← Weekdays repeat every seven days · Repeating Cycle Patterns

Weekdays repeat every seven days · 8 practice problems

2.NBT.A.2

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Generated variants — 8

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy

Part of a calendar for one month is shown. In this month, the 1th falls on a Wednesday. What day of the week is the 15th?

(The calendar row has weekday headings Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday; the dates are filled in so the 1th lands in the Wednesday column.)

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

In a month's calendar the 1th is a Wednesday. I need to find what day of the week the 15th is.

Givens

The 1th of the month falls on a Wednesday.
Weekdays run Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and then repeat.

Unknowns

The weekday of the 15th.

Constraints

The same weekday repeats every 7 days.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

A calendar repeats its weekdays every 7 days, so dates that share a column differ by a multiple of 7. Spotting this skip-counting-by-7 pattern is faster than writing out every single day.

3 · Execute3 carry out the plan

1Find the gap between the two dates

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

From the 1th to the 15th is 15 - 1 = 14 days later.

15 - 1 = 14

Subtracting to find how many days apart is Grade 2 subtraction.

2Check that the gap is a whole number of weeks

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

14 days is exactly 2 week(s) because 7 7 = 14 (skip-counting by 7). After any whole number of weeks the weekday is the same.

7 + 7 = 14

Skip-counting by 7 lands exactly on the gap, so the day stays in the same column.

3Read off the weekday

#1 Draw a Diagram 2.NBT.A.2

Because 14 days is a whole 2 week(s), the 15th is the same weekday as the 1th. The 1th is Wednesday, so the 15th is also Wednesday.

(3 + 14) \bmod 7 = 3

Stepping forward by the gap (counting weekdays mod 7) gives the answer's column.

Answer: Wednesday

4 · Reviewdoes it hold up?

Listing the Wednesday dates by adding 7 each time from the 1th, then stepping the leftover days, lands the 15th on Wednesday.

Another way: Draw the calendar grid and count forward 14 boxes from the 1th; you land in the Wednesday column.

Standardsmin grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 (and subtracting) to see how the weekday repeats and shifts.

💡Takeaway. This only needs the Grade 2 idea that weekdays repeat every 7 days, so dates 7 apart share a day!

Variant 2 easy

Part of a calendar for one month is shown. In this month, the 4th falls on a Tuesday. What day of the week is the 18th?

(The calendar row has weekday headings Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday; the dates are filled in so the 4th lands in the Tuesday column.)

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

In a month's calendar the 4th is a Tuesday. I need to find what day of the week the 18th is.

Givens

The 4th of the month falls on a Tuesday.
Weekdays run Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and then repeat.

Unknowns

The weekday of the 18th.

Constraints

The same weekday repeats every 7 days.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

A calendar repeats its weekdays every 7 days, so dates that share a column differ by a multiple of 7. Spotting this skip-counting-by-7 pattern is faster than writing out every single day.

3 · Execute3 carry out the plan

1Find the gap between the two dates

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

From the 4th to the 18th is 18 - 4 = 14 days later.

18 - 4 = 14

Subtracting to find how many days apart is Grade 2 subtraction.

2Check that the gap is a whole number of weeks

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

14 days is exactly 2 week(s) because 7 7 = 14 (skip-counting by 7). After any whole number of weeks the weekday is the same.

7 + 7 = 14

Skip-counting by 7 lands exactly on the gap, so the day stays in the same column.

3Read off the weekday

#1 Draw a Diagram 2.NBT.A.2

Because 14 days is a whole 2 week(s), the 18th is the same weekday as the 4th. The 4th is Tuesday, so the 18th is also Tuesday.

(2 + 14) \bmod 7 = 2

Stepping forward by the gap (counting weekdays mod 7) gives the answer's column.

Answer: Tuesday

4 · Reviewdoes it hold up?

Listing the Tuesday dates by adding 7 each time from the 4th, then stepping the leftover days, lands the 18th on Tuesday.

Another way: Draw the calendar grid and count forward 14 boxes from the 4th; you land in the Tuesday column.

