← Find the rule of changing clock times · Repeating Cycle Patterns

Find the rule of changing clock times · 10 practice problems

2.MD.C.7

Generated variants — 10

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

Variant 1 easy answer: 6:05

The clocks change according to a fixed rule. Find the rule for how the clocks change, then find the time shown on the last clock.

Three clock faces are placed in a row from left to right, joined by arrows. The first shows $4{:}25$ , the second shows $5{:}15$ . Find the time shown on the third (last) clock.

Show solution

1 · Understandwhat's really being asked

Three clocks in a row change by a fixed rule. From the first 2 times, find the rule and use it to find the time on the third clock.

Givens

Clock 1 shows 4:25.
Clock 2 shows 5:15.

Unknowns

The time shown on the third (last) clock.

Constraints

The same time change is applied from each clock to the next.
60 minutes make 1 hour, so minutes past 60 roll over to the next hour.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #8 Analyze the Units

The times form a sequence, so I find how much time is added at each step (the pattern), then add that same amount to the last shown time, watching the minute-to-hour rollover (units).

3 · Execute2 carry out the plan

1Find the time added each step

#5 Look for a Pattern 2.MD.C.7

Comparing each clock to the next, the same jump of +50 minutes happens every time. So the rule is: add 50 minutes each time.

4{:}25 \xrightarrow{+50} 5{:}15

Reading each clock and comparing tells you the steady jump.

2Apply the rule once more

#8 Analyze the Units 2.MD.C.7

Add 50 minutes to 5:15. Since 15 + 50 = 65 minutes, that is 1 hour past the hour with 5 minutes left, so 5:15 becomes 6:05.

5{:}15 + 50\text{ min} = 6{:}05

When the minutes pass 60 you carry one hour, just like carrying in place value.

Answer: 6:05

4 · Reviewdoes it hold up?

Each step adds 50 minutes, and 6:05 continues that pattern from 5:15, so the answer fits the sequence.

Another way: Add up the total change: 2 steps of 50 minutes from 4:25 lands on the same time, 6:05.

Standardsmin grade 2

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the clock times and adding the fixed step including the hour rollover.

💡Takeaway. Each clock jumps 50 minutes, and when minutes pass 60 you just bump up one hour!

Variant 2 easy answer: 12:40

The clocks change according to a fixed rule. Find the rule for how the clocks change, then find the time shown on the last clock.

Three clock faces are placed in a row from left to right, joined by arrows. The first shows $11{:}50$ , the second shows $12{:}15$ . Find the time shown on the third (last) clock.

Show solution

1 · Understandwhat's really being asked

Three clocks in a row change by a fixed rule. From the first 2 times, find the rule and use it to find the time on the third clock.

Givens

Clock 1 shows 11:50.
Clock 2 shows 12:15.

Unknowns

The time shown on the third (last) clock.

Constraints

The same time change is applied from each clock to the next.
60 minutes make 1 hour, so minutes past 60 roll over to the next hour.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #8 Analyze the Units

The times form a sequence, so I find how much time is added at each step (the pattern), then add that same amount to the last shown time, watching the minute-to-hour rollover (units).

3 · Execute2 carry out the plan

1Find the time added each step

#5 Look for a Pattern 2.MD.C.7

Comparing each clock to the next, the same jump of +25 minutes happens every time. So the rule is: add 25 minutes each time.

11{:}50 \xrightarrow{+25} 12{:}15

Reading each clock and comparing tells you the steady jump.

2Apply the rule once more

#8 Analyze the Units 2.MD.C.7

Add 25 minutes to 12:15. Since 15 + 25 = 40 minutes (still under 60), the hour stays the same, so 12:15 becomes 12:40.

12{:}15 + 25\text{ min} = 12{:}40

When the minutes pass 60 you carry one hour, just like carrying in place value.

Answer: 12:40

4 · Reviewdoes it hold up?

Each step adds 25 minutes, and 12:40 continues that pattern from 12:15, so the answer fits the sequence.

Another way: Add up the total change: 2 steps of 25 minutes from 11:50 lands on the same time, 12:40.

Standardsmin grade 2

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the clock times and adding the fixed step including the hour rollover.

💡Takeaway. Each clock jumps 25 minutes, and when minutes pass 60 you just bump up one hour!

Variant 3 easy answer: 7:15

The clocks change according to a fixed rule. Find the rule for how the clocks change, then find the time shown on the last clock.

