Grouping like terms means sorting an expression into matching piles, then adding or subtracting the numbers in front of each pile. Only terms with the same letters and the same powers can join. Once your child sees the piles, long expressions shrink fast.
I once watched a boy add 3x and 2y and write 5xy with total confidence. He had sorted nothing, so his answer mixed two kinds of things. I handed him two jars, one marked x and one marked y, and the piles did the teaching for me.
What Are Like Terms?
Like terms share the exact same letters raised to the same powers, so 3x and 7x are like terms, while x and x squared are not. Only the numbers in front may differ, and those numbers are the coefficients you add or subtract when you combine them.
Think of letters as labels on jars. The jar marked x holds only x items, and the jar marked y holds only y items. Powers matter too, because x squared is a different jar from x, even though both jars wear the letter x.
Order does not matter. The terms 2xy and 3yx are like terms, because both hold one x and one y. Children who check letters and powers first rarely group the wrong terms.
How Do You Group Like Terms?
Group like terms by sorting them first, then add or subtract the coefficients and keep the variable part unchanged. Circle each group in a different colour, move the terms together with their signs, and combine one group at a time until nothing can join.
I teach three steps, and I never skip the first one. Step one, underline each group in its own colour. Step two, rewrite the expression with each group together, and carry the sign with its term. Step three, add or subtract the coefficients.
Try it on 4a + 3b + 2a + 5b – 1. The a group gives 6a, the b group gives 8b, and the constant stays -1. The answer is 6a + 8b – 1, and nothing else can join.
A Worked Example With Two Variables
Take 5x + 2y – 3x + 4y + 6. First, sort the piles: x terms, y terms, and the constant. Then combine: 5x – 3x is 2x, 2y + 4y is 6y, and 6 stays put. The answer is 2x + 6y + 6.
I ask children to read the finished answer back as piles. If every pile holds one kind of thing, the grouping worked.
Why Can’t You Add Unlike Terms?
Unlike terms stay separate because they count different things, so 3a plus 2b cannot become 5ab. Adding them would mix two kinds of items into one false total, so keep both terms in the answer and only combine terms that match exactly.
You cannot add apples to chairs and call the answer fruit. Algebra works the same way. The term 3a counts a items, and 2b counts b items, so the honest answer keeps both counts side by side.
This rule also names expressions. After grouping, one term makes a monomial, two terms make a binomial, and three terms make a trinomial. Standard 6.EE.A.3 asks children to apply the properties of operations to generate equivalent expressions, and grouping is the first step toward that skill.
If your child still writes expressions from stories with shaky letters, go back to the real-life expressions worksheet first, then return here with fresh eyes.
Common Mistakes I See When Children Group Terms
The first mistake is dropping the sign when a term moves. A minus sign belongs to the term after it, so 5x – 3x keeps the minus with the 3x. I make children circle the sign with its term before they move anything.
The second mistake is mixing x with x squared. They share a letter, but their powers differ, so they are unlike terms. I ask one question every time: do the letters and the powers match exactly?
The third mistake is forgetting that a bare x means 1x. When children combine x + 4x, the answer is 5x, not 4x, because the first term quietly carries a coefficient of 1.
Practise With the Free Worksheet
The grouping like terms worksheet gives your child six pages of sorting, grouping and naming practice, with the same piles habit on every page. It moves from spotting like and unlike terms to grouping them and naming expressions by type, so the skill builds one step at a time.
Try These Three Yourself
- Simplify 4a + 3b + 2a + 5b. (Answer: 6a + 8b, because 4a + 2a is 6a and 3b + 5b is 8b.)
- Simplify 7x – 2 + 3x + 9. (Answer: 10x + 7, because 7x + 3x is 10x and -2 + 9 is 7.)
- True or false: 3x + 2y = 5xy? (Answer: False. The terms are unlike, so they stay separate.)
FAQ
Can 3x and 3y be combined?
No. They hold different letters, so they are unlike terms. The answer stays 3x + 3y.
Are 2xy and 3yx like terms?
Yes. Both terms hold one x and one y, so the order of the letters does not matter. They combine to 5xy.
What does the sign belong to?
The sign belongs to the term that follows it. In 5x – 3x, the minus belongs to the 3x, and it travels with that term.
Is x the same as 1x?
Yes. A bare letter quietly carries a coefficient of 1, so x + 4x equals 5x, not 4x.
When should children learn grouping like terms?
In Grade 6, after they can write simple expressions from words. Grouping turns those first expressions into tidy, shorter forms.
Sort one expression into piles tonight. Name each pile, combine the numbers in front, and let grouping turn long expressions into short ones. Find more Grade 6 guides on the Grade 6 hub.