Standardsmin grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 (and subtracting) to see how the weekday repeats and shifts.

💡Takeaway. This only needs the Grade 2 idea that weekdays repeat every 7 days, so dates 7 apart share a day!

Variant 3 medium

Part of a calendar for one month is shown. In this month, the 6th falls on a Thursday. What day of the week is the 20th?

(The calendar row has weekday headings Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday; the dates are filled in so the 6th lands in the Thursday column.)

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

In a month's calendar the 6th is a Thursday. I need to find what day of the week the 20th is.

Givens

The 6th of the month falls on a Thursday.
Weekdays run Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and then repeat.

Unknowns

The weekday of the 20th.

Constraints

The same weekday repeats every 7 days.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

A calendar repeats its weekdays every 7 days, so dates that share a column differ by a multiple of 7. Spotting this skip-counting-by-7 pattern is faster than writing out every single day.

3 · Execute3 carry out the plan

1Find the gap between the two dates

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

From the 6th to the 20th is 20 - 6 = 14 days later.

20 - 6 = 14

Subtracting to find how many days apart is Grade 2 subtraction.

2Check that the gap is a whole number of weeks

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

14 days is exactly 2 week(s) because 7 7 = 14 (skip-counting by 7). After any whole number of weeks the weekday is the same.

7 + 7 = 14

Skip-counting by 7 lands exactly on the gap, so the day stays in the same column.

3Read off the weekday

#1 Draw a Diagram 2.NBT.A.2

Because 14 days is a whole 2 week(s), the 20th is the same weekday as the 6th. The 6th is Thursday, so the 20th is also Thursday.

(4 + 14) \bmod 7 = 4

Stepping forward by the gap (counting weekdays mod 7) gives the answer's column.

Answer: Thursday

4 · Reviewdoes it hold up?

Listing the Thursday dates by adding 7 each time from the 6th, then stepping the leftover days, lands the 20th on Thursday.

Another way: Draw the calendar grid and count forward 14 boxes from the 6th; you land in the Thursday column.

Standardsmin grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 (and subtracting) to see how the weekday repeats and shifts.

💡Takeaway. This only needs the Grade 2 idea that weekdays repeat every 7 days, so dates 7 apart share a day!

Variant 4 medium

Part of a calendar for one month is shown. In this month, the 2th falls on a Friday. What day of the week is the 23th?

(The calendar row has weekday headings Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday; the dates are filled in so the 2th lands in the Friday column.)

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

In a month's calendar the 2th is a Friday. I need to find what day of the week the 23th is.

Givens

The 2th of the month falls on a Friday.
Weekdays run Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and then repeat.

Unknowns

The weekday of the 23th.

Constraints

The same weekday repeats every 7 days.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

A calendar repeats its weekdays every 7 days, so dates that share a column differ by a multiple of 7. Spotting this skip-counting-by-7 pattern is faster than writing out every single day.

3 · Execute3 carry out the plan

1Find the gap between the two dates

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

From the 2th to the 23th is 23 - 2 = 21 days later.

23 - 2 = 21

Subtracting to find how many days apart is Grade 2 subtraction.

2Check that the gap is a whole number of weeks

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

21 days is exactly 3 week(s) because 7 7 7 = 21 (skip-counting by 7). After any whole number of weeks the weekday is the same.

7 + 7 + 7 = 21

Skip-counting by 7 lands exactly on the gap, so the day stays in the same column.

3Read off the weekday

#1 Draw a Diagram 2.NBT.A.2

Because 21 days is a whole 3 week(s), the 23th is the same weekday as the 2th. The 2th is Friday, so the 23th is also Friday.

(5 + 21) \bmod 7 = 5

Stepping forward by the gap (counting weekdays mod 7) gives the answer's column.

Answer: Friday

4 · Reviewdoes it hold up?

Listing the Friday dates by adding 7 each time from the 2th, then stepping the leftover days, lands the 23th on Friday.

Another way: Draw the calendar grid and count forward 21 boxes from the 2th; you land in the Friday column.

Standardsmin grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 (and subtracting) to see how the weekday repeats and shifts.

