Logic Masters · Ages 11 to 12
Factorising Expressions Fill-in
Factorise algebraic expressions by taking out the highest common factor. A Grade 7–8 algebra worksheet 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 Factorising Expressions Fill-in
Factorising Expressions Fill-in helps Grade 7 and 8 learners reverse the process of expanding: taking an expression and writing it as a product of a common factor and a bracket. Each question presents an expression such as 6x + 9 and asks the student to factorise it fully, here as 3(2x + 3), by identifying the highest common factor of the terms and dividing it out. Factorising is one of the most important and most tested algebra skills of the lower secondary years, central to the UK Key Stage 3 curriculum and to the expressions strands of the US, Canadian and Australian curricula, and it is the gateway to simplifying expressions, solving equations and, later, factorising quadratics. The worksheet deliberately keeps the factor outside the bracket as the genuine highest common factor so the answer is always fully factorised, training students to spot the largest factor rather than just any factor. Because the numbers change each time, the worksheet is endlessly reusable, and the five levels increase the size of the coefficients. Each page prints cleanly on a standard A4 sheet, and every level downloads with its own answer key giving the fully factorised form for each question. There is no advertising and no sign-up.
Common questions
- What method is used?
- Taking out the highest common factor to factorise each expression fully.
- What grade is this for?
- Grade 7 to Grade 8 learners aged 11 to 13.
- Is an answer key included?
- Yes, every level gives the fully factorised form for each question.
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.