6.2 Position and Orientation Sequences

Separate where from which way

Location answers "Where is the element?" Orientation answers "Which direction does it face?" A triangle can move from the upper-left corner to the upper-right while continuing to point upward. Or it can remain in the same corner while rotating from up to right. Combining these into one vague impression produces avoidable errors.

Use two notation lines:

• Location: UL → UR → LR → LL
• Orientation: up → right → down → left

Then predict each independently.

Common location paths

Perimeter movement

An object may travel around corners or positions on a boundary. Test one-step clockwise and counterclockwise movement first. With four corners, clockwise may produce UL → UR → LR → LL → UL. Counterclockwise reverses the order.

Alternating locations

A marker may switch between two positions: left, right, left, right. Another may alternate high and low while also moving horizontally. Write each dimension separately if needed:

• Horizontal: left, center, right, left...
• Vertical: top, bottom, top, bottom...

Variable steps

Movement may increase by one position: advance 1, then 2, then 3. Do not assume this complexity until fixed-step movement fails. Verify that the proposed step pattern explains all three transitions.

Two moving elements

The official sample explanations include problems where occupied boxes move while object count and shading also change. Label the elements A and B. Track A's route on one line and B's route on another. If they overlap in a frame, record the overlap rather than assuming one disappeared.

Common orientation patterns

An arrow or asymmetric figure may rotate by a constant quarter-turn: up → right → down → left. A half-turn pattern alternates up → down → up → down. Another sequence may alternate a clockwise turn with no turn.

You do not need to assign degree measures when compass labels are clearer. If an eight-position dial is used, clock positions such as 12, 1:30, 3, and 4:30 can make a 45-degree step visible. What matters is repeatable change, not geometric vocabulary.

Rotation versus reflection

A true rotation preserves the internal arrangement while changing direction. A reflection reverses left and right or top and bottom. The official blueprint names orientation but does not promise a separate transformation-theory item, so use reflection only when the figure's handedness visibly reverses.

Choose an asymmetric anchor—a notch, dot, short arm, or dark sector. After a rotation, the anchor travels around with the figure. After a mirror change, its side relative to the figure reverses. If no asymmetric feature exists, do not invent a reflection rule.

Worked two-variable sequence

Suppose a black dot occupies:

• Frame 1: upper-left
• Frame 2: upper-right
• Frame 3: lower-right
• Frame 4: lower-left

At the same time, a small arrow points:

• up, down, up, down

The dot moves one corner clockwise and should return to upper-left. The arrow alternates and should point up. A choice with the dot upper-left but arrow down satisfies only one rule and must be rejected.

Official-example connection

One official worked example has a differently shaded sector move counterclockwise while the majority shading alternates. Another has object locations rotate counterclockwise while a center object remains gray. These examples show why an anchor may move even while another feature stays fixed. Do not demand that every visible component change.

Elimination sequence

When choices are complex:

1. Use the clearest movement rule to eliminate wrong positions.
2. Among survivors, test orientation.
3. Then test shading, count, size, or shape.
4. Confirm that an apparently irrelevant feature truly lacks a repeated rule.
5. Re-run the chosen figure as Frame 5 and check that Frame 4 → 5 uses the same change as prior transitions.

Frequent traps

• Reversing clockwise because you track from the viewer's imagined side inconsistently.
• Counting the starting location as the first movement step.
• Rotating an object when only its location moves.
• Moving an object when only its orientation changes.
• Following the most noticeable element and ignoring a second marker.
• Treating a one-time coincidence as a rule.

A written or mental coordinate map prevents these mistakes.

Practice progression

Begin with one moving dot and four locations. Add orientation as a second variable. Then add a second moving element, alternation, or a changing step size. Keep the actual UDEE structure: four given frames and five possible fifth figures. After every answer, state the location rule and orientation rule separately.