Buckinghamshire 11+ Maths
The maths in the 11+ is curriculum maths wearing unfamiliar clothes. Most marks are lost between the steps of a question a child can already do.
Maths
36 posts on this. Written by Mat and Alicia, who prepare pupils for the Buckinghamshire Transfer Test every week in Winslow.
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.
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.
Round once, from the right column: rounding in the 11+
449 does not round to 500. The four-step routine we teach in Winslow, the five traps the examiner sets, and five questions to try with full workings.
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.
From the sale price back to the original: money
Same unit first, then label every amount. Why working backwards from a sale price is where almost everybody trips, and how to compare two packs honestly.
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.
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.
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.
The first calculation is not the answer: word problems
The number you can work out first is almost never the one being asked for. Count the steps before calculating any of them, and check you answered the actual question.
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.
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.
Split it into rectangles: area
Area is length times width, which your child already knows. The 11+ asks about shapes that are not rectangles — so cut them into ones that are.
Label the sides the diagram left blank: perimeter
You already know perimeter is the distance round the edge. On a real paper the question is working out the sides nobody labelled — and there is a rule for that.
Hop to the hour: time and timetables
Time is the one measure that does not run in tens. Working out a duration by hopping to the next hour, the 24-hour clock, and journeys that cross midnight.
Make the move yourself first: transformations
Two moves at a time, diagonal mirror lines, and one option in every row designed to look right. Do the move before you look at the answers.
Packing is not dividing: volume
Volume is length times width times height. But how many boxes fit inside another box is a different question, and dividing the volumes gets it badly wrong.
Name it, then write the total down: angles
Almost every missing-angle question is one of four totals with something taken away from it. Name the angle first, and check your answer against the picture.
Corridor then stairs: coordinates
Along first, then up. The grid does not stop at zero any more, and negatives, reflections and midpoints that land on halves are what Year 5 has to handle.
Bigger to smaller, multiply: measures and units
The facts are not the hard part any more. Conversions with a decimal point in them, and making everything the same unit before you compare anything.
Find the clue that rules out: properties of shape
Knowing what a rhombus is stopped being the hard part. Three clues at once, sorting tables and Venn diagrams are what the test does with them now.
Work out the scale first: charts and graphs
Reading a bar chart is not the difficulty. Scales that go up in twenties, pie charts given one slice, and graphs that have to be read backwards are.
Count the structure, not the things: combinations and logic
In Year 4 you could write the whole list out. A question about forty-two fixtures will not let you. Write enough of the list to see how it is built, then count that.
True, and still misleading: reading a graph critically
A misleading graph almost never has wrong numbers on it. Every value is correct and the impression is false — and spotting how is a skill worth more than the mark.
Write the chain in the margin: multi-step reasoning
The last section of the paper crosses two or three topics at once, in about fifty seconds, with one number in the question you are not supposed to use.
Wanted on top, altogether underneath: probability
Writing a chance as a fraction is the easy part. The paper stops drawing you the bag, wants the fraction cancelled, and takes a counter out halfway through.
Getting the numbers out is half the question: averages
Mean, median, mode and range are four short jobs your child already knows. The 11+ stops handing over the numbers in a neat row, and that is where the marks go.
The blanks are the question: data tables
Finding a box in a table takes seconds. Working out the boxes the table has left empty, using the totals, is what the question is actually asking.
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.
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.
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.
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.
Undo it backwards: letters in maths
Swap in, order up, work down — and when the letter is what you are hunting for, take the equation apart in the reverse order it was built. Plus the index that only touches what it touches.
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.