Free Grade 3 Using Letters for Numbers Lessons
Free Grade 3 lessons for 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
Core
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain using letters for numbers
Explain using letters for numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate using letters for numbers
Calculate using letters for numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare using letters for numbers
Compare using letters for numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify using letters for numbers
Justify 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 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 4x + 5 when x = 4.[1]
- 2.Find the value of 6x + 7 when x = 5.[1]
- 3.Find the value of 3x + 16 when x = 4.[1]
- 4.Find the value of 6x + 5 when x = 6.[1]
- 5.Simplify 5x + 7y + 8x − 7y.[2]
- 6.Simplify 3x + 5y + 9x − 4y.[2]
- 7.Simplify 7x + 2y + 7x − 3y.[2]
- 8.Simplify 8x + 4y + 5x − 1y.[2]
- 9.Expand 3(2x + 8).[3]
- 10.Expand 2(3x + 2).[3]
- 11.Expand 5(4x + 4).[3]
- 12.Expand 3(5x + 6).[3]
Show answers and working
1. 21
Replace x with 4: 4 × 4 + 5. 16 + 5 = 21.
2. 37
Replace x with 5: 6 × 5 + 7. 30 + 7 = 37.
3. 28
Replace x with 4: 3 × 4 + 16. 12 + 16 = 28.
4. 41
Replace x with 6: 6 × 6 + 5. 36 + 5 = 41.
5. 13x + 0y
Collect x terms: 5x + 8x = 13x. Collect y terms: 7y − 7y = 0y.
6. 12x + 1y
Collect x terms: 3x + 9x = 12x. Collect y terms: 5y − 4y = 1y.
7. 14x − 1y
Collect x terms: 7x + 7x = 14x. Collect y terms: 2y − 3y = -1y.
8. 13x + 3y
Collect x terms: 8x + 5x = 13x. Collect y terms: 4y − 1y = 3y.
9. 6x + 24
Multiply each term inside by 3. 3 × 2x = 6x, 3 × 8 = 24.
10. 6x + 4
Multiply each term inside by 2. 2 × 3x = 6x, 2 × 2 = 4.
11. 20x + 20
Multiply each term inside by 5. 5 × 4x = 20x, 5 × 4 = 20.
12. 15x + 18
Multiply each term inside by 3. 3 × 5x = 15x, 3 × 6 = 18.
Worked examples
Find the value of 5x + 14 when x = 3.
- Replace x with 3: 5 × 3 + 14.
- 15 + 14 = 29.
- Answer: 29
Simplify 9x + 8y + 8x − 7y.
- Collect x terms: 9x + 8x = 17x.
- Collect y terms: 8y − 7y = 1y.
- Answer: 17x + 1y
Expand 3(6x + 4).
- Multiply each term inside by 3.
- 3 × 6x = 18x, 3 × 4 = 12.
- Answer: 18x + 12
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 Using Letters for Numbers
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Frequently asked
- Is this Grade 3 Using Letters for Numbers 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 Number Sense. 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 Using Letters for Numbers?
- Move on to Collecting Like Terms, Substitution, Expanding Brackets, Factorising, which build directly on this idea.
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