Free Grade 3 Term-to-term Rules in Context Lesson Plans
Free Grade 3 lesson plans for Term-to-term Rules in Context: 12 real questions with a full answer key and worked solutions. An arithmetic sequence goes up or down by the same amount each time. The nth term is (difference)n plus an adjustment.
Free
Stretch
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain term-to-term rules in context
Explain term-to-term rules in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate term-to-term rules in context
Calculate term-to-term rules in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare term-to-term rules in context
Compare term-to-term rules in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify term-to-term rules in context
Justify term-to-term rules 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 Term-to-term Rules in Context works
An arithmetic sequence goes up or down by the same amount each time. The nth term is (difference)n plus an adjustment.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Find the next two terms: 7, 11, 15, 19, …[1]
- 2.Find the next two terms: 1, 7, 13, 19, …[1]
- 3.Find the next two terms: 10, 15, 20, 25, …[1]
- 4.Find the next two terms: 1, 10, 19, 28, …[1]
- 5.Find the nth term of 15, 9, 3, -3, …[2]
- 6.Find the nth term of 17, 18, 19, 20, …[2]
- 7.Find the nth term of 4, 8, 12, 16, …[2]
- 8.Find the nth term of 14, 19, 24, 29, …[2]
- 9.Find the nth term of 11, 17, 23, 29, … and the 50th term.[3]
- 10.Find the nth term of 1, 8, 15, 22, … and the 50th term.[3]
- 11.Find the nth term of 13, 22, 31, 40, … and the 50th term.[3]
- 12.Find the nth term of 12, 16, 20, 24, … and the 50th term.[3]
Show answers and working
1. 23, 27
The difference is 4. 19 + 4 = 23, then 27.
2. 25, 31
The difference is 6. 19 + 6 = 25, then 31.
3. 30, 35
The difference is 5. 25 + 5 = 30, then 35.
4. 37, 46
The difference is 9. 28 + 9 = 37, then 46.
5. -6n + 21
Common difference -6, so start with -6n. -6 × 1 = -6; the first term is 15, so adjust by 21. nth term = -6n + 21
6. 1n + 16
Common difference 1, so start with 1n. 1 × 1 = 1; the first term is 17, so adjust by 16. nth term = 1n + 16
7. 4n + 0
Common difference 4, so start with 4n. 4 × 1 = 4; the first term is 4, so adjust by 0. nth term = 4n + 0
8. 5n + 9
Common difference 5, so start with 5n. 5 × 1 = 5; the first term is 14, so adjust by 9. nth term = 5n + 9
9. 6n + 5; 50th term = 305
Common difference 6, so start with 6n. 6 × 1 = 6; the first term is 11, so adjust by 5. nth term = 6n + 5
10. 7n − 6; 50th term = 344
Common difference 7, so start with 7n. 7 × 1 = 7; the first term is 1, so adjust by -6. nth term = 7n − 6
11. 9n + 4; 50th term = 454
Common difference 9, so start with 9n. 9 × 1 = 9; the first term is 13, so adjust by 4. nth term = 9n + 4
12. 4n + 8; 50th term = 208
Common difference 4, so start with 4n. 4 × 1 = 4; the first term is 12, so adjust by 8. nth term = 4n + 8
Worked examples
Find the next two terms: 2, 8, 14, 20, …
- The difference is 6.
- 20 + 6 = 26, then 32.
- Answer: 26, 32
Find the nth term of 19, 15, 11, 7, …
- Common difference -4, so start with -4n.
- -4 × 1 = -4; the first term is 19, so adjust by 23.
- nth term = -4n + 23
- Answer: -4n + 23
Find the nth term of 9, 11, 13, 15, … and the 50th term.
- Common difference 2, so start with 2n.
- 2 × 1 = 2; the first term is 9, so adjust by 7.
- nth term = 2n + 7
- Answer: 2n + 7; 50th term = 107
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Writes n + 3 for a sequence going up in 3s.
Correction: Going up in 3s means 3n.
Forgets to adjust for the first term.
Correction: Compare 3n with the actual sequence.
Teacher tips
- · Line the sequence up under the times table to find the adjustment.
Parent tips
- · Track weekly savings and predict week 10.
Real-life applications
- · Taxi fares, saving the same amount each week.
Assessment objectives
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Frequently asked
- Is this Grade 3 Term-to-term Rules 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 Term-to-term Rules, Introducing Term-to-term Rules, Inequalities. 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 Term-to-term Rules in Context?
- Move on to nth Term of a Linear Sequence, Quadratic Sequences, Geometric Sequences, which build directly on this idea.
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