A number line is a map of order and distance. It shows which numbers come before and after, how far apart quantities are, how addition can move forward, how subtraction can move backward or measure a gap, and why starting points and intervals matter.
This laboratory extends Number Lines, Distance, Difference, Before, After and Position, Objects, Ten Frames, Number Lines, Models and Mathematical Representation, and the Hundred Chart Laboratory.
On a number line, the points tell where numbers are. The intervals tell how far apart they are.
Session 1 | Build a Number Line From Order
Place number cards 0 to 10 in order along a strip. Keep roughly equal spacing between consecutive values. Ask the learner why 6 belongs between 5 and 7 and why 9 lies to the right of 4 on a standard left-to-right number line.
The arrangement should reflect numerical order, not card size, colour or the order in which cards were handed out.
Worked Example 1 | Before, After and Between
On a number line, 28 comes immediately before 29; 30 comes immediately after 29. Therefore 29 lies between 28 and 30.
Session 2 | Count Forward as Movement
Start at 7 and make three forward jumps of one. Land on 8, then 9, then 10. Therefore 7 + 3 = 10. The starting point 7 is not one of the three added jumps.
This helps repair the common error of counting the starting number as the first added unit.
Worked Example 2 | 8 + 4
Start at 8. Four forward jumps land at 9, 10, 11 and 12. The endpoint is 12, so 8 + 4 = 12.
Session 3 | Count Backward as Movement
Start at 13 and make five backward jumps: 12, 11, 10, 9, 8. Therefore 13 − 5 = 8.
Ask what changed at every jump. The value decreased by one. This keeps the movement connected to the operation.
Worked Example 3 | Cross a Ten
To calculate 12 − 5, move back two to 10, then three more to 7. Using 10 as a landmark can be easier than making five ungrouped jumps.
Distance Is Not the Number of Marks
From 3 to 8, the marked positions are 3, 4, 5, 6, 7 and 8, but the distance is five intervals. The difference is 8 − 3 = 5.
This same interval idea later supports ruler measurement and duration on timelines.
Worked Example 4 | Find a Difference
How much greater is 15 than 9? Count from 9 to 15: six jumps. Therefore the difference is 6.
Session 4 | Missing Numbers on Partial Lines
Show 21, 22, __, 24, 25. The missing value is 23 because the line increases by one at each equally spaced mark.
Then hide two numbers: 47, __, __, 50. The learner can reason forward from 47 or backward from 50. Both routes should produce 48 and 49.
Not Every Number Line Counts by Ones
A line may use labelled intervals of two, five or ten. The learner must inspect the rule rather than assume every neighbouring mark differs by one.
For Primary 1, keep non-one scales simple and explicit. Example: 0, 10, 20, 30, 40. Each step represents ten.
Worked Example 5 | Tens Scale
On a line labelled 20, 30, 40, __, 60, the missing value is 50 because each interval adds ten.
Session 5 | Open Number Lines
An open number line does not need every number printed. To solve 27 + 8, mark 27, jump 3 to 30, then jump 5 to 35. The chosen jumps reveal the make-ten strategy.
Different valid jump decompositions can reach the same endpoint. A learner might jump 8 in one move if the fact is known. Representation should support thinking rather than force unnecessary steps.
Worked Example 6 | 34 + 12
Mark 34. Jump 10 to 44, then 2 to 46. Therefore 34 + 12 = 46.
Session 6 | Subtraction as Take-Away and Difference
Subtraction can be shown by moving backward from a whole or by finding the distance between two values. For 14 − 9, one route moves back nine from 14. Another counts forward from 9 to 14 and finds a gap of five.
Both give 5. The second route can be efficient when the numbers are close.
Worked Example 7 | Difference by Counting On
18 − 15 asks for the difference between 18 and 15. Starting at 15, make three forward jumps to 18. The difference is 3.
