FreeMathWorksheet

Worksheet with Answers

TN-MATH-GR6-19552 · v1.4

Factorising

Grade 6 · Math · Algebra · AQA

Grade

Grade 6

Subject

Math

Topic

Algebra

Subtopic

Factorising

Curriculum

AQA

Difficulty

Core

Time

30 minutes

Total marks

Student name

Teacher name

Date

Learning objectives

Recognise factorising accurately in math contexts.
Explain the underlying rule of factorising in the student's own words.
Apply factorising to multi-step and unfamiliar problems.
Justify a chosen method and identify errors in another student's work.

Skills assessed

Fluency and recall
Method and setting out
Reasoning and justification
Problem solving in context
Self-assessment

Instructions

Write your name, your teacher's name and the date in the header.
Answer every question in the space provided. Continue on the back if needed.
Show all working — method marks are awarded even when the final answer is wrong.
Aim to finish in about 30 minutes.
Complete the reflection box at the end before you hand the sheet in.

Warm-up

Bloom: Remember · 4 marks

Answer quickly. These check you are ready for the topic.

1.Write down one fact you already know about factorising.
[1]
AnswerAccept any correct response that applies the factorising rule accurately.
2.State one fact you already know about factorising.
[1]
AnswerAccept any correct response that applies the factorising rule accurately.
3.Circle one fact you already know about factorising.
[1]
AnswerAccept any correct response that applies the factorising rule accurately.
4.State one fact you already know about factorising.
[1]
AnswerAccept any correct response that applies the factorising rule accurately.

Recall

Bloom: Remember · 4 marks

Complete from memory. No calculator, no notes.

1.List the key term used in factorising described here: item 1.
[1]
AnswerAccept any correct response that applies the factorising rule accurately.
2.List the key term used in factorising described here: item 2.
[1]
AnswerAccept any correct response that applies the factorising rule accurately.
3.Complete the key term used in factorising described here: item 3.
[1]
AnswerAccept any correct response that applies the factorising rule accurately.
4.Define the key term used in factorising described here: item 4.
[1]
AnswerAccept any correct response that applies the factorising rule accurately.

FreeMathWorksheet · Grade 6 Math

Factorising

Basic Practice

Bloom: Understand · 5 marks

Work through each item. Show the step you used.

1.Complete part 1 using the rule for factorising.
[1]
AnswerAccept any correct response that applies the factorising rule accurately.
2.Complete part 2 using the rule for factorising.
[1]
AnswerAccept any correct response that applies the factorising rule accurately.
3.Identify part 3 using the rule for factorising.
[1]
AnswerAccept any correct response that applies the factorising rule accurately.
4.Identify part 4 using the rule for factorising.
[1]
AnswerAccept any correct response that applies the factorising rule accurately.
5.Identify part 5 using the rule for factorising.
[1]
AnswerAccept any correct response that applies the factorising rule accurately.

Guided Practice

Bloom: Understand · 8 marks

The first step is given. Finish the reasoning.

1.Complete the method for part 1. Step 1 has been started for you.
[2]
AnswerAccept any correct response that applies the factorising rule accurately.
2.Continue the working for part 2. Step 1 has been started for you.
[2]
AnswerAccept any correct response that applies the factorising rule accurately.
3.Complete the method for part 3. Step 1 has been started for you.
[2]
AnswerAccept any correct response that applies the factorising rule accurately.
4.Continue the working for part 4. Step 1 has been started for you.
[2]
AnswerAccept any correct response that applies the factorising rule accurately.

FreeMathWorksheet · Grade 6 Math

Factorising

Independent Practice

Bloom: Apply · 10 marks

No scaffolding. Set out your full method.

1.Work out fully part 1 on factorising without help.
[2]
AnswerAccept any correct response that applies the factorising rule accurately.
2.Work out fully part 2 on factorising without help.
[2]
AnswerAccept any correct response that applies the factorising rule accurately.
3.Solve part 3 on factorising without help.
[2]
AnswerAccept any correct response that applies the factorising rule accurately.
4.Determine part 4 on factorising without help.
[2]
AnswerAccept any correct response that applies the factorising rule accurately.
5.Solve part 5 on factorising without help.
[2]
AnswerAccept any correct response that applies the factorising rule accurately.

Challenge Questions

Bloom: Analyse · 9 marks

Harder items. Attempt every one, even partially.

1.Find and justify the statement in part 1 about factorising.
[3]
AnswerAccept any correct response that applies the factorising rule accurately.
2.Show that the statement in part 2 about factorising.
[3]
AnswerAccept any correct response that applies the factorising rule accurately.
3.Deduce the statement in part 3 about factorising.
[3]
AnswerAccept any correct response that applies the factorising rule accurately.

