confirm the target, evidence, operation or grammar, units or referents, and claim strength. If the answer relies on a hidden assumption, state it. If the prompt does not justify that assumption, narrow the claim.

Practice 4: Repair: Moving anything closer always makes its shadow bigger.

Explained answer. Specify whether the object moves closer to the source or screen. The reference point controls the geometry.

Reasoning route. Identify light source opaque object and screen, determine boundary rays from the source past the object, apply shadow size and edge sharpness observation and audit changed distance controlled variables viewpoint source size and claim limits. Do not reveal the answer first when practising; reconstruct this chain from the prompt.

Delayed transfer. Give both contrasting cases. Return after two days and solve without the headings. Then compare the new reasoning with this explanation and mark the first step that was missing or uncertain.

Boundary test. Change one decisive condition while leaving the remaining story intact. Predict the effect before calculating or editing. A useful near-nonexample differs in only one important way, so the reason for the changed answer remains visible.

Independent proof. Restate the conclusion in your own words and give one relevant fact that would still be insufficient by itself. This separates proof from association and prevents a topic label from standing in for a mechanism.

Self-check. Confirm the target, evidence, operation or grammar, units or referents, and claim strength. If the answer relies on a hidden assumption, state it. If the prompt does not justify that assumption, narrow the claim.

Practice 5: Repair: A larger shadow proves the object grew.

Explained answer. The object may be unchanged while projection geometry changes. Shadow size is not direct evidence of physical growth.

Reasoning route. Identify light source opaque object and screen, determine boundary rays from the source past the object, apply shadow size and edge sharpness observation and audit changed distance controlled variables viewpoint source size and claim limits. Do not reveal the answer first when practising; reconstruct this chain from the prompt.

Delayed transfer. Measure the object separately. Return after two days and solve without the headings. Then compare the new reasoning with this explanation and mark the first step that was missing or uncertain.

Boundary test. Change one decisive condition while leaving the remaining story intact. Predict the effect before calculating or editing. A useful near-nonexample differs in only one important way, so the reason for the changed answer remains visible.

Independent proof. Restate the conclusion in your own words and give one relevant fact that would still be insufficient by itself. This separates proof from association and prevents a topic label from standing in for a mechanism.

Self-check. Confirm the target, evidence, operation or grammar, units or referents, and claim strength. If the answer relies on a hidden assumption, state it. If the prompt does not justify that assumption, narrow the claim.

Practice 6: Why repeat measurements?

Explained answer. Repeats reveal random variation and support a more stable comparison. One reading may be affected by alignment or edge judgement.

Reasoning route. Identify light source opaque object and screen, determine boundary rays from the source past the object, apply shadow size and edge sharpness observation and audit changed distance controlled variables viewpoint source size and claim limits. Do not reveal the answer first when practising; reconstruct this chain from the prompt.

Delayed transfer. Use the same procedure. Return after two days and solve without the headings. Then compare the new reasoning with this explanation and mark the first step that was missing or uncertain.

Boundary test. Change one decisive condition while leaving the remaining story intact. Predict the effect before calculating or editing. A useful near-nonexample differs in only one important way, so the reason for the changed answer remains visible.

Independent proof. Restate the conclusion in your own words and give one relevant fact that would still be insufficient by itself. This separates proof from association and prevents a topic label from standing in for a mechanism.

Self-check. Confirm the target, evidence, operation or grammar, units or referents, and claim strength. If the answer relies on a hidden assumption, state it. If the prompt does not justify that assumption, narrow the claim.

Practice 7: What is the nearest wrong shortcut?

Explained answer. Memorising one distance slogan without tracing rays. Different movements can produce opposite effects.

Reasoning route. Identify light source opaque object and screen, determine boundary rays from the source past the object, apply shadow size and edge sharpness observation and audit changed distance controlled variables viewpoint source size and claim limits. Do not reveal the answer first when practising; reconstruct this chain from the prompt.

Delayed transfer. Draw before deciding. Return after two days and solve without the headings. Then compare the new reasoning with this explanation and mark the first step that was missing or uncertain.

