← Time regroups in base sixty · Elapsed Time and Base-Sixty Regrouping

Time regroups in base sixty · 10 practice problems

3.MD.A.13.OA.A.3

Generated variants — 10

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

Variant 1 easy answer: 10:50

The class schedule at Mia's school is shown below. Find the time that the 3rd period starts.

Period	Start time	Class length	Break
1st period	9:10	40 min	10 min
2nd period		40 min	10 min
3rd period

The 1st period starts at 9:10. Each period lasts 40 minutes and is followed by a 10-minute break.

Show solution

1 · Understandwhat's really being asked

Periods at Mia's school each last 40 minutes and are followed by a 10-minute break. The 1st period starts at 9:10. I need to find what time the 3rd period begins.

Givens

1st period starts at 9:10.
Each period is 40 minutes long.
After each period there is a 10-minute break.

Unknowns

The start time of the 3rd period.

Constraints

60 minutes = 1 hour (regroup when minutes reach 60).
Between the start of one period and the start of the next is 40 + 10 = 50 minutes.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Each period-then-break repeats the same 50-minute block, so the gap from one start to the next is constant. Finding that pattern lets me add 2 of these blocks to reach the 3rd period, regrouping minutes into hours as needed.

3 · Execute4 carry out the plan

1Find the gap between consecutive period starts

#5 Look for a Pattern 3.MD.A.1

A period is 40 minutes and the following break is 10 minutes, so the next period starts 40 + 10 = 50 minutes after the previous one started.

40 + 10 = 50 \text{ min}

The same 'class then break' chunk repeats, so each start is one fixed step after the last.

2Count how many gaps to the 3rd period

#7 Identify Subproblems 3.OA.A.3

From the 1st period to the 3rd period there are 2 gaps. Each gap is 50 minutes.

2 \times 50 = 100 \text{ min}

2 equal 50-minute jumps gets you from the 1st start to the 3rd start.

3Convert 100 minutes to hours and minutes

#7 Identify Subproblems 3.MD.A.1

Regroup 100 minutes using 60 minutes = 1 hour: 100 = 60 + 40, so 100 minutes is 1 hour(s) 40 minute(s).

100 \text{ min} = 1 \text{ h } 40 \text{ min}

Trading every 60 minutes for an hour is the base-sixty regrouping kids use for clocks.

4Add the elapsed time to the start time

#7 Identify Subproblems 3.MD.A.1

Add 1 h 40 min to 9:10. Carry an hour whenever the minutes pass 60 to land on 10:50.

9:10 + 1{:}40 = 10:50

When the minutes pass 60 you carry an hour, just like reading the clock forward.

Answer: 10:50

4 · Reviewdoes it hold up?

Each period plus break is 50 minutes, so 3 periods span about 1 h 40 min; starting at 9:10 and reaching 10:50 is a sensible school schedule.

Another way: Make a systematic list: 1st 9:10, 2nd 10:00, 3rd 10:50 - adding 50 minutes each line gives the same 10:50.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Adding elapsed minutes to a start time and regrouping minutes into hours.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying 2 gaps x 50 minutes to find the total elapsed time.

💡Takeaway. Spot the repeating 50-minute 'class + break' chunk, multiply by 2, and add - that's all Grade 3 time sense!

Variant 2 easy answer: 10:20

The class schedule at Mia's school is shown below. Find the time that the 3rd period starts.

Period	Start time	Class length	Break
1st period	8:20	45 min	15 min
2nd period		45 min	15 min
3rd period

The 1st period starts at 8:20. Each period lasts 45 minutes and is followed by a 15-minute break.

Show solution

1 · Understandwhat's really being asked

Periods at Mia's school each last 45 minutes and are followed by a 15-minute break. The 1st period starts at 8:20. I need to find what time the 3rd period begins.

Givens

1st period starts at 8:20.
Each period is 45 minutes long.
After each period there is a 15-minute break.

Unknowns

The start time of the 3rd period.

Constraints

60 minutes = 1 hour (regroup when minutes reach 60).
Between the start of one period and the start of the next is 45 + 15 = 60 minutes.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Each period-then-break repeats the same 60-minute block, so the gap from one start to the next is constant. Finding that pattern lets me add 2 of these blocks to reach the 3rd period, regrouping minutes into hours as needed.

3 · Execute4 carry out the plan

1Find the gap between consecutive period starts

#5 Look for a Pattern 3.MD.A.1

A period is 45 minutes and the following break is 15 minutes, so the next period starts 45 + 15 = 60 minutes after the previous one started.

