Ticking Clocks and Turning Calendar (Preparatory Stage Math)
Worksheet A: Concepts
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Most years: 365; leap year: 366.
Solution
A leap year adds one day in February (29th), so total days become 366 instead of 365.
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28 days.
Solution
Only leap years include 29 February; the next year reverts to 28 days in February.
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After Monday: Tuesday; before Sunday: Saturday.
Solution
Days follow a fixed weekly order; moving forward or backward finds the neighbor days.
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AM.
Solution
AM indicates times from midnight to just before noon; PM indicates afternoon to just before midnight.
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July 8 and July 15.
Solution
Weekdays repeat every 7 days, so add 7 and 14 to the date to find the next Mondays.
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2020 and 2028.
Solution
Leap years typically occur every 4 years; 2020 before and 2028 after 2024.
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Noon: 1200 hours; Midnight: 0000 hours.
Solution
12:00 PM equals 1200; 12:00 AM starts the day at 0000 on digital clocks.
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Friday.
Solution
Move two days forward: Thursday, then Friday for the “day after tomorrow.”
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Weekday shifts by 3 days after a 31-day month and by 2 days after a 30-day month.
Solution
Since 28 days equal exactly 4 weeks, extra 2 or 3 days push the weekday forward by 2 or 3 respectively depending on month length.
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2016, 2020, 2024, 2028, 2032.
Solution
Leap years occur every 4 years in this span, so add 4 repeatedly starting from 2016.
Worksheet B: Computational Skills
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0700 hours; 1900 hours.
Solution
AM times copy as 0–11 hours; PM times add 12 to the hour except for noon which is 1200.
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60 minutes; one-half of an hour.
Solution
There are 60 minutes in an hour; 30 is half of 60, so 30 minutes is half an hour.
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30 minutes; 60 minutes.
Solution
One quarter-hour is 15 minutes; doubling gives 30, and four quarters complete 60 minutes.
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They are the same time.
Solution
08:00 PM equals 20:00 in 24-hour format; both indicate evening at the same moment.
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0100 hours; 0300 hours; 1200 hours; 2345 hours.
Solution
AM hours are written with leading zero; noon is 1200; PM hours add 12 to the hour, so 11:45 PM is 23:45.
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15 minutes.
Solution
From 8:20 to 8:35 is a difference of 15 minutes; count forward or subtract minutes directly.
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10:45 AM; 1045 hours.
Solution
Add 25 minutes to 10:20 to get 10:45; in 24-hour time this is 1045 hours.
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5:00 PM; 1700 hours.
Solution
4:15 + 45 minutes = 5:00 PM; converting PM hour 5 gives 1700 in 24-hour time.
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08:00 is 8:00 AM morning; 20:00 is 8:00 PM evening; labels avoid mixing morning/evening doses.
Solution
AM/PM or 24-hour labels clearly distinguish times that look similar on a 12-hour clock (8 o’clock twice daily).
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432 − 200 = 232; result 232.
Solution
Shift both by +2 to use friendlier numbers; equal changes preserve differences, making subtraction easier mentally.
Worksheet C: Problem-Solving & Modeling
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Yesterday: Sunday; Day after tomorrow: Wednesday.
Solution
Move one day back for yesterday; move two days forward for the day after tomorrow from Monday.
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About 6 months.
Solution
From May to November includes Jun, Jul, Aug, Sep, Oct, Nov = 6 months of shelf life.
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12 hours; 24 hours.
Solution
Morning 6 to evening 6 spans 12 hours; a full day covers 24 hours from midnight to midnight.
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15 minutes; four quarters make one hour.
Solution
One hour is 60 minutes; dividing by 4 gives 15 minutes per quarter.
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No; only 15 minutes passed for the trip.
Solution
From 8:00 to 8:15 is 15 minutes; one hour equals 60 minutes, which is larger than 15 minutes.
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Assembly continued from 8:10 to 8:30 AM.
Solution
From 8:10 (10 minutes after 8:00) to 8:30 is 20 minutes, matching the assembly duration given.
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Thursday (shift by 3 days after July’s 31 days).
Solution
A 31-day month adds 3 extra days beyond complete weeks, pushing the weekday forward by 3.
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11:45 PM; late evening/night.
Solution
Subtract 12 from the hour part for PM times beyond 12:00 to convert to 12-hour format with PM label.
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If next month has 31 days → Friday; if 30 days → Thursday.
Solution
Start from Tuesday and shift by +3 for 31-day months, +2 for 30-day months to get the next month’s weekday.
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Laali is older by about 5 years and 5 months (to Dec 2019 checkpoint).
Solution
From July 2014 to December 2019 is 5 years and 5 months; Laali’s date precedes Chotu’s by that span.
Two best activities
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Physical modeling of AM/PM and elapsed time using a floor clock face and a wall timeline.
Solution
Tape a big clock on the floor; two students are hour/minute hands to show times called out (e.g., 10:20 AM, then +25 minutes). Next, shift to a wall “day timeline” from 0000 to 2400; learners place event cards (wake, school, play, dinner) and convert each to both formats, then compute gaps (e.g., 08:20–08:35 = 15 minutes). This builds embodied sense of 12h–24h and durations.
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Make a month-wheel to track weekday shifts and circle leap-year Februaries.
Solution
Create a rotating “weekday arrow” over a printed month strip; turning from a 30-day to next month advances 2 days, from 31-day advances 3 days. Learners test July→Aug→Sep→Oct for a chosen date (like the 15th), then mark Feb 29 in leap years on a class timeline (2016, 2020, 2024, 2028…). This concretizes why weekdays shift and how leap years add a day.