Four clock faces are placed in a row from left to right, joined by arrows. The first shows $5{:}45$ , the second shows $6{:}15$ , the third shows $6{:}45$ . Find the time shown on the fourth (last) clock.

Show solution

1 · Understandwhat's really being asked

Four clocks in a row change by a fixed rule. From the first 3 times, find the rule and use it to find the time on the fourth clock.

Givens

Clock 1 shows 5:45.
Clock 2 shows 6:15.
Clock 3 shows 6:45.

Unknowns

The time shown on the fourth (last) clock.

Constraints

The same time change is applied from each clock to the next.
60 minutes make 1 hour, so minutes past 60 roll over to the next hour.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #8 Analyze the Units

The times form a sequence, so I find how much time is added at each step (the pattern), then add that same amount to the last shown time, watching the minute-to-hour rollover (units).

3 · Execute2 carry out the plan

1Find the time added each step

#5 Look for a Pattern 2.MD.C.7

Comparing each clock to the next, the same jump of +30 minutes happens every time. So the rule is: add 30 minutes each time.

5{:}45 \xrightarrow{+30} 6{:}15 \xrightarrow{+30} 6{:}45

Reading each clock and comparing tells you the steady jump.

2Apply the rule once more

#8 Analyze the Units 2.MD.C.7

Add 30 minutes to 6:45. Since 45 + 30 = 75 minutes, that is 1 hour past the hour with 15 minutes left, so 6:45 becomes 7:15.

6{:}45 + 30\text{ min} = 7{:}15

When the minutes pass 60 you carry one hour, just like carrying in place value.

Answer: 7:15

4 · Reviewdoes it hold up?

Each step adds 30 minutes, and 7:15 continues that pattern from 6:45, so the answer fits the sequence.

Another way: Add up the total change: 3 steps of 30 minutes from 5:45 lands on the same time, 7:15.

Standardsmin grade 2

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the clock times and adding the fixed step including the hour rollover.

💡Takeaway. Each clock jumps 30 minutes, and when minutes pass 60 you just bump up one hour!

Variant 4 medium answer: 2:00

The clocks change according to a fixed rule. Find the rule for how the clocks change, then find the time shown on the last clock.

Four clock faces are placed in a row from left to right, joined by arrows. The first shows $12{:}15$ , the second shows $12{:}50$ , the third shows $1{:}25$ . Find the time shown on the fourth (last) clock.

Show solution

1 · Understandwhat's really being asked

Four clocks in a row change by a fixed rule. From the first 3 times, find the rule and use it to find the time on the fourth clock.

Givens

Clock 1 shows 12:15.
Clock 2 shows 12:50.
Clock 3 shows 1:25.

Unknowns

The time shown on the fourth (last) clock.

Constraints

The same time change is applied from each clock to the next.
60 minutes make 1 hour, so minutes past 60 roll over to the next hour.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #8 Analyze the Units

The times form a sequence, so I find how much time is added at each step (the pattern), then add that same amount to the last shown time, watching the minute-to-hour rollover (units).

3 · Execute2 carry out the plan

1Find the time added each step

#5 Look for a Pattern 2.MD.C.7

Comparing each clock to the next, the same jump of +35 minutes happens every time. So the rule is: add 35 minutes each time.

12{:}15 \xrightarrow{+35} 12{:}50 \xrightarrow{+35} 1{:}25

Reading each clock and comparing tells you the steady jump.

2Apply the rule once more

#8 Analyze the Units 2.MD.C.7

Add 35 minutes to 1:25. Since 25 + 35 = 60 minutes, that is 1 hour past the hour with 0 minutes left, so 1:25 becomes 2:00.

1{:}25 + 35\text{ min} = 2{:}00

When the minutes pass 60 you carry one hour, just like carrying in place value.

Answer: 2:00

4 · Reviewdoes it hold up?

Each step adds 35 minutes, and 2:00 continues that pattern from 1:25, so the answer fits the sequence.

Another way: Add up the total change: 3 steps of 35 minutes from 12:15 lands on the same time, 2:00.

Standardsmin grade 2

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the clock times and adding the fixed step including the hour rollover.

💡Takeaway. Each clock jumps 35 minutes, and when minutes pass 60 you just bump up one hour!

Variant 5 medium answer: 3:10

The clocks change according to a fixed rule. Find the rule for how the clocks change, then find the time shown on the last clock.

Four clock faces are placed in a row from left to right, joined by arrows. The first shows $2{:}10$ , the second shows $2{:}30$ , the third shows $2{:}50$ . Find the time shown on the fourth (last) clock.