45 + 15 = 60 \text{ min}

The same 'class then break' chunk repeats, so each start is one fixed step after the last.

2Count how many gaps to the 3rd period

#7 Identify Subproblems 3.OA.A.3

From the 1st period to the 3rd period there are 2 gaps. Each gap is 60 minutes.

2 \times 60 = 120 \text{ min}

2 equal 60-minute jumps gets you from the 1st start to the 3rd start.

3Convert 120 minutes to hours and minutes

#7 Identify Subproblems 3.MD.A.1

Regroup 120 minutes using 60 minutes = 1 hour: 120 = 120 + 0, so 120 minutes is 2 hour(s) 0 minute(s).

120 \text{ min} = 2 \text{ h } 0 \text{ min}

Trading every 60 minutes for an hour is the base-sixty regrouping kids use for clocks.

4Add the elapsed time to the start time

#7 Identify Subproblems 3.MD.A.1

Add 2 h 0 min to 8:20. Carry an hour whenever the minutes pass 60 to land on 10:20.

8:20 + 2{:}00 = 10:20

When the minutes pass 60 you carry an hour, just like reading the clock forward.

Answer: 10:20

4 · Reviewdoes it hold up?

Each period plus break is 60 minutes, so 3 periods span about 2 h 0 min; starting at 8:20 and reaching 10:20 is a sensible school schedule.

Another way: Make a systematic list: 1st 8:20, 2nd 9:20, 3rd 10:20 - adding 60 minutes each line gives the same 10:20.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Adding elapsed minutes to a start time and regrouping minutes into hours.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying 2 gaps x 60 minutes to find the total elapsed time.

💡Takeaway. Spot the repeating 60-minute 'class + break' chunk, multiply by 2, and add - that's all Grade 3 time sense!

Variant 3 easy answer: 11:45

The class schedule at Mia's school is shown below. Find the time that the 4th period starts.

Period	Start time	Class length	Break
1st period	9:00	45 min	10 min
2nd period		45 min	10 min
3rd period		45 min	10 min
4th period

The 1st period starts at 9:00. Each period lasts 45 minutes and is followed by a 10-minute break.

Show solution

1 · Understandwhat's really being asked

Periods at Mia's school each last 45 minutes and are followed by a 10-minute break. The 1st period starts at 9:00. I need to find what time the 4th period begins.

Givens

1st period starts at 9:00.
Each period is 45 minutes long.
After each period there is a 10-minute break.

Unknowns

The start time of the 4th period.

Constraints

60 minutes = 1 hour (regroup when minutes reach 60).
Between the start of one period and the start of the next is 45 + 10 = 55 minutes.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Each period-then-break repeats the same 55-minute block, so the gap from one start to the next is constant. Finding that pattern lets me add 3 of these blocks to reach the 4th period, regrouping minutes into hours as needed.

3 · Execute4 carry out the plan

1Find the gap between consecutive period starts

#5 Look for a Pattern 3.MD.A.1

A period is 45 minutes and the following break is 10 minutes, so the next period starts 45 + 10 = 55 minutes after the previous one started.

45 + 10 = 55 \text{ min}

The same 'class then break' chunk repeats, so each start is one fixed step after the last.

2Count how many gaps to the 4th period

#7 Identify Subproblems 3.OA.A.3

From the 1st period to the 4th period there are 3 gaps. Each gap is 55 minutes.

3 \times 55 = 165 \text{ min}

3 equal 55-minute jumps gets you from the 1st start to the 4th start.

3Convert 165 minutes to hours and minutes

#7 Identify Subproblems 3.MD.A.1

Regroup 165 minutes using 60 minutes = 1 hour: 165 = 120 + 45, so 165 minutes is 2 hour(s) 45 minute(s).

165 \text{ min} = 2 \text{ h } 45 \text{ min}

Trading every 60 minutes for an hour is the base-sixty regrouping kids use for clocks.

4Add the elapsed time to the start time

#7 Identify Subproblems 3.MD.A.1

Add 2 h 45 min to 9:00. Carry an hour whenever the minutes pass 60 to land on 11:45.

9:00 + 2{:}45 = 11:45

When the minutes pass 60 you carry an hour, just like reading the clock forward.

Answer: 11:45

4 · Reviewdoes it hold up?

Each period plus break is 55 minutes, so 4 periods span about 2 h 45 min; starting at 9:00 and reaching 11:45 is a sensible school schedule.

Another way: Make a systematic list: 1st 9:00, 2nd 9:55, 3rd 10:50, 4th 11:45 - adding 55 minutes each line gives the same 11:45.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Adding elapsed minutes to a start time and regrouping minutes into hours.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying 3 gaps x 55 minutes to find the total elapsed time.