💡Takeaway. This only needs the Grade 2 idea that weekdays repeat every 7 days, so dates 7 apart share a day!

Variant 5 medium

Part of a calendar for one month is shown. In this month, the 3th falls on a Monday. What day of the week is the 24th?

(The calendar row has weekday headings Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday; the dates are filled in so the 3th lands in the Monday column.)

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

In a month's calendar the 3th is a Monday. I need to find what day of the week the 24th is.

Givens

The 3th of the month falls on a Monday.
Weekdays run Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and then repeat.

Unknowns

The weekday of the 24th.

Constraints

The same weekday repeats every 7 days.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

A calendar repeats its weekdays every 7 days, so dates that share a column differ by a multiple of 7. Spotting this skip-counting-by-7 pattern is faster than writing out every single day.

3 · Execute3 carry out the plan

1Find the gap between the two dates

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

From the 3th to the 24th is 24 - 3 = 21 days later.

24 - 3 = 21

Subtracting to find how many days apart is Grade 2 subtraction.

2Check that the gap is a whole number of weeks

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

21 days is exactly 3 week(s) because 7 7 7 = 21 (skip-counting by 7). After any whole number of weeks the weekday is the same.

7 + 7 + 7 = 21

Skip-counting by 7 lands exactly on the gap, so the day stays in the same column.

3Read off the weekday

#1 Draw a Diagram 2.NBT.A.2

Because 21 days is a whole 3 week(s), the 24th is the same weekday as the 3th. The 3th is Monday, so the 24th is also Monday.

(1 + 21) \bmod 7 = 1

Stepping forward by the gap (counting weekdays mod 7) gives the answer's column.

Answer: Monday

4 · Reviewdoes it hold up?

Listing the Monday dates by adding 7 each time from the 3th, then stepping the leftover days, lands the 24th on Monday.

Another way: Draw the calendar grid and count forward 21 boxes from the 3th; you land in the Monday column.

Standardsmin grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 (and subtracting) to see how the weekday repeats and shifts.

💡Takeaway. This only needs the Grade 2 idea that weekdays repeat every 7 days, so dates 7 apart share a day!

Variant 6 medium

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?

(The calendar row has weekday headings Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday; the dates are filled in so the 5th lands in the Saturday column.)

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

In a month's calendar the 5th is a Saturday. I need to find what day of the week the 26th is.

Givens

The 5th of the month falls on a Saturday.
Weekdays run Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and then repeat.

Unknowns

The weekday of the 26th.

Constraints

The same weekday repeats every 7 days.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

A calendar repeats its weekdays every 7 days, so dates that share a column differ by a multiple of 7. Spotting this skip-counting-by-7 pattern is faster than writing out every single day.

3 · Execute3 carry out the plan

1Find the gap between the two dates

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

From the 5th to the 26th is 26 - 5 = 21 days later.

26 - 5 = 21

Subtracting to find how many days apart is Grade 2 subtraction.

2Check that the gap is a whole number of weeks

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

21 days is exactly 3 week(s) because 7 7 7 = 21 (skip-counting by 7). After any whole number of weeks the weekday is the same.

7 + 7 + 7 = 21

Skip-counting by 7 lands exactly on the gap, so the day stays in the same column.

3Read off the weekday

#1 Draw a Diagram 2.NBT.A.2

Because 21 days is a whole 3 week(s), the 26th is the same weekday as the 5th. The 5th is Saturday, so the 26th is also Saturday.

(6 + 21) \bmod 7 = 6

Stepping forward by the gap (counting weekdays mod 7) gives the answer's column.

Answer: Saturday

4 · Reviewdoes it hold up?

Listing the Saturday dates by adding 7 each time from the 5th, then stepping the leftover days, lands the 26th on Saturday.

Another way: Draw the calendar grid and count forward 21 boxes from the 5th; you land in the Saturday column.

Standardsmin grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 (and subtracting) to see how the weekday repeats and shifts.

💡Takeaway. This only needs the Grade 2 idea that weekdays repeat every 7 days, so dates 7 apart share a day!

