You will learn
- Say what a variable is.
- Write a rule with a variable.
- Substitute a number.
- Name constants and variables.
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
Letter for a number.
Fixed number.
Number not yet known.
Replace by a number.
1. Discover: the mystery number
A box has some mangoes and you add 5 more. How can we write the total without knowing how many were in the box?
2. Understand: variables
- Let n be the number of mangoes in the box. The total is n + 5.
- If n = 7, the total is 7 + 5 = 12.
- If n = 10, the total is 15.
- In n + 5, n is a variable and 5 is a constant.
3. Explore: write
You need paper.
- Choose a letter.
- Say what it means.
- Write the rule.
- Try numbers.
Think about it: what did you notice?
n + 5.
4. Practise
Guided practice
Question 1. Total if n = 7?
12.
Question 2. Total if n = 10?
15.
Question 3. Which is the constant in n + 5?
5.
Independent practice
- Write 3 more than n
- Total if n = 20
- Constant in n + 8
- Variable in n + 8
- Write the cost of n pens at 2 each
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
A box has n mangoes and 5 are added. How many now?
Show a sample answer
n + 5.
6. Common mistake
Fix: A variable can change.
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
- Letters stand for numbers.
- Variables can change.
- Constants are fixed.
9. Next lesson
Next lesson: Algebraic expressions. Keep going with the next idea in this course.
Printable worksheet
- 3 more than n
- n + 5 when n = 20
- Constant in n + 8
- Variable in n + 8
- n pens at 2 each
Homework
Write a rule with a variable for a situation at home.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 3 more than n | n + 3 | 2 |
| n + 5 when n = 20 | 25 | 2 |
| Constant in n + 8 | 8 | 2 |
| Variable in n + 8 | n | 2 |
| n pens at 2 each | 2n | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 n + 3; 2 25; 3 8; 4 n; 5 2n.
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 Say what a variable is | 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 Write a rule with a variable | 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 Substitute a 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 Name constants and variables | 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: Thinking a letter has only one value always. A variable can change.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Missing-number boxes.
- 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: say what a variable is; write a rule with a variable; substitute a number; name constants and variables.
Prerequisite knowledge. Grade 5 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. 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. Thinking a letter has only one value always. A variable can change.
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. Missing-number boxes. 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.