Less algebra appears than parents fear, and more than most schools cover by Year 5. Mostly it is arithmetic with a letter standing in for a gap.
Maths carries 25% of the marks. Almost all of it arrives as worded problems rather than bare calculations, so the reading is part of the maths.
How much algebra, really
Three things, in rising order of difficulty:
- Function machines. A number goes in, operations happen, a number comes out.
- Forming an expression from a worded description.
- Solving a simple equation for an unknown.
Nothing beyond that is likely, and a child who is secure in those three is well covered.
Function machines
These are the gentlest entry and they teach the key idea: to go backwards, undo in reverse order.
If a machine does "times 3, then add 4", and 7 goes in, then 7 times 3 is 21, plus 4 is 25.
Run it backwards from 25: subtract 4 to get 21, then divide by 3 to get 7. Note the operations reversed and the order reversed. That is the whole of equation solving, learned painlessly.
Turning words into expressions
This is where the marks actually are, because the questions are worded.
| Words | Expression |
|---|---|
| Three more than a number | n + 3 |
| Three times a number | 3n |
| A number doubled, then 5 added | 2n + 5 |
| 5 less than a number | n - 5 |
| A number shared between 4 | n divided by 4 |
Watch the fourth row. "5 less than a number" is n minus 5, not 5 minus n. Children reverse it constantly because of the order the words appear in.
Solving by undoing
Solve 3n + 4 = 19.
- Undo the add 4: 19 minus 4 is 15
- Undo the times 3: 15 divided by 3 is 5
- So n is 5
Check by substituting: 3 times 5 is 15, plus 4 is 19. Correct.
Always substitute your answer back. It takes five seconds, it catches nearly every error, and it converts a guess into a certainty.
One shortcut worth knowing: in a multiple choice test, you can work backwards from the options. Try each value of n until one fits. With five options that is often faster than solving, and it cannot go wrong.
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Substitute the answer back, every time
Algebra frightens parents more than it frightens children, because they remember it from secondary school. What appears here is much gentler: a letter standing in for a number you do not know yet, and undoing operations in reverse to find it.
Function machines are where I start, because they teach reversing without anybody having to call it algebra. Times three then add four going forwards; subtract four then divide by three coming back. Once that is natural, solving an equation is the same move.
And the habit I drill hardest here is substituting the answer back into the question. Five seconds, and it turns a maybe into a certainty. In a multiple choice paper a child can also just test the five options, which is slower in principle and often quicker in practice.
Mushtaque Ahmed, Founder of GrammarPath and Bright Mentors
Frequently asked questions
How much algebra is in the 11+?
Three things: function machines, forming an expression from a worded description, and solving a simple equation for an unknown. A child secure in those is well covered, and little beyond them is likely to appear.
How do you solve a simple equation for the 11+?
Undo the operations in reverse order. For 3n + 4 = 19, undo the add 4 to get 15, then undo the times 3 to get n equals 5. Always substitute the answer back to check: 3 times 5 plus 4 is 19.
What is a function machine?
A diagram where a number goes in, operations are applied in order, and a number comes out. They teach the central idea of algebra painlessly: to go backwards you undo the operations in reverse order.
How do you turn words into an expression?
Translate phrase by phrase: three more than a number is n plus 3, three times a number is 3n, a number doubled then 5 added is 2n plus 5. Watch out for 5 less than a number, which is n minus 5 and not 5 minus n.
Can my child work backwards from the answer options?
Yes, and in a multiple choice test it is often faster. Substitute each offered value into the equation until one fits. It cannot go wrong, which makes it a good fallback when a child is unsure of the method.