Show solution

1 · Understandwhat's really being asked

Four clocks in a row change by a fixed rule. From the first 3 times, find the rule and use it to find the time on the fourth clock.

Givens

Clock 1 shows 2:10.
Clock 2 shows 2:30.
Clock 3 shows 2:50.

Unknowns

The time shown on the fourth (last) clock.

Constraints

The same time change is applied from each clock to the next.
60 minutes make 1 hour, so minutes past 60 roll over to the next hour.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #8 Analyze the Units

The times form a sequence, so I find how much time is added at each step (the pattern), then add that same amount to the last shown time, watching the minute-to-hour rollover (units).

3 · Execute2 carry out the plan

1Find the time added each step

#5 Look for a Pattern 2.MD.C.7

Comparing each clock to the next, the same jump of +20 minutes happens every time. So the rule is: add 20 minutes each time.

2{:}10 \xrightarrow{+20} 2{:}30 \xrightarrow{+20} 2{:}50

Reading each clock and comparing tells you the steady jump.

2Apply the rule once more

#8 Analyze the Units 2.MD.C.7

Add 20 minutes to 2:50. Since 50 + 20 = 70 minutes, that is 1 hour past the hour with 10 minutes left, so 2:50 becomes 3:10.

2{:}50 + 20\text{ min} = 3{:}10

When the minutes pass 60 you carry one hour, just like carrying in place value.

Answer: 3:10

4 · Reviewdoes it hold up?

Each step adds 20 minutes, and 3:10 continues that pattern from 2:50, so the answer fits the sequence.

Another way: Add up the total change: 3 steps of 20 minutes from 2:10 lands on the same time, 3:10.

Standardsmin grade 2

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the clock times and adding the fixed step including the hour rollover.

💡Takeaway. Each clock jumps 20 minutes, and when minutes pass 60 you just bump up one hour!

Variant 6 medium answer: 12:30

The clocks change according to a fixed rule. Find the rule for how the clocks change, then find the time shown on the last clock.

Five clock faces are placed in a row from left to right, joined by arrows. The first shows $9{:}30$ , the second shows $10{:}15$ , the third shows $11{:}00$ , the fourth shows $11{:}45$ . Find the time shown on the fifth (last) clock.

Show solution

1 · Understandwhat's really being asked

Five clocks in a row change by a fixed rule. From the first 4 times, find the rule and use it to find the time on the fifth clock.

Givens

Clock 1 shows 9:30.
Clock 2 shows 10:15.
Clock 3 shows 11:00.
Clock 4 shows 11:45.

Unknowns

The time shown on the fifth (last) clock.

Constraints

The same time change is applied from each clock to the next.
60 minutes make 1 hour, so minutes past 60 roll over to the next hour.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #8 Analyze the Units

The times form a sequence, so I find how much time is added at each step (the pattern), then add that same amount to the last shown time, watching the minute-to-hour rollover (units).

3 · Execute2 carry out the plan

1Find the time added each step

#5 Look for a Pattern 2.MD.C.7

Comparing each clock to the next, the same jump of +45 minutes happens every time. So the rule is: add 45 minutes each time.

9{:}30 \xrightarrow{+45} 10{:}15 \xrightarrow{+45} 11{:}00 \xrightarrow{+45} 11{:}45

Reading each clock and comparing tells you the steady jump.

2Apply the rule once more

#8 Analyze the Units 2.MD.C.7

Add 45 minutes to 11:45. Since 45 + 45 = 90 minutes, that is 1 hour past the hour with 30 minutes left, so 11:45 becomes 12:30.

11{:}45 + 45\text{ min} = 12{:}30

When the minutes pass 60 you carry one hour, just like carrying in place value.

Answer: 12:30

4 · Reviewdoes it hold up?

Each step adds 45 minutes, and 12:30 continues that pattern from 11:45, so the answer fits the sequence.

Another way: Add up the total change: 4 steps of 45 minutes from 9:30 lands on the same time, 12:30.

Standardsmin grade 2

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the clock times and adding the fixed step including the hour rollover.

💡Takeaway. Each clock jumps 45 minutes, and when minutes pass 60 you just bump up one hour!

Variant 7 medium answer: 2:00

The clocks change according to a fixed rule. Find the rule for how the clocks change, then find the time shown on the last clock.

Five clock faces are placed in a row from left to right, joined by arrows. The first shows $1{:}00$ , the second shows $1{:}15$ , the third shows $1{:}30$ , the fourth shows $1{:}45$ . Find the time shown on the fifth (last) clock.

