Maths

Common mistakes in collecting like terms

3 mistakes learners make with collecting like terms, each one named and explained.

All common mistakes

Only terms built from exactly the same letters can be combined, because only those count the same thing.

Collecting a subtracted term as if it were added

What it looks like

5a + 3b - 2a + b is answered as 7a + 4b, with the 2a added rather than taken away.

Why it happens

The terms are collected by scanning for matching letters, and the sign in front of each one is a separate thing to remember.

A worked example

Question. 5a - 2a

A common answer. 7a

The answer. 3a

Why. The minus belongs to the 2a, so there are five a s and two are taken away.

Put the two side by side

5a - 2a = 3a.
5a + 2a = 7a.

Every term travels with the sign in front of it. Circle the signs before you collect.

Collecting terms that are not alike

What it looks like

3a + 2b is answered as 5ab.

Why it happens

The instruction says simplify, and one term looks a great deal tidier than two.

A worked example

Question. 3a + 2b, with a = 10 and b = 1

A common answer. 5ab, which works out as 50

The answer. 32

Why. 3 lots of 10 and 2 lots of 1 is 32, so 5ab cannot be the same expression.

Put the two side by side

3a + 2a = 5a, because both terms count the same thing.
3a + 2b will not go any further.

Only terms built from exactly the same letters combine. Sometimes the tidy answer is the one you started with.

Reading a lone letter as nothing

What it looks like

5a + 3b - 2a + b is answered as 3a + 2b, because the b on its own was not counted.

Why it happens

A term with no number in front looks like it has no number, rather than a hidden one.

A worked example

Question. 3b + b

A common answer. 3b, because the lone b adds nothing

The answer. 4b

Why. A letter on its own means one of them, so 3b and one more b is 4b.

Put the two side by side

b means 1b.
3b + 1b = 4b.

A letter standing alone always carries an invisible 1. Write it in until it is automatic.

WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.

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