← Use the seven-day weekday cycle · Repeating Cycle Patterns

Use the seven-day weekday cycle · 10 practice problems

2.NBT.A.22.OA.B.2

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Generated variants — 10

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Variant 1 medium

The grid below is part of a calendar for the month of November one year. Using the rule that the same day of the week repeats every $7$ days, find the dates of every Thursday 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 Thursday of this month falls on the $3$ rd. Since the same weekday repeats every $7$ days, find the dates of the second, third, and fourth Thursdays.

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1 · Understandwhat's really being asked

On a November calendar the first Thursday is the 3rd. Using the rule that the same weekday repeats every 7 days, find the dates of all the Thursdays in the month.

Givens

The first Thursday falls on November 3.
The same weekday repeats every 7 days.
November has 30 days.

Unknowns

The dates of every Thursday in November.

Constraints

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

2 · Planchoose the strategy

#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 occurrence and list each date until I pass the end of the month.

3 · Execute2 carry out the plan

1Add 7 from the first Thursday

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

Start at the 3rd and add 7 each time: 3, 3{+}7{=}10, 10{+}7{=}17, 17{+}7{=}24. The next would be 24+7=31, which is past November 30, so stop.

3, 3{+}7{=}10, 10{+}7{=}17, 17{+}7{=}24

Skip-counting by 7 lands on the same weekday each time, so each jump gives the next Thursday.

2List the Thursdays within November

#2 Make a Systematic List 2.OA.B.2

Keeping only the dates that are 30 or less gives the Thursdays: 3, 10, 17, and 24. (31 is dropped because November ends at 30.)

\{3,\ 10,\ 17,\ 24\}

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

Answer: November 3, 10, 17, and 24

4 · Reviewdoes it hold up?

Consecutive Thursdays differ by exactly 7 (10-3, 17-10, 24-17), and the last one, 24, is within 30, while the next, 31, is not. So 4 Thursdays is correct for this month.

Another way: Look down the Thursday column of the calendar grid directly; the entries read 3, 10, 17, 24, matching the skip-count.

Standardsmin grade 2

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

💡Takeaway. Thursdays repeat every 7 days, so just keep adding 7: 3, 10, 17, 24!

Variant 2 medium

The grid below is part of a calendar for the month of February one year. Using the rule that the same day of the week repeats every $7$ days, find the dates of every Saturday 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 Saturday of this month falls on the $4$ th. Since the same weekday repeats every $7$ days, find the dates of the second, third, and fourth Saturdays.

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1 · Understandwhat's really being asked

On a February calendar the first Saturday is the 4th. Using the rule that the same weekday repeats every 7 days, find the dates of all the Saturdays in the month.

Givens

The first Saturday falls on February 4.
The same weekday repeats every 7 days.
February has 28 days.

Unknowns

The dates of every Saturday in February.

Constraints

Each Saturday is 7 days after the previous Saturday.
All Saturday dates must be 28 or less (February has 28 days).

2 · Planchoose the strategy

#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 occurrence and list each date until I pass the end of the month.

3 · Execute2 carry out the plan

1Add 7 from the first Saturday

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

Start at the 4th and add 7 each time: 4, 4{+}7{=}11, 11{+}7{=}18, 18{+}7{=}25. The next would be 25+7=32, which is past February 28, so stop.

4, 4{+}7{=}11, 11{+}7{=}18, 18{+}7{=}25

Skip-counting by 7 lands on the same weekday each time, so each jump gives the next Saturday.

2List the Saturdays within February

#2 Make a Systematic List 2.OA.B.2

Keeping only the dates that are 28 or less gives the Saturdays: 4, 11, 18, and 25. (32 is dropped because February ends at 28.)

\{4,\ 11,\ 18,\ 25\}

Stopping before the date passes 28 keeps every Saturday inside the month.

Answer: February 4, 11, 18, and 25

4 · Reviewdoes it hold up?

Consecutive Saturdays differ by exactly 7 (11-4, 18-11, 25-18), and the last one, 25, is within 28, while the next, 32, is not. So 4 Saturdays is correct for this month.

Another way: Look down the Saturday column of the calendar grid directly; the entries read 4, 11, 18, 25, matching the skip-count.

Standardsmin grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 from the first Saturday to reach each later Saturday.
2.OA.B.2 Fluently add and subtract within 20 using mental strategies — Adding 7 at each step and checking dates stay within 28.

💡Takeaway. Saturdays repeat every 7 days, so just keep adding 7: 4, 11, 18, 25!