Show solution

1 · Understandwhat's really being asked

Five clocks in a row change by a fixed rule. From the first 4 times, find the rule and use it to find the time on the fifth clock.

Givens

Clock 1 shows 1:00.
Clock 2 shows 1:15.
Clock 3 shows 1:30.
Clock 4 shows 1:45.

Unknowns

The time shown on the fifth (last) clock.

Constraints

The same time change is applied from each clock to the next.
60 minutes make 1 hour, so minutes past 60 roll over to the next hour.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #8 Analyze the Units

The times form a sequence, so I find how much time is added at each step (the pattern), then add that same amount to the last shown time, watching the minute-to-hour rollover (units).

3 · Execute2 carry out the plan

1Find the time added each step

#5 Look for a Pattern 2.MD.C.7

Comparing each clock to the next, the same jump of +15 minutes happens every time. So the rule is: add 15 minutes each time.

1{:}00 \xrightarrow{+15} 1{:}15 \xrightarrow{+15} 1{:}30 \xrightarrow{+15} 1{:}45

Reading each clock and comparing tells you the steady jump.

2Apply the rule once more

#8 Analyze the Units 2.MD.C.7

Add 15 minutes to 1:45. Since 45 + 15 = 60 minutes, that is 1 hour past the hour with 0 minutes left, so 1:45 becomes 2:00.

1{:}45 + 15\text{ min} = 2{:}00

When the minutes pass 60 you carry one hour, just like carrying in place value.

Answer: 2:00

4 · Reviewdoes it hold up?

Each step adds 15 minutes, and 2:00 continues that pattern from 1:45, so the answer fits the sequence.

Another way: Add up the total change: 4 steps of 15 minutes from 1:00 lands on the same time, 2:00.

Standardsmin grade 2

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the clock times and adding the fixed step including the hour rollover.

💡Takeaway. Each clock jumps 15 minutes, and when minutes pass 60 you just bump up one hour!

Variant 8 hard answer: 5:20

The clocks change according to a fixed rule. Find the rule for how the clocks change, then find the time shown on the last clock.

Five clock faces are placed in a row from left to right, joined by arrows. The first shows $3{:}20$ , the second shows $3{:}50$ , the third shows $4{:}20$ , the fourth shows $4{:}50$ . Find the time shown on the fifth (last) clock.

Show solution

1 · Understandwhat's really being asked

Five clocks in a row change by a fixed rule. From the first 4 times, find the rule and use it to find the time on the fifth clock.

Givens

Clock 1 shows 3:20.
Clock 2 shows 3:50.
Clock 3 shows 4:20.
Clock 4 shows 4:50.

Unknowns

The time shown on the fifth (last) clock.

Constraints

The same time change is applied from each clock to the next.
60 minutes make 1 hour, so minutes past 60 roll over to the next hour.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #8 Analyze the Units

The times form a sequence, so I find how much time is added at each step (the pattern), then add that same amount to the last shown time, watching the minute-to-hour rollover (units).

3 · Execute2 carry out the plan

1Find the time added each step

#5 Look for a Pattern 2.MD.C.7

Comparing each clock to the next, the same jump of +30 minutes happens every time. So the rule is: add 30 minutes each time.

3{:}20 \xrightarrow{+30} 3{:}50 \xrightarrow{+30} 4{:}20 \xrightarrow{+30} 4{:}50

Reading each clock and comparing tells you the steady jump.

2Apply the rule once more

#8 Analyze the Units 2.MD.C.7

Add 30 minutes to 4:50. Since 50 + 30 = 80 minutes, that is 1 hour past the hour with 20 minutes left, so 4:50 becomes 5:20.

4{:}50 + 30\text{ min} = 5{:}20

When the minutes pass 60 you carry one hour, just like carrying in place value.

Answer: 5:20

4 · Reviewdoes it hold up?

Each step adds 30 minutes, and 5:20 continues that pattern from 4:50, so the answer fits the sequence.

Another way: Add up the total change: 4 steps of 30 minutes from 3:20 lands on the same time, 5:20.

Standardsmin grade 2

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the clock times and adding the fixed step including the hour rollover.

💡Takeaway. Each clock jumps 30 minutes, and when minutes pass 60 you just bump up one hour!

Variant 9 hard answer: 7:00

The clocks change according to a fixed rule. Find the rule for how the clocks change, then find the time shown on the last clock.

