Help for parents: common maths mistakes

The mistakes children most often make in maths in Years 7 to 10: why they make them, and how to help at home.

Integers

• Why does my child think 5 − (−3) = 2?
• Why does my child think −4 × (−3) = −12?
• Why does my child think −7 + 3 = −10?
• Why does my child think 3 − 8 = 5?
• Why does my child think 2 + 3 × 4 = 20?
• Why does my child think 12 ÷ 2 × 3 = 2?

Powers and primes

• Why does my child think 7² = 14?
• Why does my child think √36 = 18?
• Why does my child think (−3)² = −9?
• Why does my child write 60 = 2 × 3 × 5?
• Why does my child mix up the HCF and the LCM?
• Why does my child think the LCM of 6 and 8 is 48?

Fractions and decimals

• Why does my child think 2/3 = 11/12?
• Why does my child think 1/2 + 1/3 = 2/5?
• Why does my child think 3 × 2/5 = 6/15?
• Why does my child think 2/3 ÷ 1/2 = 1/3?
• Why does my child think 2.5 + 0.75 = 1.00?
• Why does my child think 0.3 × 0.2 = 0.6?
• Why does my child round 3.146 to 3.14?
• Why does my child round 3.142 to 3.15?

Algebraic expressions

• Why does my child think 3x is 35 when x = 5?
• Why does my child think 2x + 5 is 11 when x = −3?
• Why does my child think 3x + 4 = 7x?
• Why does my child think 7x − 2 − 3x + 4 = 10x + 2?
• Why does my child think 5(x + 4) = 5x + 4?
• Why does my child think −2(x − 3) = −2x − 6?
• Why does my child think 6x + 9 = 3(2x + 9)?
• Why does my child think (6x + 9)/3 = 2x + 9?
• Why does my child get the signs wrong taking one fraction from another?

Linear equations

• Why does my child solve x − 4 = 10 as x = 6?
• Why does my child solve x + 5 = 12 as x = 17?
• Why does my child solve 3x = 12 as x = 36?
• Why does my child solve x/3 = 5 as x = 5/3?
• Why does my child solve x/3 + 4 = 9 as x = 27?
• Why does my child change only one side of an equation?
• Why does my child think 2x + 4 = 10 becomes 2x = 14?
• Why does my child think 5x + 3 = 2x + 15 gives 7x?
• Why does my child solve 4(x − 2) = 12 as x = 14?
• Why does my child get the method right but the answer wrong?
• Why does my child swap the values of x and y?
• Why does my child mix up the gradient and the y-intercept?
• Why does my child solve −2x > 6 as x > −3?
• Why does my child rearrange y = 3x + 2 as x = y/3 − 2?
• Why does my child draw y = 2x − 1 through (−1, 0)?
• Why does my child multiply only the fractions in an equation?
• Why does my child use ≥ for a dashed line?
• Why does my child write y < 2x − 1 for the region above the line?

Indices and real numbers

• Why does my child write 45 000 as 4.5 × 10³?
• Why does my child write 0.00045 as 4.5 × 10⁴?
• Why does my child think 3.2 × 10⁴ = 320 000?
• Why does my child think x² × x³ = x⁶?
• Why does my child think x⁸ ÷ x² = x⁴?
• Why does my child think 3x² × 4x³ = 7x⁵?
• Why does my child think (x²)³ = x⁵?
• Why does my child think (2x³)² = 2x⁶?
• Why does my child think 5⁰ = 0?
• Why does my child think 2⁻³ = −8?
• Why does my child think 3x⁻² × 5x⁶ = 15x⁸?
• Why does my child think √9 + √16 = √25?
• Why does my child think √48 = 16√3?
• Why does my child think 8^(1/3) = 8/3?
• Why does my child write 0.444... as 4/10?
• Why does my child think √9 is irrational?

Coordinates

• Why does my child divide the wrong way to find a gradient?
• Why does my child get the wrong sign for a gradient?
• Why does my child think the midpoint of (1, 2) and (5, 6) is (6, 8)?
• Why does my child think the midpoint of (1, 2) and (5, 6) is (2, 2)?
• Why does my child think the distance from (1, 2) to (4, 6) is 25?
• Why does my child think the distance from (1, 2) to (4, 6) is 7?
• Why does my child plot (3, −2) above the x-axis?
• Why does my child write (−4, 3) for the point (3, −4)?

Quadratics

• Why does my child think (x + 2)(x + 3) = x² + 6?
• Why does my child think (x + 3)² = x² + 9?
• Why does my child think x² + 5x + 6 = (x − 2)(x − 3)?
• Why does my child think (x − 2)(x − 3) = 0 gives x = −2 or x = −3?
• Why does my child think x² = 9 only means x = 3?
• Why does my child write (2x + 3)(x + 1) for 2x² + 7x + 3?
• Why does my child think (2x − 3)(x + 4) = 0 gives x = 3?
• Why does my child think y = (x − 2)² + 5 turns at (−2, 5)?
• Why does my child think x² + 6x + 2 = (x + 3)² + 2?
• Why does my child get the signs wrong in the quadratic formula?

Exponentials and other graphs

• Why does my child think 2^x = 32 gives x = 16?
• Why does my child think $1000 at 5% compound interest is $1100 after 2 years?
• Why does my child multiply by 0.2 when something loses 20%?
• Why does my child think x² + y² = 25 has a radius of 25?
• Why does my child think log 2 + log 3 = log 5?
• Why does my child think log₂ 8 = 4?

Percentages, ratios and rates

• Why does my child think 5% = 0.5?
• Why does my child think 15% of $80 is $1200?
• Why does my child think $80 reduced by 15% is $65?
• Why does my child think a price of $110 after a 10% rise was $99 before?
• Why does my child give the discount instead of the new price?
• Why does my child write a ratio the wrong way round?
• Why does my child take 3/5 of $40 to share it in the ratio 3:5?
• Why does my child think a 2:3 ratio with 12 boys means 13 girls?
• Why does my child work out 150 km in 3 hours as 3 ÷ 150?
• Why does my child work out only one year's interest?
• Why does my child think 12 km in 30 minutes is a speed of 0.4 km/h?

Pythagoras and trigonometry

• Why does my child think sides of 3 and 4 make a hypotenuse of 7?
• Why does my child get a shorter side longer than the hypotenuse?
• Why does my child use the whole base to find an isosceles triangle's height?
• Why does my child stop halfway through a box's diagonal?
• Why does my child mix up the opposite and adjacent sides?
• Why does my child divide when they should multiply in trigonometry?
• Why does my child get sin 30 = −0.988 on the calculator?
• Why does my child get a tiny number when finding an angle?
• Why does my child put the angle of depression in the wrong place?
• Why does my child give 300° for a bearing of 060° the other way?
• Why does my child mix up sin 30° and cos 30°?
• Why does my child think cos 120° = 1/2?
• Why does my child think y = 3 sin x has an amplitude of 6?