You will learn
- Read inequality symbols.
- List solutions.
- Graph on a number line.
- Write an inequality from words.
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
Compares unequal values.
Symbol >.
Symbol ≤.
All values that work.
1. Discover: at least
You need more than 3 points to win. Which scores win?
2. Understand: inequalities
- x > 3 means any number greater than 3: 4, 5, 6, … (3 itself is not included).
- n ≤ 5 includes 5: whole-number solutions 0, 1, 2, 3, 4, 5.
- “At least 18” is x ≥ 18.
- On a number line an open circle excludes the end and a filled circle includes it.
3. Explore: graph
You need a number line.
- Mark the end value.
- Open or filled?
- Shade the direction.
- List a few solutions.
Think about it: what did you notice?
x > 3.
4. Practise
Guided practice
Question 1. Is 3 a solution of x > 3?
No.
Question 2. Is 5 a solution of n ≤ 5?
Yes.
Question 3. “At least 18”?
x ≥ 18.
Independent practice
- Is 4 a solution of x > 3?
- Whole-number solutions of n ≤ 3
- Write: more than 10
- Write: at most 8
- Is 18 a solution of x ≥ 18?
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
You need at least 18 points to pass. Write this.
Show a sample answer
x ≥ 18.
6. Common mistake
Fix: 3 is not greater than 3.
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
- Symbols show comparison.
- Open or filled circle.
- Many solutions.
9. Next lesson
Next lesson: Number relationships. Keep going with the next idea in this course.
Printable worksheet
- 4 in x > 3 (yes/no)
- Whole numbers n ≤ 3
- More than 10
- At most 8
- 18 in x ≥ 18 (yes/no)
Homework
Write an inequality about your height and graph it.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 4 in x > 3 (yes/no) | yes | 2 |
| Whole numbers n ≤ 3 | 0, 1, 2, 3 | 2 |
| More than 10 | x > 10 | 2 |
| At most 8 | x ≤ 8 | 2 |
| 18 in x ≥ 18 (yes/no) | yes | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 yes; 2 0, 1, 2, 3; 3 x > 10; 4 x ≤ 8; 5 yes.
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 Read inequality symbols | 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 List solutions | 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 Graph on a number line | 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 Write an inequality from 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 |
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: Including 3 in x > 3. 3 is not greater than 3.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: More and less.
- 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: read inequality symbols; list solutions; graph on a number line; write an inequality from words.
Prerequisite knowledge. Lesson 6.
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 a number line. 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. Including 3 in x > 3. 3 is not greater than 3.
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. More and less. 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.