Free Grade 3 Working with Expanded Form Lessons
Free Grade 3 lessons for Working with Expanded Form: 12 real questions with a full answer key and worked solutions. An expression uses letters for numbers. Substitute a value to evaluate it, collect like terms to simplify it, and multiply every term in a bracket to expand it.
Free
Foundation
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with expanded form
Identify working with expanded form accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with expanded form
Explain working with expanded form accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with expanded form
Calculate working with expanded form accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with expanded form
Compare working with expanded form accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Working with Expanded Form works
An expression uses letters for numbers. Substitute a value to evaluate it, collect like terms to simplify it, and multiply every term in a bracket to expand it.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Find the value of 8x + 4 when x = 6.[1]
- 2.Find the value of 7x + 6 when x = 8.[1]
- 3.Find the value of 6x + 16 when x = 8.[1]
- 4.Find the value of 8x + 5 when x = 4.[1]
- 5.Simplify 4x + 6y + 9x − 9y.[2]
- 6.Simplify 5x + 6y + 6x − 4y.[2]
- 7.Simplify 4x + 4y + 7x − 4y.[2]
- 8.Simplify 7x + 8y + 6x − 6y.[2]
- 9.Expand 2(2x + 7).[3]
- 10.Expand 4(6x + 2).[3]
- 11.Expand 3(5x + 9).[3]
- 12.Expand 5(5x + 9).[3]
Show answers and working
1. 52
Replace x with 6: 8 × 6 + 4. 48 + 4 = 52.
2. 62
Replace x with 8: 7 × 8 + 6. 56 + 6 = 62.
3. 64
Replace x with 8: 6 × 8 + 16. 48 + 16 = 64.
4. 37
Replace x with 4: 8 × 4 + 5. 32 + 5 = 37.
5. 13x − 3y
Collect x terms: 4x + 9x = 13x. Collect y terms: 6y − 9y = -3y.
6. 11x + 2y
Collect x terms: 5x + 6x = 11x. Collect y terms: 6y − 4y = 2y.
7. 11x + 0y
Collect x terms: 4x + 7x = 11x. Collect y terms: 4y − 4y = 0y.
8. 13x + 2y
Collect x terms: 7x + 6x = 13x. Collect y terms: 8y − 6y = 2y.
9. 4x + 14
Multiply each term inside by 2. 2 × 2x = 4x, 2 × 7 = 14.
10. 24x + 8
Multiply each term inside by 4. 4 × 6x = 24x, 4 × 2 = 8.
11. 15x + 27
Multiply each term inside by 3. 3 × 5x = 15x, 3 × 9 = 27.
12. 25x + 45
Multiply each term inside by 5. 5 × 5x = 25x, 5 × 9 = 45.
Worked examples
Find the value of 3x + 13 when x = 7.
- Replace x with 7: 3 × 7 + 13.
- 21 + 13 = 34.
- Answer: 34
Simplify 8x + 9y + 2x − 2y.
- Collect x terms: 8x + 2x = 10x.
- Collect y terms: 9y − 2y = 7y.
- Answer: 10x + 7y
Expand 4(4x + 2).
- Multiply each term inside by 4.
- 4 × 4x = 16x, 4 × 2 = 8.
- Answer: 16x + 8
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Reads 3x as 3 + x, or as 3 with x stuck on.
Correction: 3x means 3 × x.
Only multiplies the first term when expanding.
Correction: Draw arrows from the outside to every inside term.
Teacher tips
- · Use algebra tiles to show collecting like terms.
Parent tips
- · Ask what 'number of pizzas × price' is for different orders.
Real-life applications
- · Formulas for cost: total = 5n + 2 for n items plus delivery.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Working with Expanded Form
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Working with Expanded Form lesson really free?
- Yes. Every lessons on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Introducing Expanded Form, The Number Line. Each one has its own free lesson, worksheet and quiz.
- How is the lesson sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Working with Expanded Form?
- Move on to Expanded Form in Context, Reading Whole Numbers, Place Value, Digits, which build directly on this idea.
Related resources
Stuck on Working with Expanded Form? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor