You will learn
- Plot ordered pairs.
- Read coordinates of plotted points.
- Find distance between points on the same line.
- Draw shapes by plotting.
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
- Plot across first, then up.
- Read the coordinates of a plotted point.
- Distance on a line: subtract the changing numbers.
- Plot corners to draw shapes.
Words to know
Mark a point.
(x, y).
How far apart.
Corner of a shape.
1. Discover: draw a rectangle
Plot (2, 1), (6, 1), (6, 4), (2, 4) and join them. What shape do you get?
2. Understand: plotting
- To plot (6, 4): go 6 across, then 4 up.
- (2, 1) to (6, 1): same y, so distance = 6 − 2 = 4.
- (6, 1) to (6, 4): same x, so distance = 4 − 1 = 3.
- The four points make a rectangle 4 by 3.
Idea 1: Plot
(4, 3) is 4 across and 3 up.
Idea 2: Distance
(1, 2) to (5, 2): same y, so 5 − 1 = 4. (3, 1) to (3, 7): same x, so 7 − 1 = 6.
Idea 3: Shapes
A rectangle 4 by 3 has perimeter 4 + 3 + 4 + 3 = 14 and area 4 × 3 = 12.
Why subtract? The distance is the gap between the changing numbers.
3. Worked examples
Example 1 (I show you): Distance
(1, 2) to (5, 2)
- 5 − 1.
Answer: 4
Example 2 (We do it together): Distance
(3, 1) to (3, 7)
- 7 − 1.
Answer: 6
Example 3 (You try): Area
Rectangle 4 by 3
Show the steps and answer
- 4 × 3.
Answer: 12
Did you know?
Plotting corners and joining them draws shapes exactly.
Why this matters
Plotting turns number pairs into pictures and maps.
4. Explore: plot
You need grid paper.
- Plot the four points.
- Join them.
- Find each side.
- Name the shape.
Think about it: what did you notice?
Rectangle 4 by 3.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I go ___ across and ___ up.
- The distance is ___.
- The shape has ___ vertices.
- Its perimeter is ___.
Guided practice
Question 1. Distance (2,1) to (6,1)?
4.
Question 2. Distance (6,1) to (6,4)?
3.
Question 3. Shape?
Rectangle.
Independent practice
Level 1: Start
- Distance (1,2) to (5,2)
- Distance (3,1) to (3,7)
- Plot (4,3): across and up
- Perimeter of the rectangle 4 by 3
- Area of the rectangle 4 by 3
Level 2: Grow
- Distance (0, 3) to (6, 3)
- Distance (2, 2) to (2, 8)
- (1,1), (4,1), (4,3), (1,3) form a…
Level 3: Stretch
- Perimeter of the rectangle (1,1), (6,1), (6,4), (1,4)
- Area of that rectangle
- Ben says (2, 3) to (7, 3) is 9. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Corners (2,1), (6,1), (6,4), (2,4). Find the perimeter.
Show a sample answer
14.
Another one. Plot (2,1), (6,1), (6,4), (2,4). What is the area of the shape?
Show a sample answer
4 by 3 rectangle: 12
7. Common mistakes
Fix: Same y: subtract x.
Fix: Subtract the changing numbers.
Fix: Across first.
8. Lesson summary and revision card
- I can plot ordered pairs.
- I can read coordinates.
- I can find distances on a line.
- I can draw shapes by plotting.
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
- Across then up.
- Same y/x: subtract.
- Shapes from points.
11. Next lesson
Next lesson: Symmetry. 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.
- Find the distance from (1, 2) to (5, 2). [2 marks]
- Find the distance from (3, 1) to (3, 7). [2 marks]
- Where is (4, 3)? [2 marks]
- Find the perimeter of a 4 by 3 rectangle. [2 marks]
- Ali says the area of a 4 by 3 rectangle is 7. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- Same y so subtract x [1]; 4 [1]
- Same x so subtract y [1]; 6 [1]
- 4 across [1]; 3 up [1]
- 4 + 3 + 4 + 3 [1]; 14 [1]
- No [1]. Area is 4 × 3 [1]. It is 12 [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
- Distance (1,2) to (5,2)
- Distance (3,1) to (3,7)
- (4,3): across
- Perimeter 4 by 3
- Area 4 by 3
- Distance (1,2) to (5,2):
- Distance (3,1) to (3,7):
- (4, 3) is…
- Perimeter of a 4 by 3 rectangle:
- Area of a 4 by 3 rectangle:
Homework
Plot a triangle and a rectangle and find their sides.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Distance (1,2) to (5,2) | 4 | 2 |
| Distance (3,1) to (3,7) | 6 | 2 |
| (4,3): across | 4 | 2 |
| Perimeter 4 by 3 | 14 | 2 |
| Area 4 by 3 | 12 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 4; 2 6; 3 4; 4 14; 5 12.
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 4; 7 6; 8 4 across, 3 up; 9 14; 10 12.
Independent practice answers. Level 1: 1 4; 2 6; 3 4 across and 3 up; 4 14; 5 12. Level 2: 1 6; 2 6; 3 rectangle. Level 3: 1 16; 2 15; 3 Subtract: 7 − 2 = 5..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Plot ordered pairs | 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 Read coordinates of plotted points | 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 distance between points on the same 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 Draw shapes by plotting | 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: Subtracting the wrong coordinates. Same y: subtract x.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Plot single points.
- 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 plots points and draws shapes. You do not need to be good at mathematics to help.
- Plot a treasure hunt on squared paper.
- Ask: across or up first?
- Draw shapes from coordinates.
- 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: plot ordered pairs; read coordinates of plotted points; find distance between points on the same line; draw shapes by plotting.
Prerequisite knowledge. Lesson 5.
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 grid 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. Across how many? Up how many? What is the distance?
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. Subtracting the wrong coordinates. Same y: subtract x.
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. Plot single points. 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 5 » Geometry. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 5.G.A.2; Cambridge Primary Mathematics Stage 5 (plotting points). These sources informed the lesson.