Variant 3 medium

The grid below is part of a calendar for the month of July one year. Using the rule that the same day of the week repeats every $7$ days, find the dates of every Wednesday 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 Wednesday of this month falls on the $4$ th. Since the same weekday repeats every $7$ days, find the dates of the second, third, and fourth Wednesdays.

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1 · Understandwhat's really being asked

On a July calendar the first Wednesday is the 4th. Using the rule that the same weekday repeats every 7 days, find the dates of all the Wednesdays in the month.

Givens

The first Wednesday falls on July 4.
The same weekday repeats every 7 days.
July has 31 days.

Unknowns

The dates of every Wednesday in July.

Constraints

Each Wednesday is 7 days after the previous Wednesday.
All Wednesday dates must be 31 or less (July has 31 days).

2 · Planchoose the strategy

#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 occurrence and list each date until I pass the end of the month.

3 · Execute2 carry out the plan

1Add 7 from the first Wednesday

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

Start at the 4th and add 7 each time: 4, 4{+}7{=}11, 11{+}7{=}18, 18{+}7{=}25. The next would be 25+7=32, which is past July 31, so stop.

4, 4{+}7{=}11, 11{+}7{=}18, 18{+}7{=}25

Skip-counting by 7 lands on the same weekday each time, so each jump gives the next Wednesday.

2List the Wednesdays within July

#2 Make a Systematic List 2.OA.B.2

Keeping only the dates that are 31 or less gives the Wednesdays: 4, 11, 18, and 25. (32 is dropped because July ends at 31.)

\{4,\ 11,\ 18,\ 25\}

Stopping before the date passes 31 keeps every Wednesday inside the month.

Answer: July 4, 11, 18, and 25

4 · Reviewdoes it hold up?

Consecutive Wednesdays differ by exactly 7 (11-4, 18-11, 25-18), and the last one, 25, is within 31, while the next, 32, is not. So 4 Wednesdays is correct for this month.

Another way: Look down the Wednesday column of the calendar grid directly; the entries read 4, 11, 18, 25, matching the skip-count.

Standardsmin grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 from the first Wednesday to reach each later Wednesday.
2.OA.B.2 Fluently add and subtract within 20 using mental strategies — Adding 7 at each step and checking dates stay within 31.

💡Takeaway. Wednesdays repeat every 7 days, so just keep adding 7: 4, 11, 18, 25!

Variant 4 medium

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

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

On a August calendar the first Wednesday is the 1st. Using the rule that the same weekday repeats every 7 days, find the dates of all the Wednesdays in the month.

Givens

The first Wednesday falls on August 1.
The same weekday repeats every 7 days.
August has 31 days.

Unknowns

The dates of every Wednesday in August.

Constraints

Each Wednesday is 7 days after the previous Wednesday.
All Wednesday dates must be 31 or less (August has 31 days).

2 · Planchoose the strategy

#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 occurrence and list each date until I pass the end of the month.

3 · Execute2 carry out the plan

1Add 7 from the first Wednesday

#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 August 31, 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 Wednesday.

2List the Wednesdays within August

#2 Make a Systematic List 2.OA.B.2

Keeping only the dates that are 31 or less gives the Wednesdays: 1, 8, 15, 22, and 29. (36 is dropped because August ends at 31.)

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

Stopping before the date passes 31 keeps every Wednesday inside the month.

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

4 · Reviewdoes it hold up?

Consecutive Wednesdays differ by exactly 7 (8-1, 15-8, 22-15, 29-22), and the last one, 29, is within 31, while the next, 36, is not. So 5 Wednesdays is correct for this month.

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

Standardsmin grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 from the first Wednesday to reach each later Wednesday.
2.OA.B.2 Fluently add and subtract within 20 using mental strategies — Adding 7 at each step and checking dates stay within 31.

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

Variant 5 medium

The grid below is part of a calendar for the month of September one year. Using the rule that the same day of the week repeats every $7$ days, find the dates of every Sunday 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 Sunday of this month falls on the $4$ th. Since the same weekday repeats every $7$ days, find the dates of the second, third, and fourth Sundays.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

On a September calendar the first Sunday is the 4th. Using the rule that the same weekday repeats every 7 days, find the dates of all the Sundays in the month.

Givens

The first Sunday falls on September 4.
The same weekday repeats every 7 days.
September has 30 days.

Unknowns

The dates of every Sunday in September.

Constraints

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

2 · Planchoose the strategy

#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 occurrence and list each date until I pass the end of the month.