💡Takeaway. Spot the repeating 55-minute 'class + break' chunk, multiply by 3, and add - that's all Grade 3 time sense!

Variant 4 medium answer: 11:00

The class schedule at Mia's school is shown below. Find the time that the 4th period starts.

Period	Start time	Class length	Break
1st period	8:00	50 min	10 min
2nd period		50 min	10 min
3rd period		50 min	10 min
4th period

The 1st period starts at 8:00. Each period lasts 50 minutes and is followed by a 10-minute break.

Show solution

1 · Understandwhat's really being asked

Periods at Mia's school each last 50 minutes and are followed by a 10-minute break. The 1st period starts at 8:00. I need to find what time the 4th period begins.

Givens

1st period starts at 8:00.
Each period is 50 minutes long.
After each period there is a 10-minute break.

Unknowns

The start time of the 4th period.

Constraints

60 minutes = 1 hour (regroup when minutes reach 60).
Between the start of one period and the start of the next is 50 + 10 = 60 minutes.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Each period-then-break repeats the same 60-minute block, so the gap from one start to the next is constant. Finding that pattern lets me add 3 of these blocks to reach the 4th period, regrouping minutes into hours as needed.

3 · Execute4 carry out the plan

1Find the gap between consecutive period starts

#5 Look for a Pattern 3.MD.A.1

A period is 50 minutes and the following break is 10 minutes, so the next period starts 50 + 10 = 60 minutes after the previous one started.

50 + 10 = 60 \text{ min}

The same 'class then break' chunk repeats, so each start is one fixed step after the last.

2Count how many gaps to the 4th period

#7 Identify Subproblems 3.OA.A.3

From the 1st period to the 4th period there are 3 gaps. Each gap is 60 minutes.

3 \times 60 = 180 \text{ min}

3 equal 60-minute jumps gets you from the 1st start to the 4th start.

3Convert 180 minutes to hours and minutes

#7 Identify Subproblems 3.MD.A.1

Regroup 180 minutes using 60 minutes = 1 hour: 180 = 180 + 0, so 180 minutes is 3 hour(s) 0 minute(s).

180 \text{ min} = 3 \text{ h } 0 \text{ min}

Trading every 60 minutes for an hour is the base-sixty regrouping kids use for clocks.

4Add the elapsed time to the start time

#7 Identify Subproblems 3.MD.A.1

Add 3 h 0 min to 8:00. Carry an hour whenever the minutes pass 60 to land on 11:00.

8:00 + 3{:}00 = 11:00

When the minutes pass 60 you carry an hour, just like reading the clock forward.

Answer: 11:00

4 · Reviewdoes it hold up?

Each period plus break is 60 minutes, so 4 periods span about 3 h 0 min; starting at 8:00 and reaching 11:00 is a sensible school schedule.

Another way: Make a systematic list: 1st 8:00, 2nd 9:00, 3rd 10:00, 4th 11:00 - adding 60 minutes each line gives the same 11:00.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Adding elapsed minutes to a start time and regrouping minutes into hours.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying 3 gaps x 60 minutes to find the total elapsed time.

💡Takeaway. Spot the repeating 60-minute 'class + break' chunk, multiply by 3, and add - that's all Grade 3 time sense!

Variant 5 medium answer: 10:35

The class schedule at Mia's school is shown below. Find the time that the 4th period starts.

Period	Start time	Class length	Break
1st period	7:50	40 min	15 min
2nd period		40 min	15 min
3rd period		40 min	15 min
4th period

The 1st period starts at 7:50. Each period lasts 40 minutes and is followed by a 15-minute break.

Show solution

1 · Understandwhat's really being asked

Periods at Mia's school each last 40 minutes and are followed by a 15-minute break. The 1st period starts at 7:50. I need to find what time the 4th period begins.

Givens

1st period starts at 7:50.
Each period is 40 minutes long.
After each period there is a 15-minute break.

Unknowns

The start time of the 4th period.

Constraints

60 minutes = 1 hour (regroup when minutes reach 60).
Between the start of one period and the start of the next is 40 + 15 = 55 minutes.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

3 · Execute4 carry out the plan

1Find the gap between consecutive period starts

#5 Look for a Pattern 3.MD.A.1

A period is 40 minutes and the following break is 15 minutes, so the next period starts 40 + 15 = 55 minutes after the previous one started.

40 + 15 = 55 \text{ min}

The same 'class then break' chunk repeats, so each start is one fixed step after the last.

