Problem
Use the seven-day weekday cycle
On a June calendar the first Tuesday is the 1st. Using the rule that the same weekday repeats every 7 days, find the dates of all the Tuesdays in the month.
Operations
Your answer
Watch out Stop at the last date that still fits in the month — adding 7 past the 29th gives 36, which is not a real June date.
How to solve
Strategy Look for a Pattern — Weekdays repeat on a 7-day cycle, so I add 7 repeatedly starting from the first Tuesday and list each date until I pass the end of the month.
1STEP 1
Add 7 from the first Tuesday
Add 7 starting at the 1st: 8, 15, 22, 29. Next is 29+7=36, past June 30, so stop.
1, 1+7=8, 8+7=15, 15+7=22, 22+7=29
Skip-counting by 7 lands on the same weekday each time, so each jump gives the next Tuesday.
2.NBT.A.2Look For A PatternAdding 7 again and again, starting from the first Tuesday on the 1st, lands on the date of each following Tuesday.
Why?
Each following Tuesday sits a full 7 days after the Tuesday before it, so its date is 7 larger.
Why?
Tuesday comes back every 7 days because the weekday names run in a fixed loop of 7 that returns to where it started after 7 steps.
🧱A cycle returns after a full periodA fixed repeating cycle of length p comes back to the same position every p steps.
Why?
A gap of 7 single days raises the date by 7, since each day forward adds 1 and the seven days join with no gaps into one step of 7.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
Reaching every later Tuesday means taking that same 7-day step over and over, which is just adding the same 7 repeatedly.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
2STEP 2
List the Tuesdays within June
Keep only dates 30 or less: the Tuesdays are 1, 8, 15, 22, 29 — 36 is dropped.
{1, 8, 15, 22, 29}
Stopping before the date passes 30 keeps every Tuesday inside the month.
2.OA.B.2Make A Systematic ListAnswer
June 1, 8, 15, 22, and 29
Consecutive Tuesdays differ by exactly 7 (8-1, 15-8, 22-15, 29-22), and the last one, 29, is within 30, while the next, 36, is not. So June 1, 8, 15, 22, and 29 is correct for this month.
Takeaway
Tuesdays repeat every 7 days, so just keep adding 7: 1, 8, 15, 22, 29!
- Add 7 from the first Tuesday
- List the Tuesdays within June
Where next?
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