Primary Mathematics: Time, Money and Schedules | Worked Learning Guide

Time and money are difficult not because the arithmetic is always hard, but because the units and conditions change while the learner is calculating.

BTT Mathematics / Primary Mathematics Learning Hub / Guide 14

Wait, What? Clock Notation Is Not Ordinary Decimal Notation

9:45 and 10:15 look like decimal-style numbers, but time is organised in hours and minutes, with sixty minutes in one hour. Subtracting 10.15 – 9.45 as though 15 and 45 were hundredths produces nonsense. Time problems require unit control before arithmetic.

Money creates a similar challenge. $4.70 is four dollars and seventy cents, not four dollars and “seventy hundredths” in a purely abstract sense. The decimal notation works because one dollar is one hundred cents. A correct calculation still needs the correct currency unit and context.

The Five Control Questions

1. What quantity is being measured: time, duration, cost, change, rate or schedule position?
2. What units are being used?
3. Do the units need conversion before calculating?
4. Does the answer represent a clock reading, an elapsed duration or a monetary amount?
5. What real-world condition must the final answer satisfy?

Reading Clock Time

A clock reading names a position in the day. A duration measures how long an interval lasts. These are different quantities. 3:20 p.m. is a clock time; 45 minutes is a duration.

Worked Example 1: Convert Hours and Minutes

Convert 2 h 35 min to minutes.

Two hours = 120 minutes. Add 35 minutes.

Answer: 155 minutes.

Worked Example 2: Convert Minutes Back to Mixed Units

Convert 185 minutes to hours and minutes.

180 minutes = 3 hours, with 5 minutes remaining.

Answer: 3 h 5 min.

Elapsed Time by Crossing Friendly Boundaries

For many learners, counting through an hour boundary is safer than subtracting mixed time units directly.

Worked Example 3: 9:35 a.m. to 12:20 p.m.

• 9:35 to 10:00 = 25 min
• 10:00 to 12:00 = 2 h
• 12:00 to 12:20 = 20 min

Total = 2 h 45 min.

Worked Example 4: Find the End Time

A lesson begins at 2:45 p.m. and lasts 1 h 35 min.

2:45 + 1 h = 3:45. Add 15 min to reach 4:00, then another 20 min.

End time: 4:20 p.m.

Worked Example 5: Find the Start Time

A movie ends at 8:10 p.m. and lasts 2 h 25 min.

Subtract 2 h to get 6:10. Subtract 10 min to get 6:00, then 15 more min.

Start time: 5:45 p.m.

12-Hour and 24-Hour Time

24-hour time removes the need for a.m. and p.m. but requires careful conversion. 14:30 is 2:30 p.m. and 08:05 is 8:05 a.m. Midnight is 00:00 and noon is 12:00.

Worked Example 6: Timetable Difference

A train departs at 13:48 and arrives at 15:17.

13:48 to 14:00 = 12 min; 14:00 to 15:00 = 1 h; 15:00 to 15:17 = 17 min.

Journey time: 1 h 29 min.

Schedules Are Constraint Problems

A timetable problem often contains more than arithmetic. A bus may depart every 20 minutes, a transfer may require 8 minutes, or an appointment may have to begin before a closing time. The learner must satisfy every condition.

Worked Example 7: Catch the Next Bus

Buses leave at 3:00, 3:20, 3:40 and 4:00 p.m. A student reaches the stop at 3:27 p.m.

The 3:20 bus has already left. The next possible departure is 3:40 p.m.

Worked Example 8: Transfer Constraint

A train arrives at 10:42. A connecting bus leaves at 10:47 and 11:02. Walking to the bus stop takes 8 minutes.

Earliest arrival at the bus stop is 10:50, so the 10:47 bus cannot be caught. The first feasible bus is 11:02.

Calendars and Day Counting

Calendar questions can ask for days between dates, inclusive day counts or future dates. The phrase “from Monday to Friday” may include or exclude endpoints depending on the context, so read the wording carefully.

Worked Example 9: Inclusive Count

A camp runs from 5 June to 8 June inclusive.

Count 5, 6, 7, 8 June: 4 days.

Money as Place Value

One dollar = 100 cents. Therefore $3.50 = 350 cents. Converting to cents can simplify subtraction and sharing; converting back restores the familiar money notation.

Worked Example 10: Add Money

$12.75 + $8.60 = $21.35.

Align decimal places because cents represent hundredths of a dollar.

Worked Example 11: Find Change

An item costs $17.85. Payment is $20.

Think $17.85 to $18.00 = $0.15, then $18.00 to $20.00 = $2.00.

Change = $2.15.

Worked Example 12: Equal Sharing of Money

$18.60 is shared equally among 3 children.

1860 cents ÷ 3 = 620 cents = $6.20 each.

Unit Price and Best Value

Comparing two packs fairly often requires a common basis: price per item, price per gram or price per litre. A lower total price is not always better value if the quantity is also smaller.

Worked Example 13: Price per Item

Pack A: 6 pens for $9.00. Pack B: 10 pens for $14.00.

A costs $1.50 per pen. B costs $1.40 per pen.

Pack B has the lower unit price.

Worked Example 14: Cost From a Rate

A service costs $3.20 per hour for 4 hours.

$3.20 × 4 = $12.80.

Budget Problems

A budget is a maximum condition. If a learner has $50 and items total $48.70, the purchase fits. If the total is $50.40, it does not. Estimation can quickly test plausibility before exact addition.

Worked Example 15: Budget and Remaining Amount

A family budgets $60. Purchases cost $18.75, $12.40 and $21.90.

Total = $53.05. Remaining budget = $60.00 – $53.05 = $6.95.

