Use the seven-day weekday cycle

4.OA.C.5 · adapt · grade 4

Archetype: Repeating Cycle Patterns · step in a 6-type progression

The grid below is part of a calendar for the month of June one year. Using the rule that the same day of the week repeats every $7$ days, find the dates of every Tuesday in this month.

On the calendar the days of the week run in the order Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and the first Tuesday of this month falls on the $1$ st. Since the same weekday repeats every $7$ days, find the dates of the second, third, fourth, and fifth Tuesdays.

Show solution

Understand

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.

Givens

The first Tuesday falls on June 1.
The same weekday repeats every 7 days.
June has 30 days.

Unknowns

The dates of every Tuesday in June (the 2nd through 5th Tuesdays).

Constraints

Each Tuesday is 7 days after the previous Tuesday.
All Tuesday dates must be 30 or less (June has 30 days).

Plan

#5 Look for a Pattern · also uses: #2 Make a Systematic List

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.

Execute

#5 Look for a Pattern 2.NBT.A.2

Start at the 1st and add 7 each time: 1, 1+7=8, 8+7=15, 15+7=22, 22+7=29. The next would be 29+7=36, which is 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 Make a Systematic List 2.OA.B.2

Keeping only the dates that are 30 or less gives the Tuesdays: 1, 8, 15, 22, 29. (36 is dropped because June ends at 30.)

\{1,\ 8,\ 15,\ 22,\ 29\}

Stopping before the date passes 30 keeps every Tuesday inside the month.

Answer: June 1, 8, 15, 22, and 29

Review

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 five Tuesdays is correct for this month.

Look down the Tuesday column of the calendar grid directly; the entries read 1, 8, 15, 22, 29, matching the skip-count.

Standards · min grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 from the first Tuesday to reach each later Tuesday.
2.OA.B.2 Fluently add and subtract within 20 using mental strategies — Adding 7 at each step and checking dates stay within 30.

💡 Tuesdays repeat every 7 days, so just keep adding 7: 1, 8, 15, 22, 29!