You will learn
- Find the rule of a pattern.
- Extend a pattern.
- Make a pattern from a rule.
- Describe growing and shrinking patterns.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Find what changes each time.
- The rule may add, subtract or multiply.
- Extend the pattern with the rule.
- Describe it as growing or shrinking.
Words to know
A set of numbers following a rule.
How each term changes.
One number in a pattern.
An ordered list of terms.
1. Discover: saving money
Ada saves 3, then 7, then 11, then 15 thousand naira. What is the next amount?
2. Understand: number patterns
To find a rule, look at the difference between neighbouring terms.
- 3, 7, 11, 15: add 4 each time. Next: 19.
- 100, 90, 80, 70: subtract 10. Next: 60.
- 2, 4, 8, 16: multiply by 2. Next: 32.
Start with 5 and a rule “add 3”: 5, 8, 11, 14, 17.
Idea 1: Add
5, 10, 15, 20: the rule is add 5. The next term is 25.
Idea 2: Subtract
50, 45, 40: the rule is subtract 5. The next term is 35.
Idea 3: Multiply
2, 6, 18, 54: each term is multiplied by 3. 1, 2, 4, 8: next is 16.
Why a rule? A rule lets us find any term, not just the next.
3. Worked examples
Example 1 (I show you): Add
5, 10, 15, 20, __
- Add 5.
Answer: 25
Example 2 (We do it together): Multiply
2, 6, 18, 54
- 6 ÷ 2 = 3.
Answer: multiply by 3
Example 3 (You try): Start 5, add 3
First five terms
Show the steps and answer
- 5, 8, 11, …
Answer: 5, 8, 11, 14, 17
Did you know?
Patterns that multiply grow much faster than patterns that add.
Why this matters
Patterns help us predict savings, growth and speed.
4. Explore: pattern detective
You need paper.
- Write 3, 7, 11, 15.
- Find the difference.
- Write the next three terms.
- Make your own pattern.
Think about it: what did you notice?
19, 23, 27.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The rule is ___.
- The next term is ___.
- The pattern is growing / shrinking.
- The ___th term is ___.
Guided practice
Question 1. Rule for 3, 7, 11, 15?
Add 4.
Question 2. Next after 70 in 100, 90, 80, 70?
60.
Question 3. Next after 16 in 2, 4, 8, 16?
32.
Independent practice
Level 1: Start
- Next: 5, 10, 15, 20, __
- Next: 50, 45, 40, __
- Rule: 2, 6, 18, 54
- Start 5, add 3: first five terms
- Next: 1, 2, 4, 8, __
Level 2: Grow
- Next: 6, 12, 18, 24, __
- Rule: 100, 93, 86, 79
- Start 4, add 6: first five terms
Level 3: Stretch
- Next: 2, 6, 18, 54, __
- A plant is 8 cm and grows 2 cm each week. How tall after 6 weeks?
- Ben says the rule of 2, 4, 8, 16 is add 2. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A plant is 5 cm tall and grows 3 cm each week. How tall after 4 weeks?
Show a sample answer
17 cm.
Another one. A saver puts 500 in a box and adds 250 each week. How much is in the box after 4 weeks?
Show a sample answer
500 + 4 × 250 = 1,500
7. Common mistakes
Fix: Check the rule on every pair.
Fix: Check the rule on every pair of terms.
Fix: Read whether the start is week 0 or week 1.
8. Lesson summary and revision card
- I can find the rule of a pattern.
- I can extend a pattern.
- I can make a pattern from a rule.
- I can describe growing and shrinking patterns.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Find the rule.
- Test it on every pair.
- Use it to continue.
11. Next lesson
Next lesson: Reviewing fractions. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Find the rule and the next term: 5, 10, 15, 20. [2 marks]
- Find the rule and the next term: 50, 45, 40. [2 marks]
- Find the rule of 2, 6, 18, 54. [2 marks]
- Start at 5 and add 3. Write the first five terms. [2 marks]
- Ana says the next term in 1, 2, 4, 8 is 10. Is she right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- Add 5 [1]; 25 [1]
- Subtract 5 [1]; 35 [1]
- Each term × 3 [1]; multiply by 3 [1]
- 5, 8, 11 [1]; 14, 17 [1]
- No [1]. Each term doubles [1]. The next is 16 [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- Next: 5, 10, 15, 20
- Next: 50, 45, 40
- Rule of 2, 6, 18, 54
- Fifth term from 5 adding 3
- Next: 1, 2, 4, 8
- Rule of 3, 7, 11, 15:
- Next: 100, 90, 80, 70:
- Next: 2, 4, 8, 16:
- Next: 5, 10, 15, 20:
- Start 5, add 3: fifth term is
Homework
Make two patterns with different rules and ask a friend to continue them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Next: 5, 10, 15, 20 | 25 | 2 |
| Next: 50, 45, 40 | 35 | 2 |
| Rule of 2, 6, 18, 54 | multiply by 3 | 2 |
| Fifth term from 5 adding 3 | 17 | 2 |
| Next: 1, 2, 4, 8 | 16 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 25; 2 35; 3 multiply by 3; 4 17; 5 16.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 add 4; 7 60; 8 32; 9 25; 10 17.
Independent practice answers. Level 1: 1 25; 2 35; 3 multiply by 3; 4 5, 8, 11, 14, 17; 5 16. Level 2: 1 30; 2 subtract 7; 3 4, 10, 16, 22, 28. Level 3: 1 162; 2 20 cm; 3 4 + 2 = 6, not 8. Each term is multiplied by 2..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Find the rule of a pattern | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Extend a pattern | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Make a pattern from a rule | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Describe growing and shrinking patterns | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Looking only at the first two terms. Check the rule on every pair.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise skip counting.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child finds rules in number patterns and extends them. You do not need to be good at mathematics to help.
- Spot patterns in house numbers.
- Ask: what is the rule?
- Make your own pattern together.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: find the rule of a pattern; extend a pattern; make a pattern from a rule; describe growing and shrinking patterns.
Prerequisite knowledge. Lessons 1 to 5.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need paper. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. What changes each time? Does the rule work for every term?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Looking only at the first two terms. Check the rule on every pair.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Practise skip counting. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
Alignment is pending verification and no external endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Specific standard codes will be added once checked against the official documents.
Research used to shape this lesson. Common Core 4.OA.C.5 (patterns); Cambridge Primary Mathematics Stage 4 (number sequences). These sources informed the lesson; no official alignment is claimed.