Time and Money Together

Many real problems combine a duration and a rate. The learner must first determine the correct duration, then apply the cost per unit time.

Worked Example 16: Hourly Charge

A facility charges $4 per hour. A booking runs from 2:00 p.m. to 5:00 p.m.

Duration = 3 h. Cost = 3 × $4 = $12.

Worked Example 17: Partial-Hour Rule

A car park charges $2 for each started hour. A car stays 2 h 10 min.

The phrase “each started hour” means the third hour has begun, so three chargeable hours are required.

Cost = $6.

Common Time and Money Errors

• Treating 1 h 30 min as 1.30 h without checking the conversion.
• Subtracting clock notation as ordinary decimals.
• Forgetting a.m./p.m. or 24-hour conversion.
• Finding a departure time but ignoring transfer time.
• Comparing total prices instead of unit prices.
• Writing $4.5 when $4.50 is clearer in money notation.
• Returning a negative budget amount instead of interpreting it as over budget.
• Ignoring rules such as “per started hour”, “before 5 p.m.” or “inclusive”.

Practice: 24 Questions

Questions 1–8: Time and Duration

1. Convert 3 h 25 min to minutes.
2. Convert 250 minutes to hours and minutes.
3. Find the duration from 8:45 a.m. to 11:20 a.m.
4. A lesson begins at 1:35 p.m. and lasts 2 h 15 min. Find the end time.
5. A film ends at 9:10 p.m. and lasts 1 h 55 min. Find the start time.
6. Convert 16:45 to 12-hour time.
7. A bus leaves at 14:28 and arrives at 15:53. Find the journey time.
8. A camp runs from 12 June to 16 June inclusive. How many days is that?

Questions 9–16: Money

9. Add $14.75 and $8.90.
10. Find the change from $50 after spending $36.45.
11. Share $24.60 equally among 4 people.
12. Five notebooks cost $3.80 each. Find the total.
13. Pack A has 8 items for $12. Pack B has 10 items for $14. Which has the lower unit price?
14. A budget is $75. Purchases total $68.55. How much remains?
15. A $40 budget is exceeded by a purchase total of $43.20. By how much?
16. A taxi-style service costs $5 fixed plus $2 per kilometre for 7 km. Find the total.

Questions 17–24: Schedules and Mixed Problems

17. Buses leave every 15 minutes from 3:00 p.m. A learner arrives at 3:23 p.m. What is the next departure?
18. A train arrives at 10:42. Walking to the bus stop takes 9 minutes. Buses leave at 10:48 and 11:03. Which bus can be caught first?
19. A class begins at 4:10 p.m. A student needs 35 minutes to travel there. What is the latest departure time?
20. A facility costs $6 per hour. A booking lasts from 2:30 p.m. to 5:30 p.m. Find the cost.
21. A car park charges $3 for each started hour. A car stays 2 h 20 min. Find the charge.
22. A trip has two stages: 45 min and 1 h 35 min, with a 20 min break. Find the total elapsed time including the break.
23. A shop closes at 6:00 p.m. A task takes 1 h 25 min. What is the latest start time?
24. A learner has $30 and wants three books at $7.95 each. Is the budget enough, and how much remains?

Worked Answers

1. 205 min. 2. 4 h 10 min. 3. 2 h 35 min. 4. 3:50 p.m. 5. 7:15 p.m. 6. 4:45 p.m. 7. 1 h 25 min. 8. 5 days.

9. $23.65. 10. $13.55. 11. $6.15 each. 12. $19.00. 13. A = $1.50 each; B = $1.40 each, so B is lower. 14. $6.45. 15. $3.20 over budget. 16. $19.

17. 3:30 p.m. 18. 11:03. 19. 3:35 p.m. 20. 3 h × $6 = $18. 21. 3 started hours × $3 = $9. 22. 45 min + 1 h 35 min + 20 min = 2 h 40 min. 23. 4:35 p.m. 24. Three books cost $23.85; budget is enough and $6.15 remains.

Transfer Test

A school excursion starts at 08:35. Travel takes 1 h 25 min, an activity lasts 2 h 40 min, lunch lasts 45 min and return travel takes 1 h 35 min. Find the return time. Then suppose transport costs $6.50 per student for 28 students and the class budget is $200. Determine whether the transport budget is sufficient and state the amount remaining or exceeded.

Delayed Return

Three days later, solve one elapsed-time problem, one backwards-start-time problem, one unit-price comparison and one schedule constraint without looking at the examples. Label whether each answer is a clock time, duration, cost, change or rate.

Parent and Tutor Guide

When time errors occur, ask whether the child is manipulating clock readings or durations. When money errors occur, convert to cents temporarily if decimal notation is obscuring the structure. For schedule questions, ask the learner to list every condition before calculating. A correct calculation that violates the departure or budget rule is not yet a correct solution.

Mastery Receipt

• I distinguish clock time from duration.
• I convert hours and minutes using sixty, not one hundred.
• I use 12-hour and 24-hour notation correctly.
• I solve start-time, end-time and elapsed-time problems.
• I calculate with dollars and cents accurately.
• I compare unit prices rather than total prices when needed.
• I use timetable and budget conditions before finalising an answer.
• I can combine time and money in multi-step problems.

Official Reference Route

Singapore Ministry of Education — Primary Mathematics Syllabus P1–P6, updated October 2025

Continue the Primary Mathematics Worked Series

• BTT Primary Mathematics Learning Hub
• Mental Calculation, Number Bonds and Compensation
• Fractions of a Quantity, Equivalence and Operations
• Decimals, Rounding and Four Operations

The Quiet Return

Time and money are unit systems. Once the learner keeps the units, interval boundaries and schedule conditions visible, the arithmetic becomes easier to trust.