Free Grade 3 Expanded Form in Context Lesson Plans
Free Grade 3 lesson plans for Expanded Form in Context: 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
Stretch
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain expanded form in context
Explain expanded form in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate expanded form in context
Calculate expanded form in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare expanded form in context
Compare expanded form in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify expanded form in context
Justify expanded form in context 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 Expanded Form in Context 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 4x + 11 when x = 3.[1]
- 2.Find the value of 8x + 12 when x = 9.[1]
- 3.Find the value of 5x + 17 when x = 2.[1]
- 4.Find the value of 7x + 9 when x = 5.[1]
- 5.Simplify 7x + 2y + 5x − 1y.[2]
- 6.Simplify 8x + 6y + 4x − 4y.[2]
- 7.Simplify 8x + 2y + 9x − 8y.[2]
- 8.Simplify 2x + 8y + 6x − 5y.[2]
- 9.Expand 4(5x + 4).[3]
- 10.Expand 5(2x + 3).[3]
- 11.Expand 2(3x + 8).[3]
- 12.Expand 4(4x + 7).[3]
Show answers and working
1. 23
Replace x with 3: 4 × 3 + 11. 12 + 11 = 23.
2. 84
Replace x with 9: 8 × 9 + 12. 72 + 12 = 84.
3. 27
Replace x with 2: 5 × 2 + 17. 10 + 17 = 27.
4. 44
Replace x with 5: 7 × 5 + 9. 35 + 9 = 44.
5. 12x + 1y
Collect x terms: 7x + 5x = 12x. Collect y terms: 2y − 1y = 1y.
6. 12x + 2y
Collect x terms: 8x + 4x = 12x. Collect y terms: 6y − 4y = 2y.
7. 17x − 6y
Collect x terms: 8x + 9x = 17x. Collect y terms: 2y − 8y = -6y.
8. 8x + 3y
Collect x terms: 2x + 6x = 8x. Collect y terms: 8y − 5y = 3y.
9. 20x + 16
Multiply each term inside by 4. 4 × 5x = 20x, 4 × 4 = 16.
10. 10x + 15
Multiply each term inside by 5. 5 × 2x = 10x, 5 × 3 = 15.
11. 6x + 16
Multiply each term inside by 2. 2 × 3x = 6x, 2 × 8 = 16.
12. 16x + 28
Multiply each term inside by 4. 4 × 4x = 16x, 4 × 7 = 28.
Worked examples
Find the value of 3x + 18 when x = 4.
- Replace x with 4: 3 × 4 + 18.
- 12 + 18 = 30.
- Answer: 30
Simplify 7x + 6y + 2x − 1y.
- Collect x terms: 7x + 2x = 9x.
- Collect y terms: 6y − 1y = 5y.
- Answer: 9x + 5y
Expand 2(6x + 8).
- Multiply each term inside by 2.
- 2 × 6x = 12x, 2 × 8 = 16.
- Answer: 12x + 16
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.
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Frequently asked
- Is this Grade 3 Expanded Form in Context lesson plan really free?
- Yes. Every lesson plans 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 Working with Expanded Form, Introducing Expanded Form, The Number Line. Each one has its own free lesson, worksheet and quiz.
- How is the lesson plan 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 Expanded Form in Context?
- Move on to Reading Whole Numbers, Place Value, Digits, Comparing Numbers, which build directly on this idea.
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