Compare Number Line and Hundred Chart
Both representations show order. The hundred chart compresses one hundred values into a two-dimensional grid and makes +10 movement especially visible. The number line makes distance and directional movement especially visible.
Ask which representation better shows the gap between 42 and 47. A number line may make the five-unit distance more direct. For ten more than 42, a hundred chart may be faster.
Estimate Position on an Open Line
Draw a line from 0 to 100 and mark 50 in the middle. Ask where 20, 75 and 90 should be placed approximately. The task is about relative magnitude, not exact centimetre measurement.
A learner placing 90 near 10 may know the numeral but not its magnitude relative to the endpoints.
Boundary and Feasibility Checks
If a task begins on a 0–20 line and asks for 18 + 5, the correct result 23 lies beyond the printed line. The representation is incomplete for the final position; the arithmetic does not become wrong merely because the page ends.
This is a useful model-limit lesson: a number line is a representation of the number system, not the number system itself.
Common Number-Line Errors
| Error | Likely weak link |
|---|---|
| counts starting point as first jump | position and change confused |
| counts marks instead of intervals for difference | distance concept weak |
| moves wrong direction for subtraction | operation direction not linked to change |
| assumes every scale step is one | interval rule not read |
| cannot use open line without every numeral | representation dependence too literal |
| places large number near small endpoint | magnitude sense weak |
Twenty Practice Questions
- What number comes after 37?
- What number comes before 50?
- What number lies between 68 and 70?
- Start at 6 and make 4 forward jumps. Where do you land?
- Start at 14 and make 5 backward jumps. Where do you land?
- Find the distance from 3 to 8.
- Find the difference between 15 and 9.
- Complete 21, 22, __, 24, 25.
- Complete 47, __, __, 50.
- Complete the tens scale: 10, 20, __, 40, 50.
- Use an open number line to solve 27 + 8.
- Use an open number line to solve 34 + 12.
- Use a number line to solve 13 − 5.
- Find 18 − 15 by counting on.
- Which is farther from 20: 16 or 19?
- Place 75 approximately on a 0–100 line. Is it left or right of 50?
- Is 90 closer to 100 or 0?
- A line ends at 20. Can 18 + 5 still equal 23? Explain.
- Which tool better shows +10 from 42: a hundred chart or a number line? Give a reason.
- Create one number-line jump story for 9 + 4.
Explained Answers
1. 38. 2. 49. 3. 69. 4. 10. Four jumps from 6 reach 7, 8, 9, 10. 5. 9. Five backward jumps from 14 reach 13, 12, 11, 10, 9.
6. 5. There are five intervals from 3 to 8. 7. 6. Nine to fifteen is six units. 8. 23. 9. 48, 49. 10. 30. The scale increases by ten.
11. 35. Jump 3 to 30, then 5. 12. 46. Jump 10 then 2. 13. 8. Five backward jumps from 13. 14. 3. Count from 15 to 18. 15. 16. It is four away from 20, while 19 is one away.
16. Right of 50. Seventy-five is greater than fifty and about three quarters of the way to 100. 17. 100. Ninety is ten from 100 and ninety from 0. 18. Yes. The printed line is too short, not the number system. 19. A hundred chart is often efficient because one row down adds ten directly, though a correctly scaled number line can also work. 20. Many stories are valid if four forward units are added to a starting quantity of nine.
A Strong Practice Progression
- Order consecutive numbers.
- Identify before, after and between.
- Make forward jumps of one.
- Make backward jumps of one.
- Count intervals for distance.
- Fill missing values.
- Read simple non-one scales.
- Use open number lines for tens-and-ones jumps.
- Use subtraction as difference.
- Estimate relative position on 0–100.
What Adults Can Ask
- “Where are you starting?”
- “How many jumps are you making?”
- “What does each interval represent?”
- “Are you counting positions or distance?”
- “Could a landmark like 10, 20 or 50 help?”
- “Does the page end, or does the number system end?”
Return to the Primary 1 Mathematics Learning Hub for the complete route.