3 · Execute2 carry out the plan

1Add 7 from the first Sunday

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

Start at the 4th and add 7 each time: 4, 4{+}7{=}11, 11{+}7{=}18, 18{+}7{=}25. The next would be 25+7=32, which is past September 30, so stop.

4, 4{+}7{=}11, 11{+}7{=}18, 18{+}7{=}25

Skip-counting by 7 lands on the same weekday each time, so each jump gives the next Sunday.

2List the Sundays within September

#2 Make a Systematic List 2.OA.B.2

Keeping only the dates that are 30 or less gives the Sundays: 4, 11, 18, and 25. (32 is dropped because September ends at 30.)

\{4,\ 11,\ 18,\ 25\}

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

Answer: September 4, 11, 18, and 25

4 · Reviewdoes it hold up?

Consecutive Sundays differ by exactly 7 (11-4, 18-11, 25-18), and the last one, 25, is within 30, while the next, 32, is not. So 4 Sundays is correct for this month.

Another way: Look down the Sunday column of the calendar grid directly; the entries read 4, 11, 18, 25, matching the skip-count.

Standardsmin grade 2

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

💡Takeaway. Sundays repeat every 7 days, so just keep adding 7: 4, 11, 18, 25!

Variant 6 medium

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

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

On a May calendar the first Sunday is the 1st. Using the rule that the same weekday repeats every 7 days, find the dates of all the Sundays in the month.

Givens

The first Sunday falls on May 1.
The same weekday repeats every 7 days.
May has 31 days.

Unknowns

The dates of every Sunday in May.

Constraints

Each Sunday is 7 days after the previous Sunday.
All Sunday dates must be 31 or less (May has 31 days).

2 · Planchoose the strategy

#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 occurrence and list each date until I pass the end of the month.

3 · Execute2 carry out the plan

1Add 7 from the first Sunday

#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 May 31, 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 Sunday.

2List the Sundays within May

#2 Make a Systematic List 2.OA.B.2

Keeping only the dates that are 31 or less gives the Sundays: 1, 8, 15, 22, and 29. (36 is dropped because May ends at 31.)

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

Stopping before the date passes 31 keeps every Sunday inside the month.

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

4 · Reviewdoes it hold up?

Consecutive Sundays differ by exactly 7 (8-1, 15-8, 22-15, 29-22), and the last one, 29, is within 31, while the next, 36, is not. So 5 Sundays is correct for this month.

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

Standardsmin grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 from the first Sunday to reach each later Sunday.
2.OA.B.2 Fluently add and subtract within 20 using mental strategies — Adding 7 at each step and checking dates stay within 31.

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

Variant 7 medium

The grid below is part of a calendar for the month of March one year. Using the rule that the same day of the week repeats every $7$ days, find the dates of every Monday 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 Monday of this month falls on the $4$ th. Since the same weekday repeats every $7$ days, find the dates of the second, third, and fourth Mondays.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

On a March calendar the first Monday is the 4th. Using the rule that the same weekday repeats every 7 days, find the dates of all the Mondays in the month.

Givens

The first Monday falls on March 4.
The same weekday repeats every 7 days.
March has 31 days.

Unknowns

The dates of every Monday in March.

Constraints

Each Monday is 7 days after the previous Monday.
All Monday dates must be 31 or less (March has 31 days).

2 · Planchoose the strategy

#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 occurrence and list each date until I pass the end of the month.

3 · Execute2 carry out the plan

1Add 7 from the first Monday

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

Start at the 4th and add 7 each time: 4, 4{+}7{=}11, 11{+}7{=}18, 18{+}7{=}25. The next would be 25+7=32, which is past March 31, so stop.

4, 4{+}7{=}11, 11{+}7{=}18, 18{+}7{=}25

Skip-counting by 7 lands on the same weekday each time, so each jump gives the next Monday.

2List the Mondays within March

#2 Make a Systematic List 2.OA.B.2

Keeping only the dates that are 31 or less gives the Mondays: 4, 11, 18, and 25. (32 is dropped because March ends at 31.)

\{4,\ 11,\ 18,\ 25\}

Stopping before the date passes 31 keeps every Monday inside the month.

Answer: March 4, 11, 18, and 25

4 · Reviewdoes it hold up?

Consecutive Mondays differ by exactly 7 (11-4, 18-11, 25-18), and the last one, 25, is within 31, while the next, 32, is not. So 4 Mondays is correct for this month.

Another way: Look down the Monday column of the calendar grid directly; the entries read 4, 11, 18, 25, matching the skip-count.

