Algebra
Algebra is brand new in Year 6, and it is the first time children use letters to stand for numbers. They learn to use a simple formula by putting values in for the letter, to spot the rule that links one number to another, and to carry on a sequence that grows by the same step each time. None of it is as daunting as it sounds: a letter is really just a number we have not been told yet.
Practise Algebra
Have a guess, even if you're not sure. Get one wrong and we'll show you why, so every miss is a chance to learn.
Timed practice
The same practice, just with a gentle clock. Pick a length and see how many you can answer.
Good to know
A rule shown as a table
A formula links each position to its value. Here the rule is cost = 3n + 2, so you times the position by 3 and add 2.
For grown-ups
Year 6 algebra also asks children to work backwards from the answer. They solve missing-number problems written with a letter, find the pairs of values that make a two-unknown equation true, and list all the possibilities that fit a description, learning that a problem like this can have more than one right answer. This is the reasoning that sits underneath secondary maths, so a calm, confident start in Year 6 makes the move to Year 7 far smoother.
What is in this topic
- Using a simple formula by substituting in values
- Choosing the rule that describes a relationship
- Generating and describing linear number sequences
- Solving missing-number problems written with a letter
- Finding pairs of values that fit a two-unknown equation
- Listing all the possibilities that fit a description
How to help at home
Algebra at this stage is not a new kind of maths, it is a new kind of shorthand: a letter simply stands in for a number we have not been told yet. Children cope far better when they read every letter out loud as "some number" rather than treating it as a mysterious symbol.
- When you meet a formula, say the rule in full words first, then swap the letter for its value. For cost = 3n + 2 with n = 4, read it as 'three lots of the number, add two', then work 3 x 4 + 2 = 14.
- Turn a sequence into a 'position' game. For the rule 'times the position by 3, then take away 1', ask what the 1st, 2nd and 3rd terms are: 2, 5, 8. Notice it goes up by 3 each time, which is the number the letter was multiplied by.
- For a missing-number puzzle like a + 7 = 12, cover the letter and ask 'what plus 7 makes 12?'. The answer 5 is a, and they can check by putting it back: 5 + 7 = 12.
- When an equation has two letters, like a + b = 10, hunt for ALL the pairs in order, starting from zero: 0 and 10, 1 and 9, 2 and 8, 3 and 7. Working up in steps from zero stops them missing any and shows there is more than one right answer.
Where children get stuck
The most common slip is reading 3n as 'three then n', so they write 34 instead of 3 x 4 when n is 4. The fix is to insist the letter always means 'multiply': have them rewrite 3n as 3 x n every single time before they put a number in, so 3n with n = 4 becomes 3 x 4 = 12, never 34.
The other frequent wobble is assuming a missing-number or two-unknown problem has just one answer. For a + b = 10 a child will often find 5 and 5 and stop. Ask 'is there another pair that works?' and list them together in order, beginning at zero (0 and 10, 1 and 9, 2 and 8, and so on); seeing several correct pairs side by side teaches them that a problem like this can have more than one answer.