FreeMathWorksheet · Grade 6 Math

Factorising

Real-life Application

Bloom: Apply · 6 marks

Use the skill in context. State units in your answer.

1.Use the information to decide a real math situation that depends on factorising.
[3]
AnswerAccept any correct response that applies the factorising rule accurately.
2.Use the information to decide a real math situation that depends on factorising.
[3]
AnswerAccept any correct response that applies the factorising rule accurately.

Critical Thinking

Bloom: Evaluate · 8 marks

Explain your reasoning in full sentences.

1.Compare and justify a student's method for factorising is or is not efficient.
[4]
AnswerAccept any correct response that applies the factorising rule accurately.
2.Evaluate whether a student's method for factorising is or is not efficient.
[4]
AnswerAccept any correct response that applies the factorising rule accurately.

Reflection

Bloom: Create · 0 marks

Not marked. Answer honestly — this guides your next worksheet.

1.Describe how confident you feel with factorising and what you will practise next.
[—]
AnswerStudent response — not marked.
2.Record how confident you feel with factorising and what you will practise next.
[—]
AnswerStudent response — not marked.

FreeMathWorksheet

Answer key · Factorising

Warm-up

1.Accept any correct response that applies the factorising rule accurately.[1]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the factorising rule accurately.[1]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
3.Accept any correct response that applies the factorising rule accurately.[1]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
4.Accept any correct response that applies the factorising rule accurately.[1]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Recall

1.Accept any correct response that applies the factorising rule accurately.[1]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the factorising rule accurately.[1]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
3.Accept any correct response that applies the factorising rule accurately.[1]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
4.Accept any correct response that applies the factorising rule accurately.[1]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Basic Practice

1.Accept any correct response that applies the factorising rule accurately.[1]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the factorising rule accurately.[1]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
3.Accept any correct response that applies the factorising rule accurately.[1]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
4.Accept any correct response that applies the factorising rule accurately.[1]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
5.Accept any correct response that applies the factorising rule accurately.[1]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Guided Practice

1.Accept any correct response that applies the factorising rule accurately.[2]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the factorising rule accurately.[2]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
3.Accept any correct response that applies the factorising rule accurately.[2]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
4.Accept any correct response that applies the factorising rule accurately.[2]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Independent Practice

1.Accept any correct response that applies the factorising rule accurately.[2]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the factorising rule accurately.[2]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
3.Accept any correct response that applies the factorising rule accurately.[2]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
4.Accept any correct response that applies the factorising rule accurately.[2]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
5.Accept any correct response that applies the factorising rule accurately.[2]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Challenge Questions

1.Accept any correct response that applies the factorising rule accurately.[3]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the factorising rule accurately.[3]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
3.Accept any correct response that applies the factorising rule accurately.[3]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Real-life Application

1.Accept any correct response that applies the factorising rule accurately.[3]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the factorising rule accurately.[3]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Critical Thinking

1.Accept any correct response that applies the factorising rule accurately.[4]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the factorising rule accurately.[4]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Reflection

1.Student response — not marked.[0]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Student response — not marked.[0]
1. Recall the definition that underpins factorising.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

FreeMathWorksheet

Teacher pack · Factorising

Marking scheme

Band	Marks	Descriptor
Mastered	46–54	Applies factorising fluently, including in unfamiliar contexts, with clear justification.
Secure	35–45	Reliable in routine questions; reasoning is mostly complete.
Developing	22–34	Secure in scaffolded items, inconsistent once support is removed.
Emerging	0–21	Needs re-teaching of the core rule before progressing.

Teacher notes

Set the warm-up as a five-minute starter; it diagnoses readiness for factorising before you teach.
Guided practice is the pivot point — circulate here rather than during independent practice.
Mark the reasoning questions with the marking scheme bands, not raw totals, so progress is comparable across variants.
Students who band Emerging should repeat the Easy variant of this same subtopic before moving on within Algebra.

Common student mistakes

Confusing factorising with a neighbouring idea in algebra.

Teaching tips

Model one worked example of factorising under a visualiser before handing the sheet out.
Ask students to predict which question they will find hardest, then check the prediction afterwards.
Pair Developing students with Secure students for the guided practice block only.
Use the answer key as a self-marking station rather than collecting the sheets in.

Extension activities

Challenge worksheet on factorising with justification-only questions.
Design your own factorising question and write the mark scheme for it.
Link factorising to the next subtopic in Algebra and explain the connection.
Ten-minute timed practice to convert accuracy into fluency.