Standardsmin grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 from the first Monday to reach each later Monday.
2.OA.B.2 Fluently add and subtract within 20 using mental strategies — Adding 7 at each step and checking dates stay within 31.

💡Takeaway. Mondays repeat every 7 days, so just keep adding 7: 4, 11, 18, 25!

Variant 8 medium

The grid below is part of a calendar for the month of October 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 $4$ th. Since the same weekday repeats every $7$ days, find the dates of the second, third, and fourth Tuesdays.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

On a October calendar the first Tuesday is the 4th. 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 October 4.
The same weekday repeats every 7 days.
October has 31 days.

Unknowns

The dates of every Tuesday in October.

Constraints

Each Tuesday is 7 days after the previous Tuesday.
All Tuesday dates must be 31 or less (October has 31 days).

2 · Planchoose the strategy

#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 occurrence and list each date until I pass the end of the month.

3 · Execute2 carry out the plan

1Add 7 from the first Tuesday

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

Start at the 4th and add 7 each time: 4, 4{+}7{=}11, 11{+}7{=}18, 18{+}7{=}25. The next would be 25+7=32, which is past October 31, so stop.

4, 4{+}7{=}11, 11{+}7{=}18, 18{+}7{=}25

Skip-counting by 7 lands on the same weekday each time, so each jump gives the next Tuesday.

2List the Tuesdays within October

#2 Make a Systematic List 2.OA.B.2

Keeping only the dates that are 31 or less gives the Tuesdays: 4, 11, 18, and 25. (32 is dropped because October ends at 31.)

\{4,\ 11,\ 18,\ 25\}

Stopping before the date passes 31 keeps every Tuesday inside the month.

Answer: October 4, 11, 18, and 25

4 · Reviewdoes it hold up?

Consecutive Tuesdays differ by exactly 7 (11-4, 18-11, 25-18), and the last one, 25, is within 31, while the next, 32, is not. So 4 Tuesdays is correct for this month.

Another way: Look down the Tuesday column of the calendar grid directly; the entries read 4, 11, 18, 25, matching the skip-count.

Standardsmin 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 31.

💡Takeaway. Tuesdays repeat every 7 days, so just keep adding 7: 4, 11, 18, 25!

Variant 9 medium

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.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

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.

Constraints

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

2 · Planchoose the strategy

#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 occurrence and list each date until I pass the end of the month.

3 · Execute2 carry out the plan

1Add 7 from the first Tuesday

#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.

2List the Tuesdays within June

#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, and 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

4 · Reviewdoes it hold up?

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 5 Tuesdays is correct for this month.

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

Standardsmin 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.

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

Variant 10 medium

The grid below is part of a calendar for the month of April one year. Using the rule that the same day of the week repeats every $7$ days, find the dates of every Friday 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 Friday of this month falls on the $5$ th. Since the same weekday repeats every $7$ days, find the dates of the second, third, and fourth Fridays.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

On a April calendar the first Friday is the 5th. Using the rule that the same weekday repeats every 7 days, find the dates of all the Fridays in the month.

Givens

The first Friday falls on April 5.
The same weekday repeats every 7 days.
April has 30 days.

Unknowns

The dates of every Friday in April.

Constraints

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

2 · Planchoose the strategy

#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 occurrence and list each date until I pass the end of the month.

3 · Execute2 carry out the plan

1Add 7 from the first Friday

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

Start at the 5th and add 7 each time: 5, 5{+}7{=}12, 12{+}7{=}19, 19{+}7{=}26. The next would be 26+7=33, which is past April 30, so stop.

5, 5{+}7{=}12, 12{+}7{=}19, 19{+}7{=}26

Skip-counting by 7 lands on the same weekday each time, so each jump gives the next Friday.

2List the Fridays within April

#2 Make a Systematic List 2.OA.B.2

Keeping only the dates that are 30 or less gives the Fridays: 5, 12, 19, and 26. (33 is dropped because April ends at 30.)

\{5,\ 12,\ 19,\ 26\}

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

Answer: April 5, 12, 19, and 26

4 · Reviewdoes it hold up?

Consecutive Fridays differ by exactly 7 (12-5, 19-12, 26-19), and the last one, 26, is within 30, while the next, 33, is not. So 4 Fridays is correct for this month.

Another way: Look down the Friday column of the calendar grid directly; the entries read 5, 12, 19, 26, matching the skip-count.

Standardsmin grade 2

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

💡Takeaway. Fridays repeat every 7 days, so just keep adding 7: 5, 12, 19, 26!

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