Math // Measurement

Numbers on a number line

Solve word problems involving elapsed time by adding and subtracting time intervals in minutes, including using a number line

Ages
8 to 9
Type
Method
Builds on
2 topics
Leads to
2 topics
Standards
2 codes

Quick check

If the learner starts football practice at 3:20 p.m. and it lasts 75 minutes, can they work out what time it finishes — using a number line to help?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • A film starts at 2:15 and lasts 47 minutes — when does it end?
  • Calculate how many minutes between 9:20 and 10:05
  • Use a number line to show the elapsed time between two events

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics

You are here

Numbers on a number line

Ages 8 to 9 // Method

Leads to

2 topics

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Children solve elapsed-time word problems in both directions — finding the END time from a start and a duration, and finding the DURATION between two times — using a blank number line and counting on in convenient jumps (to the next o'clock, then whole hours, then minutes). The core teaching move is showing that the SAME number line solves both 'when does it end?' and 'how long is it?', so elapsed time becomes one count-on method rather than two mysterious sums. Persistent errors to target: treating time as base-10 by writing minutes past 60 without rolling the hour over (2:15 + 47 -> '2:62'), column subtraction that fails across the hour boundary, and counting in the wrong direction.

Common misconceptions

  • Adds the duration to the minutes only, ignoring the hour roll-over past 60 (2:15 + 47 -> '2:62')
  • Column subtraction of the two times, failing across the hour boundary
  • Counts in the wrong direction (subtracts a duration instead of adding, or vice versa)
  • Overshoots or undershoots the o'clock bridge (base-10 slip)

Useful representations

  • Blank number line with labelled jumps
  • Clocks marking start and end
  • The 'bridge to the next o'clock' jump

Teaching practices

  • Use a blank number line for both problem types; count on in jumps (next o'clock, whole hours, minutes)
  • Decide the direction first: adding a duration forwards vs finding the gap between two times
  • Bridge the o'clock rather than subtracting in columns
  • Represent the story on the line before calculating (start, jumps, end)
  • Check the answer against a clock face

Activities to try

  1. 1

    Count on along a number line to find the end time

    Why it works: Adding a duration means counting FORWARD from the start; bridging to the next o'clock first makes the hour roll over correctly, so you never write an impossible time like 2:62 or 3:75.

    1. Read a word problem such as: 'A film starts at 2:15 and lasts 47 minutes — when does it end?'
    2. Draw a blank number line and mark the start time (2:15).
    3. Make a first jump that bridges to the next o'clock: +45 minutes to reach 3:00.
    4. Make a second jump with the remaining minutes: +2 to reach 3:02; label each jump and read off the end time.
    5. Repeat with a harder bridge: 'Swimming starts at 3:40 and lasts 35 minutes — when does it finish?' Jump +20 to 4:00, then +15 to reach 4:15.
  2. 2

    Fill the gap to find a duration

    Why it works: Finding a duration means filling the GAP between two times with jumps and summing them — not subtracting in columns and not adding the two clock times together. Bridging the o'clock keeps the base-60 boundary correct.

    1. Read a problem such as: 'How many minutes are there between 9:20 and 10:05?'
    2. On a blank number line, mark both times (9:20 and 10:05).
    3. Jump from the earlier time to the next o'clock: +40 minutes to reach 10:00.
    4. Jump the remaining minutes: +5 to reach 10:05.
    5. Add the jumps together (40 + 5) to get the total duration of 45 minutes.
  3. 3

    Decide the direction before you jump

    Why it works: Choosing the direction first — forward to find an end, backward to find a start, or filling the gap to find a duration — prevents counting the wrong way or adding two clock times together.

    1. Before calculating any problem, state out loud whether the unknown is an END time (jump forward from the start by the duration), a START time (jump backward from the end by the duration) or a GAP (fill the space between two given times).
    2. Solve a mixed set, e.g. 'A show ends at 10:05 and lasted 45 minutes — when did it START?' by counting BACKWARD: -5 to 10:00, then -40 to 9:20.
    3. Compare a forward problem and a backward problem side by side, labelling which way the jumps go.
    4. Say which number is unknown and which direction the jumps travel before marking the line.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
3.MD.1
The national curriculum in England: Key stages 1 and 2 framework document
Ma/KS2/Y4/M/6

Math // Measurement

More in Measurement

All 68 topics