TimeGrades 1–6
Today is Tuesday: what day will it be in 30 days? Mum is 30 and Ann is 6: how old will Ann be when Mum is twice her age? In these tasks a child works with weeks, months and years, and two facts carry most of them: the week comes round every 7 days, and the difference between two ages never changes.
Mo Tu We Th Fr Sa Su
1 2 3 4 5
6 7 8 9 10 11 12
13 14 15 16 17 18 19Every 7 days the same day of the week comes back. So for 30 days ahead, only the 2 days left after 4 whole weeks matter.
From 3 May to 10 May is 7 days ahead, but a holiday from the 3rd to the 10th lasts 8 days, because both the first and the last day count.
Mum is 24 years older than Ann now, and she will be 24 years older in 10 years: each of them gets one year older every year.
What day of the week will it be in so many days? Only what is left after the whole weeks matters.
| In how many days | Whole weeks and days left | If today is a Monday |
|---|---|---|
| 10 | 1 week and 3 days | Thursday |
| 15 | 2 weeks and 1 day | Tuesday |
| 30 | 4 weeks and 2 days | Wednesday |
| 100 | 14 weeks and 2 days | Wednesday |
Look for what stays the same: the week comes round every 7 days, and the gap between two ages never changes. Use it to drop what does not matter, then count only what is left. The examples below go from the simplest to an olympiad's.
Example 1 · Grades 1–2
Kate waters the flowers every 3 days. The first time she waters them on a Monday. On which day of the week does she water them for the 4th time?
Mo Tu We Th Fr Sa Su
1 2 3
4Answer On a Wednesday.
Example 2 · Grades 3–4
Dad is 28 years older than Vera. In 4 years he will be 3 times as old as she will be. How old is Vera now?
Vera [ ]
Dad [ ][ ][ ]
└─ 28 ─┘Answer 10 years old.
Example 3 · Grades 5–6
In some month, three Saturdays fall on even dates. What day of the week is the 25th of that month?
Answer Monday.
MathTrail explains every wrong answer by the trap it fell into. These are the commonest in this topic, with something you can say to your child.
The day count is one off: the child counts today as the first of the days ahead, finds 4 gaps between 4 waterings, or leaves out one end of a period, such as holidays from Monday to Sunday.
What to say
“Which day is day 1: today or tomorrow?”
The child does an action the question does not ask for: adds the two ages when it asks how much older one is, or takes one date from another when they are in different months.
What to say
“Say it in words: does the number grow, shrink or stay?”
A fact of the calendar or of the task is lost: that this month has 30 days and not 31, or that 365 days are whole weeks and one day more.
What to say
“How many days does this month have?”
Hang a paper calendar where the child can reach it and ask about it: on which day of the week is the 1st of next month? How many Fridays are there this month?
Write down everyone's age and the differences between them. A year later, look again: the ages have changed, and the differences have not.
Count the days to a birthday or a holiday together, first one by one, then by whole weeks, and see that both ways agree.