Boundary test. Change one decisive condition while leaving the remaining story intact. Predict the effect before calculating or editing. A useful near-nonexample differs in only one important way, so the reason for the changed answer remains visible.

Independent proof. Restate the conclusion in your own words and give one relevant fact that would still be insufficient by itself. This separates proof from association and prevents a topic label from standing in for a mechanism.

Self-check. Confirm the target, evidence, operation or grammar, units or referents, and claim strength. If the answer relies on a hidden assumption, state it. If the prompt does not justify that assumption, narrow the claim.

Practice 8: State the complete method.

Explained answer. Identify source, opaque object and screen; change one distance; trace boundary rays; predict and measure the shadow; then separate size from sharpness. Keep all other conditions controlled.

Reasoning route. Identify light source opaque object and screen, determine boundary rays from the source past the object, apply shadow size and edge sharpness observation and audit changed distance controlled variables viewpoint source size and claim limits. Do not reveal the answer first when practising; reconstruct this chain from the prompt.

Delayed transfer. Plan a three-position investigation. Return after two days and solve without the headings. Then compare the new reasoning with this explanation and mark the first step that was missing or uncertain.

Boundary test. Change one decisive condition while leaving the remaining story intact. Predict the effect before calculating or editing. A useful near-nonexample differs in only one important way, so the reason for the changed answer remains visible.

Independent proof. Restate the conclusion in your own words and give one relevant fact that would still be insufficient by itself. This separates proof from association and prevents a topic label from standing in for a mechanism.

Self-check. Confirm the target, evidence, operation or grammar, units or referents, and claim strength. If the answer relies on a hidden assumption, state it. If the prompt does not justify that assumption, narrow the claim.

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11. Delayed transfer

Use three passes. On day one, solve clear examples and explain each step. On day three, mix valid examples, near-nonexamples and incomplete evidence. On day seven, answer without a word bank or chapter heading. The delay tests reconstruction rather than short-term recognition.

Keep an error log that records the first failed stage: reading, representation, rule, execution or checking. Repair that stage with a changed example before completing another full set. Ten repeated answers are less useful than one accurately diagnosed error.

Interleave this skill with neighbouring ideas that use similar words or diagrams. Before solving, classify the relationship and state the condition that distinguishes it from the neighbour. Classification should follow evidence, not topic appearance.

In timed work, mark the controlling words or quantities, write one intermediate relationship, complete the answer and audit one boundary condition. If checking changes the answer, record the overlooked feature so the same error becomes easier to recognise.

For a second delayed test, begin with a conclusion and construct sufficient evidence for it. Then construct evidence that is relevant but insufficient. Reversing the direction makes the boundary between support and proof visible.

Finish with a basic case, a boundary case and a transfer case from a different context. Explain all three to a classmate who is allowed to ask, “Which exact condition makes that true?”

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12. Family guidance and FAQs

Guidance for parents and tutors

Ask for the decisive condition before confirming an answer. Helpful prompts include “What exactly is related?”, “Which word or quantity controls the result?”, “What stayed fixed?” and “What would make the answer change?”

Fade support from labelled examples to mixed questions and delayed open response. Praise precise claim control, visible units and the willingness to narrow a conclusion when evidence is incomplete.

Frequently asked questions

Should I memorise the compact rule?

Yes, but pair it with examples and near-nonexamples. Memory supplies speed; contrast practice protects the conditions.

What if two answers seem possible?

Return to the exact relationship and choose the answer that satisfies every stated condition without inventing facts.

Why write an intermediate step?

It makes the controlling relationship visible and gives you something specific to audit.

Why delay practice?

Immediate repetition may rely on the recent explanation. Delay reveals whether the method can be rebuilt independently.

How should an error be corrected?

Name the earliest failed stage, repair it with one changed example and then retry the original question.

When is the skill ready?

When the learner can explain, apply and transfer it after a delay while preserving the relevant conditions.

Next routes

Continue at the Science learning hub or return to the series directory.

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