Maths Skills Lab

Every skill in the Maths Skills Lab

47 skills so far, from place value and times tables up to GCSE Higher algebra. Click any skill to open it, pick a level, and the Lab teaches the method one step at a time before your child practises it.

Number 25 skills

• Negative numbersWhere you start, which way you go and how far. Then the sign rule for multiplying and dividing.
• Counting in stepsRepeated addition and repeated subtraction: the same number added again and again, or subtracted again and again. Counting on and counting back in any step, then the question turned round: how many steps, what is the remainder, and what was the starting number?
• Place valueThe value of each digit, partitioning a number into its parts and recombining them, from tens and units to billions and then past the decimal point.
• 10 more, 10 lessOne, ten, a hundred or a thousand more or less than a number, and how to exchange when the digit in that place is a 9 or a 0.
• Multiplying and dividing by 10, 100 and 1000The digits move and the decimal point stays still: multiplying and dividing whole numbers and decimals by 10, 100 and 1000, then missing number problems.
• Numbers in words and figuresReading a number in words and writing it in figures, and the other way round, from two-digit numbers to a billion and then decimals.
• Comparing and ordering numbersWhich is greater, and putting a list in ascending or descending order: whole numbers, then decimals, then negatives.
• Roman numeralsReading and writing Roman numerals, from the clock face to years, one place at a time: each place has its own symbols, a smaller symbol before a larger one is subtracted, and zero is not written.
• Simplifying surds Questions with answersFind the largest square number that is a factor, take its square root out in front, and collect like surds the way you collect like terms.
• Rationalising the denominatorMultiply the numerator and the denominator by the same surd (or by the conjugate) so the denominator becomes a whole number, then simplify.
• Recurring decimals and fractions Questions with answersMultiply by a power of ten so the repeating digits line up, subtract to make them disappear, then divide and simplify.
• Times tablesRecall of the multiplication facts to 12 × 12 and the division facts that come with them, in the order the tables are learnt. Then the three things to do with a fact once it is known: read it backwards, fill in a missing factor, and scale it.
• Grid method multiplicationPartition both numbers, multiply every part by every part, then add the parts back up.
• Column multiplicationShort and long multiplication set out in columns, including the placeholder zero that starts the second row.
• Short divisionBus stop division by a single digit, with the remainder written three ways.
• Multiplying and dividing decimalsMultiply decimals by taking the decimal points out and putting them back, and divide by writing it as a fraction first.
• Laws of indicesMultiply powers of the same base by adding the indices, divide by subtracting them, and raise a power to a power by multiplying them.
• Negative and fractional indicesA negative index means the reciprocal, the denominator of a fractional index is a root and the numerator is a power.
• Standard formWrite a number as a number from 1 up to 10 multiplied by a power of ten, and calculate with numbers written that way.
• Squares, cubes and rootsSquare and cube numbers, and the square and cube roots that are their inverses.
• Fraction of an amountFind a fraction of a number, money or a measure: divide by the denominator, multiply by the numerator.
• Equivalent and simplifying fractionsMultiply or divide the numerator and the denominator by the same number to make an equivalent fraction, and divide by the highest common factor for the simplest form.
• Improper fractions and mixed numbersTurn an improper fraction into a mixed number by dividing, and a mixed number back into an improper fraction by multiplying the whole number by the denominator and adding the numerator.
• Adding and subtracting fractionsFind a common denominator first, write each fraction as an equivalent fraction over it, then add or subtract the numerators and simplify.
• Multiplying and dividing fractionsMultiply the numerators and the denominators, cancelling first where you can; to divide, keep the first fraction, flip the second and change ÷ to ×.

Algebra 22 skills

• Expanding single bracketsMultiply the term outside by every term inside the bracket, sign included.
• Expanding double brackets Questions with answersMultiply every term in the first bracket by every term in the second. Then collect the like terms.
• Expanding three bracketsExpand two of the brackets first, simplify, then multiply the result by the third bracket.
• Expanding brackets with surdsExpand as usual, then simplify: a square root multiplied by itself gives the number under it.
• Completing the square Questions with answersWrite a quadratic in completed square form, then use it to find the turning point and to solve.
• Factorising quadraticsFind the factor pair whose product is the constant term and whose sum is the coefficient of the linear term, then write the two brackets. Includes the difference of two squares.
• Quadratic formulaRead a, b and c from the equation, work out b² − 4ac, then substitute into the quadratic formula to find both solutions.
• Linear sequences: nth term Questions with answersFind the difference, write out the multiples of it under the sequence, compare, and write the nth term. Then use it to find which term a number is, or whether it is a term at all.
• Quadratic sequences: nth termFind the second difference and halve it for the coefficient of n², subtract the n² part from each term, then find the nth term of what is left and combine.
• Solving quadratics by factorisingRearrange so one side is 0, factorise, then set each bracket equal to 0: if two things multiply to give 0, one of them must be 0.
• Simplifying algebraic fractionsFactorise the numerator and the denominator, then cancel the factors they share. Only whole factors cancel, never single terms.
• Multiplying and dividing algebraic fractionsTo divide, multiply by the reciprocal of the second fraction. Then factorise every part, cancel factors that appear on a numerator and a denominator, and multiply what is left.
• Adding and subtracting algebraic fractionsFind the lowest common denominator, write each fraction over it, combine the numerators, then check whether the answer simplifies.
• Equations with algebraic fractionsClear the fractions by multiplying every term by the lowest common denominator, then solve the equation that is left.
• Rearranging formulaeUse the inverse operation on both sides, in the reverse order to the way the formula was built, until the subject stands alone.
• Algebraic proofWrite each number as an expression in n, simplify, then factorise so the required factor is there to see.
• Solving linear equationsDo the same inverse operation to both sides until the unknown is the subject.
• Equations with squaresMake x² the subject, then take the square root of both sides: two solutions, one positive and one negative.
• Simultaneous equationsEliminate one letter by adding or subtracting the equations, solve for the other, then substitute back.
• Non-linear simultaneous equationsSubstitute the line into the curve, solve the quadratic, then pair each x with its y.
• Plotting linear graphsFill in a table of values by substituting each x, plot the points and rule a straight line through them.
• Gradient and y = mx + cFind the gradient from a graph or two points, read m and c, and write the equation of a straight line.