You will learn
- Complete an input-output table.
- Find the rule.
- Write the rule in words.
- Use the rule to predict.
Version 0.1 · published for early use · expert review pending Standards alignment: pending verification. Not yet reviewed against the Courseversity scorecard.
Student lesson
Words to know
What goes in.
What comes out.
Operation(s) linking them.
Rows of input and output.
1. Discover: a function machine
A machine takes 1 and gives 6, takes 2 and gives 10, takes 3 and gives 14. What does it do?
2. Understand: rules and tables
Rule: “multiply by 4, then add 2”.
| Input | Output |
|---|---|
| 1 | 6 |
| 2 | 10 |
| 3 | 14 |
| 5 | 22 |
- 3 → 3 × 4 + 2 = 14.
- Input 10 gives 10 × 4 + 2 = 42.
3. Explore: find the rule
You need paper.
- Look at the inputs and outputs.
- Guess a rule.
- Test on every row.
- Predict input 10.
Think about it: what did you notice?
42.
4. Practise
Guided practice
Question 1. Rule: ×4 then +2. Input 5?
22.
Question 2. Input 10?
42.
Question 3. Output 14 comes from?
3.
Independent practice
- Rule: ×3. Input 7
- Rule: +8. Input 15
- Rule: ×2 then +1. Input 6
- Table 1→2, 2→4, 3→6: rule
- Rule ×5: output 40 from input?
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
A taxi charges 4 per km plus 2. Cost for 5 km?
Show a sample answer
22.
6. Common mistake
Fix: Test every row.
7. Check and master
Answer all questions. You will see feedback after each one.
Your result appears here after you answer every question.
8. Key takeaways
- Input, rule, output.
- Test every row.
- Predict with the rule.
9. Next lesson
Next lesson: Numerical expressions. Keep going with the next idea in this course.
Printable worksheet
- Rule ×3, input 7
- Rule +8, input 15
- Rule ×2 then +1, input 6
- Rule for 1→2, 2→4, 3→6
- ×5 gives 40 from input
Homework
Make an input-output table with your own rule.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Rule ×3, input 7 | 21 | 2 |
| Rule +8, input 15 | 23 | 2 |
| Rule ×2 then +1, input 6 | 13 | 2 |
| Rule for 1→2, 2→4, 3→6 | ×2 | 2 |
| ×5 gives 40 from input | 8 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 21; 2 23; 3 13; 4 ×2; 5 8.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, challenge C.
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Complete an input-output table | 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 Find the 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 |
| O3 Write the rule in words | 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 Use the rule to predict | 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 3 of 5 core questions correct; Silver = all 5; Gold = all 5 plus the challenge. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Testing only the first row. Test every row.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise one-step rules.
- 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.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: complete an input-output table; find the rule; write the rule in words; use the rule to predict.
Prerequisite knowledge. Lesson 1.
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. 35–45 minutes.
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.
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. Testing only the first row. Test every row.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-mark scheme and all answers are in the answer key above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Practise one-step rules. 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.