Five clock faces are placed in a row from left to right, joined by arrows. The first shows $6{:}40$ , the second shows $6{:}45$ , the third shows $6{:}50$ , the fourth shows $6{:}55$ . Find the time shown on the fifth (last) clock.

Show solution

1 · Understandwhat's really being asked

Five clocks in a row change by a fixed rule. From the first 4 times, find the rule and use it to find the time on the fifth clock.

Givens

Clock 1 shows 6:40.
Clock 2 shows 6:45.
Clock 3 shows 6:50.
Clock 4 shows 6:55.

Unknowns

The time shown on the fifth (last) clock.

Constraints

The same time change is applied from each clock to the next.
60 minutes make 1 hour, so minutes past 60 roll over to the next hour.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #8 Analyze the Units

The times form a sequence, so I find how much time is added at each step (the pattern), then add that same amount to the last shown time, watching the minute-to-hour rollover (units).

3 · Execute2 carry out the plan

1Find the time added each step

#5 Look for a Pattern 2.MD.C.7

Comparing each clock to the next, the same jump of +5 minutes happens every time. So the rule is: add 5 minutes each time.

6{:}40 \xrightarrow{+5} 6{:}45 \xrightarrow{+5} 6{:}50 \xrightarrow{+5} 6{:}55

Reading each clock and comparing tells you the steady jump.

2Apply the rule once more

#8 Analyze the Units 2.MD.C.7

Add 5 minutes to 6:55. Since 55 + 5 = 60 minutes, that is 1 hour past the hour with 0 minutes left, so 6:55 becomes 7:00.

6{:}55 + 5\text{ min} = 7{:}00

When the minutes pass 60 you carry one hour, just like carrying in place value.

Answer: 7:00

4 · Reviewdoes it hold up?

Each step adds 5 minutes, and 7:00 continues that pattern from 6:55, so the answer fits the sequence.

Another way: Add up the total change: 4 steps of 5 minutes from 6:40 lands on the same time, 7:00.

Standardsmin grade 2

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the clock times and adding the fixed step including the hour rollover.

💡Takeaway. Each clock jumps 5 minutes, and when minutes pass 60 you just bump up one hour!

Variant 10 hard answer: 7:55

The clocks change according to a fixed rule. Find the rule for how the clocks change, then find the time shown on the last clock.

Six clock faces are placed in a row from left to right, joined by arrows. The first shows $7{:}05$ , the second shows $7{:}15$ , the third shows $7{:}25$ , the fourth shows $7{:}35$ , the fifth shows $7{:}45$ . Find the time shown on the sixth (last) clock.

Show solution

1 · Understandwhat's really being asked

Six clocks in a row change by a fixed rule. From the first 5 times, find the rule and use it to find the time on the sixth clock.

Givens

Clock 1 shows 7:05.
Clock 2 shows 7:15.
Clock 3 shows 7:25.
Clock 4 shows 7:35.
Clock 5 shows 7:45.

Unknowns

The time shown on the sixth (last) clock.

Constraints

The same time change is applied from each clock to the next.
60 minutes make 1 hour, so minutes past 60 roll over to the next hour.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #8 Analyze the Units

The times form a sequence, so I find how much time is added at each step (the pattern), then add that same amount to the last shown time, watching the minute-to-hour rollover (units).

3 · Execute2 carry out the plan

1Find the time added each step

#5 Look for a Pattern 2.MD.C.7

Comparing each clock to the next, the same jump of +10 minutes happens every time. So the rule is: add 10 minutes each time.

7{:}05 \xrightarrow{+10} 7{:}15 \xrightarrow{+10} 7{:}25 \xrightarrow{+10} 7{:}35 \xrightarrow{+10} 7{:}45

Reading each clock and comparing tells you the steady jump.

2Apply the rule once more

#8 Analyze the Units 2.MD.C.7

Add 10 minutes to 7:45. Since 45 + 10 = 55 minutes (still under 60), the hour stays the same, so 7:45 becomes 7:55.

7{:}45 + 10\text{ min} = 7{:}55

When the minutes pass 60 you carry one hour, just like carrying in place value.

Answer: 7:55

4 · Reviewdoes it hold up?

Each step adds 10 minutes, and 7:55 continues that pattern from 7:45, so the answer fits the sequence.

Another way: Add up the total change: 5 steps of 10 minutes from 7:05 lands on the same time, 7:55.

Standardsmin grade 2

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the clock times and adding the fixed step including the hour rollover.

💡Takeaway. Each clock jumps 10 minutes, and when minutes pass 60 you just bump up one hour!