You will learn
- Name the four quadrants.
- Plot negative coordinates.
- Find the quadrant.
- Reflect a point.
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
- The axes make four quadrants.
- Signs tell the quadrant.
- Negative x is left; negative y is down.
- Reflecting changes one sign.
Words to know
One of four regions.
Mirror image.
Left or below zero.
(x, y).
1. Discover: beyond the corner
A point is 3 left of the origin and 2 up. How do we write it?
2. Understand: four quadrants
- 3 left, 2 up is (−3, 2) in quadrant II.
- (−2, −4) is in quadrant III; (4, −1) is in quadrant IV; (3, 2) is in quadrant I.
- Reflect (3, 2) in the x-axis: (3, −2).
- Reflect (3, 2) in the y-axis: (−3, 2).
Idea 1: Quadrants
(3, 2) is in quadrant I. (4, −1) is in quadrant IV. II is (−, +) and III is (−, −).
Idea 2: Negatives
4 left and 1 down is (−4, −1). 3 left and 2 up is (−3, 2).
Idea 3: Reflect
Reflect (3, 2) in the y-axis: (−3, 2). In the x-axis: (3, −2).
Why change one sign? The mirror line flips only one direction.
3. Worked examples
Example 1 (I show you): Quadrant
(4, −1)
- x positive, y negative.
Answer: IV
Example 2 (We do it together): Plot
4 left, 1 down
- x −, y −.
Answer: (−4, −1)
Example 3 (You try): Reflect
(3, 2) in the x-axis
Show the steps and answer
- y changes sign.
Answer: (3, −2)
Did you know?
Quadrants are numbered anticlockwise from the top right.
Why this matters
Four quadrants let us show positive and negative values together.
4. Explore: plot
You need squared paper.
- Start at the origin.
- Move x (left is −).
- Move y (down is −).
- Name the quadrant.
Think about it: what did you notice?
(−3, 2).
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- x is ___ and y is ___, so quadrant ___.
- Left means x is ___.
- Reflecting changes the sign of ___.
- The image is ( ___ , ___ ).
Guided practice
Question 1. 3 left and 2 up?
(−3, 2).
Question 2. Quadrant of (−2, −4)?
III.
Question 3. Reflect (3, 2) in the x-axis?
(3, −2).
Independent practice
Level 1: Start
- Quadrant of (3, 2)
- Quadrant of (4, −1)
- Reflect (3, 2) in the y-axis
- Point 4 left and 1 down
- Reflect (3, 2) in the x-axis
Level 2: Grow
- Quadrant of (−2, 5)
- Quadrant of (−4, −3)
- 2 right and 6 down
Level 3: Stretch
- Reflect (5, 1) in the y-axis
- Reflect (−3, 4) in the x-axis then the y-axis
- Ben says 4 left and 1 down is (4, −1). What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A drone is 3 m left and 2 m up from the start. Coordinates?
Show a sample answer
(−3, 2).
Another one. A point is 3 left and 2 up of the origin. Write it and name the quadrant.
Show a sample answer
(−3, 2); quadrant II
7. Common mistakes
Fix: Left is negative.
Fix: Left and down are negative.
Fix: Reflect in one axis changes only one sign.
8. Lesson summary and revision card
- I can name the four quadrants.
- I can plot negative coordinates.
- I can find the quadrant.
- I can reflect a point.
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
- Left and down are negative.
- Quadrants I–IV.
- Reflections change a sign.
11. Next lesson
Next lesson: Geometric properties. 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.
- In which quadrant is (3, 2)? Explain. [2 marks]
- In which quadrant is (4, −1)? Explain. [2 marks]
- Reflect (3, 2) in the y-axis. [2 marks]
- Reflect (3, 2) in the x-axis. [2 marks]
- Ali says 4 left and 1 down is (4, −1). Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- Both coordinates positive [1]; I [1]
- x positive and y negative [1]; IV [1]
- x changes sign [1]; (−3, 2) [1]
- y changes sign [1]; (3, −2) [1]
- No [1]. Left means x is negative [1]. It is (−4, −1) [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- Quadrant of (3, 2)
- Quadrant of (4, −1)
- Reflect (3, 2) in y-axis
- 4 left 1 down
- Reflect (3, 2) in x-axis
- Quadrant of (3, 2)
- Quadrant of (4, −1)
- Reflect (3, 2) in the y-axis
- 4 left and 1 down
- Reflect (3, 2) in the x-axis
Homework
Plot a shape in all four quadrants.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Quadrant of (3, 2) | I | 2 |
| Quadrant of (4, −1) | IV | 2 |
| Reflect (3, 2) in y-axis | (−3, 2) | 2 |
| 4 left 1 down | (−4, −1) | 2 |
| Reflect (3, 2) in x-axis | (3, −2) | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 I; 2 IV; 3 (−3, 2); 4 (−4, −1); 5 (3, −2).
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 I; 7 IV; 8 (−3, 2); 9 (−4, −1); 10 (3, −2).
Independent practice answers. Level 1: 1 I; 2 IV; 3 (−3, 2); 4 (−4, −1); 5 (3, −2). Level 2: 1 II; 2 III; 3 (2, −6). Level 3: 1 (−5, 1); 2 (3, −4); 3 Left means x negative: (−4, −1)..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Name the four quadrants | 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 Plot negative coordinates | 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 the quadrant | 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 Reflect a point | 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: Writing left moves as positive. Left is negative.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: First quadrant.
- 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 uses all four quadrants and reflects points. You do not need to be good at mathematics to help.
- Draw axes on the floor.
- Ask: left or right? up or down?
- Use compass directions.
- 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: name the four quadrants; plot negative coordinates; find the quadrant; reflect a point.
Prerequisite knowledge. Lesson 6 and integers.
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 squared 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 are the signs? Which axis is the mirror?
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. Writing left moves as positive. Left is negative.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-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. First quadrant. 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 6 » Geometry. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 6.NS.C.6 and 6.NS.C.8; Cambridge Primary Mathematics Stage 6 (four quadrants). These sources informed the lesson.