You will learn
- Generate a pattern from a rule.
- Compare two patterns.
- Find relationships between corresponding terms.
- Extend patterns.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- A pattern follows a rule.
- Each number is a term.
- Compare terms in the same position.
- Use the rule to extend the pattern.
Words to know
Numbers following a rule.
How terms change.
One number in a pattern.
Terms in the same position.
1. Discover: two savings plans
Ada saves 3 each week. Bayo saves 6 each week. Compare their savings after 1, 2, 3, 4 weeks.
2. Understand: patterns
- Ada: 3, 6, 9, 12. Rule: add 3 starting from 0.
- Bayo: 6, 12, 18, 24. Rule: add 6 starting from 0.
- Each Bayo term is twice the matching Ada term.
- Start at 4, add 6: 4, 10, 16, 22.
Idea 1: Add rule
Start 5, add 4: 5, 9, 13, 17. Start 0, add 7: 0, 7, 14, 21.
Idea 2: Find the rule
2, 5, 8, 11 adds 3, so next is 14. 50, 45, 40, 35 subtracts 5.
Idea 3: Compare
A: 0, 2, 4, 6 and B: 0, 4, 8, 12. Each B term is 2 times the A term.
Why compare? It shows how rules are related.
3. Worked examples
Example 1 (I show you): Extend
Start 5, add 4
- Add 4 each time.
Answer: 5, 9, 13, 17
Example 2 (We do it together): Rule
50, 45, 40, 35
- Going down by 5.
Answer: subtract 5
Example 3 (You try): Compare
add 2 vs add 4
Show the steps and answer
- Corresponding terms.
Answer: 2 times
Did you know?
Patterns that add can be called arithmetic sequences.
Why this matters
Patterns help us predict and plan.
4. Explore: two patterns
You need paper.
- Write Ada’s pattern.
- Write Bayo’s pattern.
- Compare matching terms.
- State the relationship.
Think about it: what did you notice?
Bayo = 2 × Ada.
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 terms are ___ times as big.
- The ___th term is ___.
Guided practice
Question 1. Rule: start 4, add 6. Third term?
16.
Question 2. Ada 12, Bayo ?
24.
Question 3. Relationship?
Bayo is twice Ada.
Independent practice
Level 1: Start
- Start 5, add 4: first four terms
- Start 0, add 7: fourth term
- Pattern A: add 2; B: add 4 from 0; B is ___ times A
- Next: 2, 5, 8, 11
- Rule for 50, 45, 40, 35
Level 2: Grow
- Start 10, add 5: third term
- Next in 3, 6, 9, 12
- Rule for 1, 3, 5, 7
Level 3: Stretch
- Next in 100, 93, 86, 79
- Start 1, multiply by 3: fifth term
- Ben says start 4, add 6 has third term 14. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A plant grows 4 cm a week from 10 cm. Height after 3 weeks?
Show a sample answer
22 cm.
Another one. A plant is 10 cm tall and grows 4 cm a week. How tall after 3 weeks?
Show a sample answer
10 + 3 × 4 = 22 cm
7. Common mistakes
Fix: Match the same term numbers.
Fix: List each term.
Fix: Check if terms grow or shrink.
8. Lesson summary and revision card
- I can generate a pattern from a rule.
- I can compare two patterns.
- I can find relationships between corresponding terms.
- I can extend 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
- Rules make patterns.
- Match corresponding terms.
- State the relationship.
11. Next lesson
Next lesson: Rules and relationships. 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.
- Start at 5 and add 4. Write the first four terms. [2 marks]
- Start at 0 and add 7. Find the fourth term. [2 marks]
- A adds 2 from 0 and B adds 4 from 0. B is how many times A? [3 marks]
- Find the next term in 2, 5, 8, 11. [2 marks]
- Ali says the rule for 50, 45, 40, 35 is add 5. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 5 and 9 [1]; 13 and 17 [1]
- 0, 7, 14 [1]; 21 [1]
- A: 0, 2, 4, 6 and B: 0, 4, 8, 12 [1]; each B term is 2 × A [1]; 2 times [1]
- Add 3 [1]; 14 [1]
- No [1]. The terms go down [1]. The rule is subtract 5 [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- Start 5, add 4: terms
- Start 0, add 7: fourth term
- A add 2, B add 4 from 0: B is ___ times A
- Next: 2, 5, 8, 11
- Rule for 50, 45, 40, 35
- Start 4, add 6. The third term is…
- Add 3 vs add 6 from 0: the second is…
- Next in 2, 5, 8, 11:
- Rule for 50, 45, 40, 35:
- Start 5, add 4: second term is…
Homework
Make two patterns with a relationship and describe it.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Start 5, add 4: terms | 5, 9, 13, 17 | 2 |
| Start 0, add 7: fourth term | 21 | 2 |
| A add 2, B add 4 from 0: B is ___ times A | 2 | 2 |
| Next: 2, 5, 8, 11 | 14 | 2 |
| Rule for 50, 45, 40, 35 | subtract 5 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 5, 9, 13, 17; 2 21; 3 2; 4 14; 5 subtract 5.
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 16; 7 twice the first; 8 14; 9 subtract 5; 10 9.
Independent practice answers. Level 1: 1 5, 9, 13, 17; 2 21; 3 2 times; 4 14; 5 subtract 5. Level 2: 1 20; 2 15; 3 add 2. Level 3: 1 72; 2 81; 3 4, 10, 16. The third term is 16..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Generate 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 |
| O2 Compare two 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 |
| O3 Find relationships between corresponding terms | 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 Extend 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 |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Comparing wrong positions. Match the same term numbers.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Skip count by 2, 5, 10.
- 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 works with number patterns and rules. You do not need to be good at mathematics to help.
- Find patterns in house numbers or calendars.
- Ask: what is the rule?
- Make a pattern with beads.
- 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: generate a pattern from a rule; compare two patterns; find relationships between corresponding terms; extend patterns.
Prerequisite knowledge. Grade 4 patterns.
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 is the rule? What comes next?
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. Comparing wrong positions. Match the same term numbers.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-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. Skip count by 2, 5, 10. 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
This lesson is based on the sources below, and no official 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. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 5 » Operations & Algebraic Thinking. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 5.OA.B.3; Cambridge Primary Mathematics Stage 5 (number patterns). These sources informed the lesson.