Free Grade 3 Working with Using Letters for Numbers Lesson Plans
Free Grade 3 lesson plans for Working with Using Letters for Numbers: 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
Higher
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with using letters for numbers
Identify working with using letters for numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with using letters for numbers
Explain working with using letters for numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with using letters for numbers
Calculate working with using letters for numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with using letters for numbers
Compare working with using letters for numbers 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 Using Letters for Numbers 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 + 10 when x = 6.[1]
- 2.Find the value of 8x + 14 when x = 4.[1]
- 3.Find the value of 7x + 20 when x = 3.[1]
- 4.Find the value of 2x + 16 when x = 9.[1]
- 5.Simplify 8x + 9y + 3x − 1y.[2]
- 6.Simplify 9x + 9y + 5x − 1y.[2]
- 7.Simplify 3x + 1y + 2x − 3y.[2]
- 8.Simplify 2x + 7y + 3x − 2y.[2]
- 9.Expand 3(5x + 8).[3]
- 10.Expand 3(3x + 7).[3]
- 11.Expand 2(5x + 2).[3]
- 12.Expand 3(6x + 5).[3]
Show answers and working
1. 58
Replace x with 6: 8 × 6 + 10. 48 + 10 = 58.
2. 46
Replace x with 4: 8 × 4 + 14. 32 + 14 = 46.
3. 41
Replace x with 3: 7 × 3 + 20. 21 + 20 = 41.
4. 34
Replace x with 9: 2 × 9 + 16. 18 + 16 = 34.
5. 11x + 8y
Collect x terms: 8x + 3x = 11x. Collect y terms: 9y − 1y = 8y.
6. 14x + 8y
Collect x terms: 9x + 5x = 14x. Collect y terms: 9y − 1y = 8y.
7. 5x − 2y
Collect x terms: 3x + 2x = 5x. Collect y terms: 1y − 3y = -2y.
8. 5x + 5y
Collect x terms: 2x + 3x = 5x. Collect y terms: 7y − 2y = 5y.
9. 15x + 24
Multiply each term inside by 3. 3 × 5x = 15x, 3 × 8 = 24.
10. 9x + 21
Multiply each term inside by 3. 3 × 3x = 9x, 3 × 7 = 21.
11. 10x + 4
Multiply each term inside by 2. 2 × 5x = 10x, 2 × 2 = 4.
12. 18x + 15
Multiply each term inside by 3. 3 × 6x = 18x, 3 × 5 = 15.
Worked examples
Find the value of 3x + 8 when x = 9.
- Replace x with 9: 3 × 9 + 8.
- 27 + 8 = 35.
- Answer: 35
Simplify 5x + 9y + 7x − 9y.
- Collect x terms: 5x + 7x = 12x.
- Collect y terms: 9y − 9y = 0y.
- Answer: 12x + 0y
Expand 5(2x + 8).
- Multiply each term inside by 5.
- 5 × 2x = 10x, 5 × 8 = 40.
- Answer: 10x + 40
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 Working with Using Letters for Numbers 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 Introducing Using Letters for Numbers, Number Sense. 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 Working with Using Letters for Numbers?
- Move on to Using Letters for Numbers in Context, Collecting Like Terms, Substitution, Expanding Brackets, which build directly on this idea.
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