Problem
Weekdays repeat every seven days
Part of a calendar for one month is shown. In this month, the 5th falls on a Saturday. What day of the week is the 26th?
Base-ten numbers
Your answer
Watch out Counting all 21 days one by one is easy to get wrong. Weekdays repeat every 7 days, so use the remainder when the gap is divided by 7.
How to solve
Strategy Look for a Pattern — A calendar repeats its weekdays every 7 days, so the dates sharing a column with the 5th are 5, 12, 19, 26. Spotting this skip-counting-by-7 pattern is faster than counting every single day.
1STEP 1
Find the gap between the dates
The 5th to the 26th is a gap of 21 days.
26 − 5 = 21
2STEP 2
Confirm the gap is whole weeks
21 days is 7 + 7 + 7 — exactly 3 weeks.
7 + 7 + 7 = 21
21 days splits into three equal weeks of 7 with nothing left over — three groups of 7 add up to 21, so 21 days is exactly three whole weeks.
Look For A Pattern2.NBT.A.2TimeBecause the 21 days from the 5th to the 26th make three whole weeks, the 26th lands on the same weekday as the 5th.
Why?
The 21 days split into three equal weeks of 7 days with nothing left over.
Why?
Three groups of 7 days counted together make 21, so 21 days is exactly three whole weeks.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Because each whole week ends back on the same weekday it started, three whole weeks in a row still finish on that same weekday.
Why?
Weekdays run in a fixed repeating cycle of seven, so every whole seven-day period lands back on the same weekday.
🧱A cycle returns after a full periodA fixed repeating cycle of length p comes back to the same position every p steps.
3STEP 3
Read off the weekday
After exactly 3 whole weeks the weekday repeats, so the 26th is also Saturday.
Weekdays run in a fixed repeating cycle of seven, so every whole week returns to the same weekday it started on — three whole weeks in a row still finish on that same weekday.
Draw A DiagramTimeAnswer
Saturday
26 − 5 = 21 = 7 × 3
Check — adding 7 repeatedly from the 5th gives 5, 12, 19, 26 — the 26th appears, confirming Saturday.
Takeaway
Weekdays repeat every 7 days. When the gap between dates is a multiple of 7, they share the same weekday.
- 5th to 26th is a gap of 21 days
- 21 = 7+7+7, exactly 3 weeks
- A whole number of weeks later, the 26th is also Saturday
Where next?
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