Reasoning and 11 Plus

Common mistakes in ordering and logic

7 mistakes learners make with ordering and logic, each one named and explained.

All common mistakes

Write the chain out in order before answering anything about it.

A rule read backwards

What it looks like

All Zibs are Trins becomes all Trins are Zibs.

Why it happens

The sentence contains the same words both ways round, so the reverse feels like the same fact.

A worked example

Question. All Zibs are Gloops. All Gloops are Trins. What must be true?

A common answer. All Trins are Zibs

The answer. All Zibs are Trins

Why. Every Zib is inside Gloops, and every Gloop is inside Trins, so every Zib is a Trin. Nothing says every Trin is a Zib; the arrow only points one way.

Put the two side by side

All cats are animals does not make all animals cats.
All cats are animals means each cat is an animal.

An all statement points one way. Never turn it round for free.

An answer that breaks a given clue

What it looks like

Aisha is given red when the clue says Aisha does not like red.

Why it happens

With several clues in play, the first one read fades by the time the answer is chosen.

A worked example

Question. Aisha does not like red or blue. Ben likes green. Which colour is Aisha's?

A common answer. Red

The answer. Yellow

Why. Red and blue are ruled out for Aisha by her own clue, and green is taken by Ben. Only yellow is left standing.

Put the two side by side

Red ignores the clue that rules it out.
Yellow survives every clue.

Check your answer against each clue, one by one, before moving on.

Clues not joined, so the answer looks unknowable

What it looks like

Cannot tell is chosen when combining the clues settles it.

Why it happens

Each clue on its own really is not enough, and the step of joining them is the easy one to miss.

A worked example

Question. The red box does not hold apples. The blue box holds plums. What is in the red box?

A common answer. Cannot tell

The answer. Pears

Why. The red box cannot hold apples by its own clue, and it cannot hold plums because the blue box has them. Only pears are left, so the clues together do tell.

Put the two side by side

Each clue alone leaves choices open.
The clues together leave exactly one.

When one clue is not enough, put it next to the other clues before saying cannot tell.

More certainty claimed than the clues allow

What it looks like

Some sheep have patches becomes the animal must be a cow.

Why it happens

A confident answer feels better than a careful one, even when the clues stop short of proof.

A worked example

Question. All cows have patches. Some sheep have patches. An animal has patches. What is it?

A common answer. It must be a cow

The answer. It is either a sheep or a cow

Why. Patches do not belong only to cows here, because some sheep have them too. The clues allow both, so certainty is not available.

Put the two side by side

It must be a cow claims more than the clues say.
It could be either follows exactly what the clues say.

Only say must when the clues rule out every other possibility.

The chain not joined up

What it looks like

The answer given is that it cannot be worked out, when the statements do settle it.

Why it happens

The two statements never compare the first and last people directly.

A worked example

Question. Tom > Sam and Sam > Ben, who is shortest

A common answer. cannot tell

The answer. Ben

Why. If Tom is above Sam and Sam is above Ben, the whole order is fixed.

Put the two side by side

No statement compares Tom and Ben directly.
The chain still puts them in order.

Link the statements through the name they share. That is usually enough to fix everything.

The middle person chosen

What it looks like

The person in the middle of the chain is given for a question about either end.

Why it happens

The middle name appears in both statements, so it is the one that stands out.

A worked example

Question. Tom > Sam > Ben, who is shortest

A common answer. Sam

The answer. Ben

Why. Sam is taller than Ben, so Sam is not the shortest.

Put the two side by side

Sam appears twice in the question.
Ben appears once, at the end of the chain.

The answer to an extreme question is always at an end, and ends appear only once.

The order read the wrong way

What it looks like

The tallest is given when the shortest was asked for.

Why it happens

The chain has been built correctly and only the last reading of it is inverted.

A worked example

Question. Tom is taller than Sam, Sam is taller than Ben. Who is shortest?

A common answer. Tom

The answer. Ben

Why. Tom is at the tall end of the chain, so he cannot be the shortest.

Put the two side by side

Tallest: Tom.
Shortest: Ben.

Write the names in a line, tallest first. Then read from whichever end the question wants.

WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.

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