Ring the gap before you calculate
Two sides, one gap, and a mark that goes to whoever remembers what they were looking for. Do the complete side first, then fill the gap — and check you wrote the gap, not the total.
Number
18 posts on this. Written by Mat and Alicia, who prepare pupils for the Buckinghamshire Transfer Test every week in Winslow.
Compare, then test
Six rules to choose between, and the one that costs the marks takes two steps rather than one. The number you get halfway is the tempting wrong answer.
The trap is not the maths, it is the order
Letters stand for numbers, the arithmetic is easy, and the marks go on order, a dropped step and a misread sign. Count the operators before you start — that is how many steps you owe.
The little two does not mean times two
Seven squared is forty-nine, not fourteen. That single mistake costs more marks than anything else on this topic — and the squares to 144 are worth knowing cold.
You cannot borrow from nothing: subtraction
Subtracting through a row of zeros is where this topic is won and lost. What actually happens when you exchange, and why the estimate matters even more here.
0.45 is smaller than 0.5: place value
Every column is worth ten times the one to its right, and that one fact settles most place value questions. Grouping in threes, and why longer decimals are not bigger.
Same form, then compare: fractions
Fractions, decimals and percentages are one idea wearing three coats. Convert everything into the same coat before comparing, and per cent means out of a hundred.
Write every gap, with its sign: number sequences
Write the gap between every pair before naming any rule. When the gaps themselves change, the pattern is in the second row rather than the first.
Estimate first, then be exact: addition
By Year 5 the arithmetic is not the problem — the setting out is. Why decimals with different lengths wreck a column before it starts, and the estimate that catches it.
Exactly two factors: prime numbers
Not one factor, not three. Exactly two — which settles both of the arguments children have about primes, and explains why 1 is not one and 2 is.
Line up the points, then pad the gaps
Calculating with decimals goes wrong at the setting-out stage, not the arithmetic. Line the points up, fill the gaps with zeros, and the sum becomes an ordinary sum.
What does the remainder mean? division
The division is rarely the hard part. Deciding what to do with what is left over — round up, round down, or write it as a fraction — is where the marks actually sit.
Into it, or out of it? factors and multiples
The two words swapped more often than any others in maths. Factors divide into a number; multiples come out of it — and finding factors in pairs means none get missed.
Wrong order, wrong answer
Divide and multiply are equal partners, and so are add and subtract. The wrong-order answers are printed among the options because the exam knows exactly which mistake you will make.
If you are given a fact, use it: multiplication
The paper often hands you a multiplication you did not ask for. Spotting that the next question is the same sum ten times smaller is worth more than being quick at long multiplication.
The discount is not the answer
Twenty per cent off ten pounds fifty is two pounds ten — and that is not what the question asked. Build every percentage from ten per cent, then read the last line again.
Straight through zero: negative numbers
Counting through zero rather than stopping at it, and remembering that minus six is colder than minus two. The number line does the work if you draw it.
Part to part, or part to whole? ratio and proportion
A ratio compares part to part. A proportion compares part to the whole. Getting that one distinction right decides how a child does on this entire topic.