Mixed Review: Laws of Integers for Grade 6

Mixed review of the laws of integers means revising all three laws together, commutative, associative, and distributive, and learning to name the right law before solving each sum. If your child can name the law first, the sum itself rarely causes trouble.

I have taught Grade 6 math for over thirty years, and I run mixed review exactly as I do below: quick revision of each law, one spotting trick, then mixed practice with the traps called out. A free worksheet waits at the end for practice.

What Should You Revise First?

Revise the three laws in this order: commutative first, associative second, and distributive last. Commutative covers order, associative covers grouping, and distributive covers multiplication spreading over addition. This order moves from the simplest idea to the hardest, so each law builds on the last.

Start with commutative, because it is the easiest to see. The sum (-2 + 5) equals (5 + -2), and both give 3. Only the order changed, nothing else. A child who sees that once rarely forgets it.

Next comes associative, which moves brackets instead of order. The sum (-3 + 4) + 5 equals -3 + (4 + 5), and both give 6. Then finish with distributive, the law that removes brackets: 3 x (5 + 2) equals 3 x 5 + 3 x 2, and both give 21.

This is the same idea Common Core standard 6.EE.A.3 builds at this level: applying the properties of operations to make equivalent expressions. Three laws, one revision order, and the hardest law lands last, when your child is already warm.

How Do You Spot Which Law Fits?

Spot the law by asking what changed between the two sides of the sum. If only the order changed, it is commutative; if only the brackets moved, it is associative; if brackets vanished and multiplication spread, it is distributive. One question, asked every time, names the law.

I teach this as a one-question test, and I make my class ask it out loud. Look at the two sides. Did the numbers swap places? That is commutative. Did the brackets shift while the numbers stayed in place? That is associative. Did an outside number multiply every number inside the brackets? That is distributive.

Try it on (7 + -3) + 3 = 7 + (-3 + 3). The numbers stayed in order, but the brackets moved. That is associative, and the fast path gives 7 + 0 = 7. One question, one answer, and the sum solves itself.

What Does Mixed Practice Look Like?

Mixed practice mixes all three laws in one set of questions, so your child must name the law before solving. That naming step is the real skill, because real tests never label the law for you. Ten mixed questions teach more than thirty questions on one law alone.

Single-law practice feels easy because the child already knows which law to use. Mixed practice removes that comfort, and that is why it works. Each question asks two things: which law is this, and what answer does it give?

For a full page of mixed questions, try my free Mixed Review Laws of Integers Worksheet for Grade 6. It mixes fill-ins, true-or-false checks, and short sums, so your child practises naming laws under test-like conditions.

Where Do Children Slip in Mixed Review?

Children slip most when they stretch a law to subtraction or division, where no law holds. They also slip when they drop a minus sign while regrouping, or spread multiplication over only the first number inside brackets. Check signs and brackets first, and most mixed-review marks stop leaking away.

The subtraction trap is the most common. A child who knows 5 + 2 = 2 + 5 will write 5 – 2 = 2 – 5 without thinking, and lose the mark. Test it with small numbers first: 5 – 2 gives 3, but 2 – 5 gives -3. Different answers, so no law covers subtraction.

The sign trap runs close behind. In (-6 + 4) + 6, a careless regroup turns (-6) into 6 mid-sum, and the answer flips. Carry the sign with the number, like luggage that never leaves its owner. And in distributive sums, the outside number must visit every number inside the brackets, not just the first one.

A 10-Minute Mixed Revision Plan

This plan is the one I give parents before a test, and it fits in ten minutes flat.

Minute 0 to 2: say each law in one sentence. Commutative is order, associative is grouping, distributive is spreading. If your child cannot say it, she does not own it yet.

Minute 3 to 6: work three sums, one per law, and name the law out loud before solving. Naming first is the whole trick of mixed review.

Minute 7 to 10: work two trap sums, one subtraction swap and one half-spread distributive sum, and explain why each fails. Traps learned at home never cost marks in a test.

End on a win. Let the last sum be an easy one your child solves fast, so revision ends with a smile instead of a sigh.

Try It Yourself: 3 Quick Questions

Cover the answers, let your child try, then check together.

1. Which law is shown by (4 x -3) = (-3 x 4)?
   Answer: commutative law of multiplication. Only the order changed.
2. Use the distributive law to solve 5 x (6 + -2).
   Answer: 5 x 6 + 5 x -2 = 30 + -10 = 20.
3. Group (8 + -5) + 5 two ways. What answer do both give, and which law is it?
   Answer: 8, associative law of addition. Grouping (-5 + 5) first gives 8 + 0 = 8.

Key Takeaways

• Revise in order: commutative, associative, then distributive.
• Spot the law by asking what changed: order, brackets, or spreading.
• Mixed practice works because tests never label the law for you.
• No law covers subtraction or division, so never stretch one there.
• Carry the minus sign with its number, and spread multiplication over every number inside.

If your child handled those three questions, she is ready for a full page of practice. Print the free Mixed Review Laws of Integers Worksheet for Grade 6 and sit with her for the first two questions only. You will be surprised how quickly she takes over.

For more topics at this level, browse our Grade 6 math worksheets page. Every sheet is free to print, and each one grows out of a lesson I have taught in a real classroom.