Lesson Guide
Explanation
Two facts do all the calendar work: how long each month is, and that a week is seven days. Thirty days has September, April, June and November; February has twenty-eight, or twenty-nine in a leap year; every other month has thirty-one. A fortnight is fourteen days, six weeks is forty-two, and forty days is five weeks and five days. You need the month lengths to count past the end of a month, and the seven to move a weekday name.
Your Turn
How many days in 3 weeks? And 40 days is how many weeks and days? Check: 21; 5 weeks and 5 days.
Watch Out
June has 30 days, not 31. Counting "31 June" puts every date after it one day out.
Explanation
The same weekday comes back every seven days. If the first of May is a Wednesday, the first Sunday is the fifth, and the Sundays are the fifth, twelfth, nineteenth and twenty-sixth. The third Sunday is the first Sunday plus fourteen: the nineteenth. Find the first one, then add sevens. A thirty-one-day month has five of the weekday it starts on, and four of most others.
Your Turn
May starts on a Wednesday. Which dates are Tuesdays? Check: 7, 14, 21, 28.
Watch Out
The third Sunday is the first Sunday plus 14, not plus 21. Count: first, second, third.
Explanation
To find the weekday some number of days later, divide by seven and keep only the remainder, because whole weeks bring you back to the same day. Fifteen days after a Wednesday is two weeks and one day, Thursday. Six weeks later is still Wednesday. Forty days later is five weeks and five days: count five on from Wednesday, Thursday, Friday, Saturday, Sunday, Monday. A year is fifty-two weeks and one day, which is why a birthday moves one weekday each year.
Your Turn
100 days after a Friday is what day? Check: 100 ÷ 7 = 14 r 2 → Sunday.
Watch Out
Count the remainder from the day AFTER. Wednesday + 1 is Thursday. Wednesday itself is + 0.
Explanation
Counting across the end of a month: the days left in this month are the month length minus today's date, and then you carry on into the next month. From the twentieth of May to the tenth of June is eleven days left in May plus ten, twenty-one days, exactly three weeks. Going forwards, add the days to the date and take off the month length when you pass it: forty days after the first of May is forty-one, minus thirty-one, the tenth of June.
Your Turn
Library books are due 3 weeks after 20 May. What date in June? Check: 20 + 21 = 41 → 41 − 31 = 10 June.
Watch Out
Subtract THIS month's length when you cross its end. From May, take off 31; from June, take off 30.
Explanation
Some questions ask for both the date and the day. Forty days after Wednesday the first of May: the date is the tenth of June, from counting across the month end; the day is Wednesday plus the remainder five, Monday. Check by another route: the twenty-ninth of May is also a Wednesday, so the thirty-first is Friday, the first of June Saturday, and counting on, the tenth is Monday. Two methods that agree is the check. Quiz and exercises now.
Your Turn
1 May is a Wednesday. What day is 31 May? Check: 29 May is Wednesday (1 + 28), so 31 May is Friday.
Watch Out
Keep the two parts apart: the remainder gives the day NAME, the month lengths give the DATE.
📌 Key Points — this lesson in a nutshell
- Days in a month: 30 for April, June, September, November; 28 (29 in a leap year) for February; 31 for the rest.
- The same weekday comes back every 7 days. If the 5th is a Sunday, so are the 12th, 19th and 26th.
- To move a day name, divide the days by 7 and use the remainder: 15 days after a Wednesday is 2 weeks + 1 day → Thursday.
- Across a month end: count the days left in this month, then carry on into the next. 20 May to 10 June is 11 + 10 = 21 days.
Step 1: Introduction
Step 1 of 5
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