Problem
Weekdays repeat every seven days
In a month's calendar the 5th is a Saturday. I need to find what day of the week the 26th is.
Base-ten numbers
Your answer
Watch out Counting both the 5th and the 26th makes the gap look like 22 days, which nudges the weekday one step too far.
How to solve
Strategy Look for a Pattern — A calendar repeats its weekdays every 7 days, so the dates that share a column with the 5th are 5, 12, 19, 26. Spotting this skip-counting-by-7 pattern is faster than writing out every single day.
1STEP 1
Find the gap between the two dates
From the 5th to the 26th is 26 - 5 = 21 days later.
26 - 5 = 21
Subtracting to find how many days apart is a Grade 2 subtraction students can do.
2.NBT.A.2Look For A Pattern2STEP 2
Check that the gap is a whole number of weeks
21 days is exactly 3 weeks because 7 + 7 + 7 = 21, and after a whole number of weeks the weekday stays the same.
7 + 7 + 7 = 21
Skip-counting by 7 to land exactly on 21 shows the day lands in the same column.
2.NBT.A.2Look For A PatternBecause 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
Because 21 days is a whole 3 weeks, the 26th shares the 5th's weekday — Saturday (the Saturdays are 5, 12, 19, 26).
Same column on the calendar means same weekday.
2.NBT.A.2Draw A DiagramAnswer
Saturday
Listing the Saturdays from the 5th by adding 7 each time gives 5, 12, 19, 26 — the 26th appears, confirming it is a Saturday.
Takeaway
This only needs the Grade 2 idea that weekdays repeat every 7 days, so dates 7 apart share a day!
- Find the gap between the two dates
- Check that the gap is a whole number of weeks
- Read off the weekday
Where next?
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