The mistakes learners actually make

Every wrong answer has a reason behind it. These pages name 471 of them across 104 topics: what each one looks like in your child's work, why it happens, and the one thing that puts it right. Free to read, no account needed.

Maths

4 mistakes explained

Adding and subtracting negatives

Movement along the number line in the wrong direction. Ordering negatives by the size of the digits.

5 mistakes explained

Angles in polygons

An angle given where the number of sides was wanted. Interior and exterior angles swapped.

5 mistakes explained

Angles on lines and at a point

Subtracted from 360 instead of 180. Subtracted from 90 instead of 180.

4 mistakes explained

Area and perimeter of rectangles

Area given where perimeter was asked for. One side used for both dimensions.

3 mistakes explained

Averages from a frequency table

Divided by the number of rows instead of the number of items. The frequency column ignored.

4 mistakes explained

Circles

Circumference calculated where area was wanted. The diameter used where the radius belongs.

3 mistakes explained

Collecting like terms

Collecting a subtracted term as if it were added. Collecting terms that are not alike.

5 mistakes explained

Combined events

An overlap counted twice. More events multiplied than the question has.

4 mistakes explained

Compound shapes

The corners of a surrounding path left out. The cut-out piece added on.

3 mistakes explained

Decimal place value

The decimal digits copied straight into a fraction. The longer decimal is the bigger one.

4 mistakes explained

Enlargement

A transformation that preserves size thought to change it. Divided by the scale factor.

3 mistakes explained

Factorising harder quadratics

A common factor left inside a bracket. Finding numbers that multiply but do not add.

3 mistakes explained

Fractions of an amount

A different fraction of the amount found. Finding one part and stopping.

3 mistakes explained

Gradient from two points

A coordinate given as the gradient. The change in y given without dividing.

5 mistakes explained

Hypothesis testing

Certainty claimed from a test. The critical region put in the wrong tail.

10 mistakes explained

Integration

A constant term not integrated. Divided by the original power rather than the new one.

5 mistakes explained

Linear sequences

Counting the position wrong. Doing the operations in the order they are written.

3 mistakes explained

Magnitude

The components added to give the magnitude. The sides added without squaring.

5 mistakes explained

Parallel and perpendicular lines

Parallel judged by the constant. The perpendicular gradient used for a parallel line.

3 mistakes explained

Parallel vectors

A sign change treated as a scalar multiple. Only one component checked for the multiple.

4 mistakes explained

Percentage change

A repeated change applied only once. Adding the percentages instead of multiplying.

3 mistakes explained

Percentages of an amount

Comparing a decimal, a fraction and a percentage as they stand. Giving the discount instead of the price.

3 mistakes explained

Powers and indices

Multiplying the powers instead of adding them. Reading a power as multiply by the index.

5 mistakes explained

Probability of one event

Only one favourable outcome counted. The boundary value counted in.

3 mistakes explained

Probability without replacement

Only the count reduced. Only the total reduced.

3 mistakes explained

Proof

A counterexample offered without testing it. Examples offered as a proof.

5 mistakes explained

Proportion and scale

Adding the difference instead of scaling. Losing a factor of ten in the units.

3 mistakes explained

Pythagoras' theorem

Added when the hypotenuse was already known. The root taken before the squaring.

6 mistakes explained

Quadratic and other sequences

Accepting a position that is not a whole number. Answering from a property of the number instead of solving.

6 mistakes explained

Range and spread

The extremes added rather than subtracted. The largest value given as the range.

4 mistakes explained

Rotation

A full turn given as the answer. A quarter turn given for a half turn.

3 mistakes explained

Rounding and significant figures

Cutting the digits off instead of rounding. Rounding a 5 down.

5 mistakes explained

Sharing in a ratio

A ratio simplified with the wrong divisor. Dividing by one part instead of the total parts.

6 mistakes explained

Solving linear equations

Collecting the letters with the wrong sign. Repeating the operation instead of undoing it.

7 mistakes explained

Solving quadratics

Minus b used without dividing by 2a. Only the square root part divided by 2a.

5 mistakes explained

Standard form

Adding the front numbers instead of multiplying. Counting the zeros instead of the places moved.

4 mistakes explained

Stationary points

A turning point given a nature it cannot have. The derivative set to zero and solved wrongly.

4 mistakes explained

Surds

Leaving the root on the bottom. Losing the sign when a root multiplies itself.

3 mistakes explained

The binomial expansion

The choose number left out of the term. The minus dropped from a negative term.

3 mistakes explained

The chain rule

The inside function never differentiated. The outer power dropped.

5 mistakes explained

The discriminant

A surd left unsimplified. The coefficient not halved when completing the square.

8 mistakes explained

The equation of a straight line

A y-coordinate used as the intercept. Only part of the equation divided.

7 mistakes explained

The mean

A zero left out of the count. The group sizes attached to the wrong means.