Variant 7 hard

Part of a calendar for one month is shown. In this month, the 7th falls on a Sunday. What day of the week is the 28th?

(The calendar row has weekday headings Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday; the dates are filled in so the 7th lands in the Sunday column.)

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

In a month's calendar the 7th is a Sunday. I need to find what day of the week the 28th is.

Givens

The 7th of the month falls on a Sunday.
Weekdays run Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and then repeat.

Unknowns

The weekday of the 28th.

Constraints

The same weekday repeats every 7 days.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

A calendar repeats its weekdays every 7 days, so dates that share a column differ by a multiple of 7. Spotting this skip-counting-by-7 pattern is faster than writing out every single day.

3 · Execute3 carry out the plan

1Find the gap between the two dates

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

From the 7th to the 28th is 28 - 7 = 21 days later.

28 - 7 = 21

Subtracting to find how many days apart is Grade 2 subtraction.

2Check that the gap is a whole number of weeks

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

21 days is exactly 3 week(s) because 7 7 7 = 21 (skip-counting by 7). After any whole number of weeks the weekday is the same.

7 + 7 + 7 = 21

Skip-counting by 7 lands exactly on the gap, so the day stays in the same column.

3Read off the weekday

#1 Draw a Diagram 2.NBT.A.2

Because 21 days is a whole 3 week(s), the 28th is the same weekday as the 7th. The 7th is Sunday, so the 28th is also Sunday.

(0 + 21) \bmod 7 = 0

Stepping forward by the gap (counting weekdays mod 7) gives the answer's column.

Answer: Sunday

4 · Reviewdoes it hold up?

Listing the Sunday dates by adding 7 each time from the 7th, then stepping the leftover days, lands the 28th on Sunday.

Another way: Draw the calendar grid and count forward 21 boxes from the 7th; you land in the Sunday column.

Standardsmin grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 (and subtracting) to see how the weekday repeats and shifts.

💡Takeaway. This only needs the Grade 2 idea that weekdays repeat every 7 days, so dates 7 apart share a day!

Variant 8 hard

Part of a calendar for one month is shown. In this month, the 10th falls on a Monday. What day of the week is the 31th?

(The calendar row has weekday headings Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday; the dates are filled in so the 10th lands in the Monday column.)

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

In a month's calendar the 10th is a Monday. I need to find what day of the week the 31th is.

Givens

The 10th of the month falls on a Monday.
Weekdays run Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and then repeat.

Unknowns

The weekday of the 31th.

Constraints

The same weekday repeats every 7 days.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

A calendar repeats its weekdays every 7 days, so dates that share a column differ by a multiple of 7. Spotting this skip-counting-by-7 pattern is faster than writing out every single day.

3 · Execute3 carry out the plan

1Find the gap between the two dates

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

From the 10th to the 31th is 31 - 10 = 21 days later.

31 - 10 = 21

Subtracting to find how many days apart is Grade 2 subtraction.

2Check that the gap is a whole number of weeks

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

21 days is exactly 3 week(s) because 7 7 7 = 21 (skip-counting by 7). After any whole number of weeks the weekday is the same.

7 + 7 + 7 = 21

Skip-counting by 7 lands exactly on the gap, so the day stays in the same column.

3Read off the weekday

#1 Draw a Diagram 2.NBT.A.2

Because 21 days is a whole 3 week(s), the 31th is the same weekday as the 10th. The 10th is Monday, so the 31th is also Monday.

(1 + 21) \bmod 7 = 1

Stepping forward by the gap (counting weekdays mod 7) gives the answer's column.

Answer: Monday

4 · Reviewdoes it hold up?

Listing the Monday dates by adding 7 each time from the 10th, then stepping the leftover days, lands the 31th on Monday.

Another way: Draw the calendar grid and count forward 21 boxes from the 10th; you land in the Monday column.

Standardsmin grade 2

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Skip-counting by 7 (and subtracting) to see how the weekday repeats and shifts.

💡Takeaway. This only needs the Grade 2 idea that weekdays repeat every 7 days, so dates 7 apart share a day!

Where next?

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