You will learn
- Find a rule for a number pattern.
- Continue a pattern.
- Find a missing number.
- Make a pattern of your own.
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.
- Find the rule by comparing neighbours.
- Continue the pattern with the rule.
- Find a missing term.
Words to know
Numbers that follow a rule.
What changes each time.
One number in a pattern.
Not shown yet.
1. Discover: a growing savings jar
Ada saves 25 on week 1, 50 on week 2, 75 on week 3. How much will she have saved after week 6?
2. Understand: number patterns
A number pattern follows a rule. Find how much changes each time.
- 100, 125, 150, 175: add 25. Next is 200.
- 1,000, 950, 900: subtract 50. Next is 850.
- 2,500, 3,500, 4,500: add 1,000. Next is 5,500.
To find a missing term, use the rule: 10, 20, __, 40 is add 10, so the missing term is 30.
Idea 1: Find the rule
300, 350, 400: each term is +50. The next is 450.
Idea 2: Going down
2,000, 1,800, 1,600: each term is −200. The next is 1,400.
Idea 3: Missing term
10, 20, __, 40 follows +10, so the missing term is 30.
Why find the rule? The rule lets us carry on without guessing.
3. Worked examples
Example 1 (I show you): Next term
300, 350, 400, __
- Rule +50.
Answer: 450
Example 2 (We do it together): Decreasing
2,000, 1,800, 1,600, __
- Rule −200.
Answer: 1,400
Example 3 (You try): Missing
10, 20, __, 40
Show the steps and answer
- Rule +10.
Answer: 30
Did you know?
The numbers in a pattern are called terms.
Why this matters
Patterns help us predict and are the start of algebra.
4. Explore: find the rule
You need paper and a pencil.
- Write 100, 125, 150, 175 and find the rule.
- Continue three more terms.
- Write 1,000, 950, 900 and continue.
- Make your own pattern.
Think about it: what did you notice?
Add 25: 200, 225, 250.
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 missing term is ___.
- My pattern starts at ___ and adds ___.
Guided practice
Question 1. 100, 125, 150, 175, __
200.
Question 2. Rule for 1,000, 950, 900?
subtract 50.
Question 3. 2,500, 3,500, 4,500, __
5,500.
Independent practice
Level 1: Start
- Next: 300, 350, 400, __
- Next: 2,000, 1,800, 1,600, __
- Rule: 3, 6, 9, 12
- Missing: 10, 20, __, 40
- Make a pattern that adds 5.
Level 2: Grow
- 10, 20, 30, 40, __
- Rule for 100, 200, 300
- 5,000, 4,000, __, 2,000
Level 3: Stretch
- 7, 14, 21, 28, __
- 1,250, 1,500, 1,750, __
- Ben says 90, 80, 70 has rule add 10. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Ada saves 25, 50, 75 … How much in week 6?
Show a sample answer
150 (25 × 6).
Another one. Make a pattern that starts at 20 and adds 5. Write five terms.
Show a sample answer
20, 25, 30, 35, 40
7. Common mistakes
Fix: Check the change between every pair.
Fix: Check the rule on every pair.
Fix: Check whether the numbers rise or fall.
8. Lesson summary and revision card
- I can find the rule.
- I can continue a pattern.
- I can find a missing number.
- I can make my own pattern.
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
- A pattern has a rule.
- Check every jump.
- Use the rule to find missing terms.
11. Next lesson
Next lesson: Reviewing multidigit addition. 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.
- Next term: 300, 350, 400, __ [1 mark]
- Next term: 2,000, 1,800, 1,600, __ [1 mark]
- What is the rule for 3, 6, 9, 12? [1 mark]
- Find the missing term: 10, 20, __, 40. [1 mark]
- Ama says 5, 10, 20 has rule add 5. Is she right? Explain. [3 marks]
Total: 7 marks.
Marking guide and model answers
- 450 [1]
- 1,400 [1]
- Add 3 [1]
- 30 [1]
- No [1]. 5 + 5 = 10 but 10 + 5 is not 20 [1]. The rule must work for every pair [1].
Score guide: 6 to 7 = secure. 5 to 5 = nearly there, revise the parts you missed. Under 5 = work through the lesson again with a grown-up.
Printable worksheet
- Next: 300, 350, 400, __
- Next: 2,000, 1,800, 1,600, __
- Rule: 3, 6, 9, 12
- Missing: 10, 20, __, 40
- Next: 5, 10, 15, __
- 100, 125, 150, 175, __
- Rule for 1,000, 950, 900
- 2,500, 3,500, 4,500, __
- Missing: 10, 20, __, 40
- 2,000, 1,800, 1,600, __
Homework
Make two number patterns with different rules and ask a family member to find them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Next: 300, 350, 400, __ | 450 | 2 |
| Next: 2,000, 1,800, 1,600, __ | 1,400 | 2 |
| Rule: 3, 6, 9, 12 | add 3 | 2 |
| Missing: 10, 20, __, 40 | 30 | 2 |
| Next: 5, 10, 15, __ | 20 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 450; 2 1,400; 3 add 3; 4 30; 5 20.
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): 6 200; 7 subtract 50; 8 5,500; 9 30; 10 1,400.
Independent practice answers. Level 1: 1 450; 2 1,400; 3 add 3; 4 30; 5 for example 5, 10, 15, 20. Level 2: 1 50; 2 add 100; 3 3,000. Level 3: 1 35; 2 2,000; 3 The numbers go down, so the rule is subtract 10..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Find a rule for a number 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 Continue 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 Find a missing number | 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 Make a pattern of your own | 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: Checking only the first jump. Check the change between every pair.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use a number line to see the jumps.
- 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 and continues number patterns. You do not need to be good at mathematics to help.
- Make patterns with counters or coins.
- Ask: what is the rule?
- Skip count 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 a rule for a number pattern; continue a pattern; find a missing number; make a pattern of your own.
Prerequisite knowledge. Lessons 1 to 7.
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 and a pencil. 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. Do the numbers go up or down? By how much? Does the rule work every time?
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. Checking only the first jump. Check the change between every pair.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 7-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. Use a number line to see the jumps. 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 3 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 3.OA.D.9 (patterns); Cambridge Primary Mathematics Stage 3 (sequences). These sources informed the lesson.