3 mistakes explained

The median

The mean given where the median was asked for. The middle position counted wrongly.

6 mistakes explained

The mode

Any repeated value taken as the mode. How often it appeared given instead of the value.

6 mistakes explained

The normal distribution

Divided by n rather than the root of n. The population standard deviation used unchanged.

4 mistakes explained

The probability of not happening

A count given where a probability was wanted. The complement given as the same number.

3 mistakes explained

The product rule

Only one term of the product rule written. The product rule terms subtracted.

3 mistakes explained

Trigonometry

The ratio written the wrong way up. The rearrangement done the wrong way.

4 mistakes explained

Turning a problem into an equation

A negative root kept as a length. Only two sides counted.

5 mistakes explained

Vector arithmetic

A multiplier applied to only one component. A scalar multiplier ignored.

3 mistakes explained

Vector arithmetic

One component added, the other subtracted. The components multiplied.

3 mistakes explained

Vector paths

A side of the shape given for a different vector. An arrow travelled the wrong way without a sign change.

3 mistakes explained

Volume

Only two of the three dimensions used. Surface area given where volume was wanted.

Science

5 mistakes explained

Atomic structure

A particle given a charge it does not carry. Electrons not matched to protons.

8 mistakes explained

Bonding

A metal property given as an explanation. An element put on the wrong side of the table.

4 mistakes explained

Cells

A bacterium given a nucleus. Membrane-bound organelles given to a bacterium.

6 mistakes explained

Chemical reactions

A chemistry term swapped for a similar one. A common gas named at random.

3 mistakes explained

Circuits

Current thought to be used up round the circuit. Parallel branches thought to change nothing.

6 mistakes explained

Density

Adding mass thought to lower density. Density and mass treated as the same thing.

8 mistakes explained

Ecosystems and food chains

A decomposer counted as a producer. A feeding group given the wrong definition.

8 mistakes explained

Energy stores and transfers

A physics term swapped for a similar one. Conservation of energy read as perfect efficiency.

7 mistakes explained

Evolution and natural selection

A famous scientist attached to the wrong idea. Animals thought to change themselves to suit the environment.

4 mistakes explained

Forces

Adding the quantities together. Balanced forces expected to produce acceleration.

8 mistakes explained

Genetics and inheritance

A genetics term swapped for a neighbour. Alleles thought to blend.

3 mistakes explained

Muscles and movement

A muscle given an action it cannot cause. Muscles thought to push as well as pull.

6 mistakes explained

Respiration

A product of respiration misremembered. Breathing and respiration treated as one.

3 mistakes explained

Rocks and the rock cycle

A property offered as a rock type. A rock type matched to the wrong formation.

7 mistakes explained

Separating mixtures

A separating method matched to the wrong job. Dissolved solids thought to be filterable.

6 mistakes explained

Speed and acceleration

A number from the question copied out. Multiplying where you should divide.

4 mistakes explained

The atmosphere

A gas named that is barely in the air. A gas that is not a greenhouse gas chosen as one.

4 mistakes explained

The periodic table

Every atom given a full outer shell. Period number used for outer electrons.

4 mistakes explained

The reactivity series

A metal denied being a metal. All metals treated as equally reactive.

4 mistakes explained

The skeleton

A job given to the skeleton that is not its own. Another tissue named at the joint.

4 mistakes explained

Variation

A biology term swapped for a similar one. Environmental variation labelled genetic.

English

5 mistakes explained

Apostrophes

An apostrophe added after the s on an irregular plural. An apostrophe used to make a plural.

4 mistakes explained

Commas

A comma between the subject and its verb. A comma dropped inside a phrase that should stay whole.

4 mistakes explained

Comparing texts

A general assertion with no method behind it. Context listed instead of used.

3 mistakes explained

Homophones

A near twin that sounds or looks the same. Affect and effect swapped.

4 mistakes explained

Inference

A motive invented that the text does not support. The behaviour repeated instead of what it shows.

5 mistakes explained

Language techniques

A speech verb that fights the feeling. A technique that works against the wanted effect.

4 mistakes explained

Punctuating speech

No comma before the closing speech mark. Speech not started with a capital letter.

3 mistakes explained

Sentence types

A complex sentence called compound. A participial opener mistaken for a clause.

5 mistakes explained

Spelling patterns

A letter doubled that should be single, or single that should be double. The i and e the wrong way round.

3 mistakes explained

Suffixes and word building

A noun ending invented for the verb. The root spelled through unchanged when the ending changes it.

3 mistakes explained

Tense

The continuous form chosen for the simple past. The future chosen for the past.

3 mistakes explained

Word classes

A content word offered where a joining word was asked for. An adverb identified as an adjective.

4 mistakes explained

Word meaning

A meaning chosen because it sounds connected. A word from the same scene, not the same meaning.

Want to know which of these your own child is making? Answer ten free questions and WAJD names the pattern behind the wrong ones.