Logic Masters · Ages 11 to 12
Integer Multiplication Division Rules
Apply the sign rules for multiplying and dividing integers. Five levels with answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Integer Multiplication Division Rules
The sign rules for multiplication and division are short enough to memorise in a minute and are misapplied for years afterwards, usually because they were memorised rather than understood. This worksheet tests the rule directly. Every statement gives a complete calculation and asks only whether it is correct — and the false ones keep the magnitude exactly right and flip only the sign. That is the entire design: a pupil cannot get through by checking the digits, because the digits are always correct. The only way to answer is to apply the rule. All four multiplication cases appear, and division joins from the second level once multiplication signs are secure, with every division built from its quotient so the arithmetic is always exact. Numbers stay deliberately small, because the numbers are not the obstacle here and large ones would only disguise what is being tested. True and False are balanced by construction rather than left to chance — exactly half of each on every page, shuffled, with no run longer than three, so neither ticking a column nor spotting a pattern will carry anyone through. Eight statements per page with tick boxes. Each level prints cleanly and downloads with its own separate answer key.
Common questions
- Why do the false statements have the right digits?
- Because only the sign is flipped. A pupil cannot get through by checking the arithmetic — the rule has to be applied.
- Are the numbers large?
- No, deliberately. The numbers are not the obstacle here and large ones would only disguise what is being tested.
- Is the True/False split balanced?
- Yes, by construction — exactly half of each, shuffled, with no run longer than three.
- When does division appear?
- From the second level, once the multiplication sign cases are secure.
A hand for grown-ups
- Before you start
- Find a calm few minutes with no rush. Let your child know it is fine to find some of it tricky — that is what practice is for.
- While they work
- Sit nearby but let them lead. If they get stuck, ask "what could you try?" rather than giving the answer — the thinking is the point.
- Afterwards
- Ask them to show you one they found easy and one they found hard. Praise the effort on the hard one, not just the right answers.
- Watch out for
- Rushing. If answers come too fast and wrong, slow the pace down together rather than pushing for more.
- Away from the screen
- Look for the same maths in everyday life — counting stairs, sharing snacks, spotting shapes on a walk.
Where to go next
Chosen by the skills this activity practises.