2Count how many gaps to the 4th period

#7 Identify Subproblems 3.OA.A.3

From the 1st period to the 4th period there are 3 gaps. Each gap is 55 minutes.

3 \times 55 = 165 \text{ min}

3 equal 55-minute jumps gets you from the 1st start to the 4th start.

3Convert 165 minutes to hours and minutes

#7 Identify Subproblems 3.MD.A.1

Regroup 165 minutes using 60 minutes = 1 hour: 165 = 120 + 45, so 165 minutes is 2 hour(s) 45 minute(s).

165 \text{ min} = 2 \text{ h } 45 \text{ min}

Trading every 60 minutes for an hour is the base-sixty regrouping kids use for clocks.

4Add the elapsed time to the start time

#7 Identify Subproblems 3.MD.A.1

Add 2 h 45 min to 7:50. Carry an hour whenever the minutes pass 60 to land on 10:35.

7:50 + 2{:}45 = 10:35

When the minutes pass 60 you carry an hour, just like reading the clock forward.

Answer: 10:35

4 · Reviewdoes it hold up?

Each period plus break is 55 minutes, so 4 periods span about 2 h 45 min; starting at 7:50 and reaching 10:35 is a sensible school schedule.

Another way: Make a systematic list: 1st 7:50, 2nd 8:45, 3rd 9:40, 4th 10:35 - adding 55 minutes each line gives the same 10:35.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Adding elapsed minutes to a start time and regrouping minutes into hours.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying 3 gaps x 55 minutes to find the total elapsed time.

💡Takeaway. Spot the repeating 55-minute 'class + break' chunk, multiply by 3, and add - that's all Grade 3 time sense!

Variant 6 medium answer: 11:00

The class schedule at Mia's school is shown below. Find the time that the 4th period starts.

Period	Start time	Class length	Break
1st period	8:15	50 min	5 min
2nd period		50 min	5 min
3rd period		50 min	5 min
4th period

The 1st period starts at 8:15. Each period lasts 50 minutes and is followed by a 5-minute break.

Show solution

1 · Understandwhat's really being asked

Periods at Mia's school each last 50 minutes and are followed by a 5-minute break. The 1st period starts at 8:15. I need to find what time the 4th period begins.

Givens

1st period starts at 8:15.
Each period is 50 minutes long.
After each period there is a 5-minute break.

Unknowns

The start time of the 4th period.

Constraints

60 minutes = 1 hour (regroup when minutes reach 60).
Between the start of one period and the start of the next is 50 + 5 = 55 minutes.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

3 · Execute4 carry out the plan

1Find the gap between consecutive period starts

#5 Look for a Pattern 3.MD.A.1

A period is 50 minutes and the following break is 5 minutes, so the next period starts 50 + 5 = 55 minutes after the previous one started.

50 + 5 = 55 \text{ min}

The same 'class then break' chunk repeats, so each start is one fixed step after the last.

2Count how many gaps to the 4th period

#7 Identify Subproblems 3.OA.A.3

From the 1st period to the 4th period there are 3 gaps. Each gap is 55 minutes.

3 \times 55 = 165 \text{ min}

3 equal 55-minute jumps gets you from the 1st start to the 4th start.

3Convert 165 minutes to hours and minutes

#7 Identify Subproblems 3.MD.A.1

Regroup 165 minutes using 60 minutes = 1 hour: 165 = 120 + 45, so 165 minutes is 2 hour(s) 45 minute(s).

165 \text{ min} = 2 \text{ h } 45 \text{ min}

Trading every 60 minutes for an hour is the base-sixty regrouping kids use for clocks.

4Add the elapsed time to the start time

#7 Identify Subproblems 3.MD.A.1

Add 2 h 45 min to 8:15. Carry an hour whenever the minutes pass 60 to land on 11:00.

8:15 + 2{:}45 = 11:00

When the minutes pass 60 you carry an hour, just like reading the clock forward.

Answer: 11:00

4 · Reviewdoes it hold up?

Each period plus break is 55 minutes, so 4 periods span about 2 h 45 min; starting at 8:15 and reaching 11:00 is a sensible school schedule.

Another way: Make a systematic list: 1st 8:15, 2nd 9:10, 3rd 10:05, 4th 11:00 - adding 55 minutes each line gives the same 11:00.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Adding elapsed minutes to a start time and regrouping minutes into hours.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying 3 gaps x 55 minutes to find the total elapsed time.

💡Takeaway. Spot the repeating 55-minute 'class + break' chunk, multiply by 3, and add - that's all Grade 3 time sense!

Variant 7 medium answer: 11:20

The class schedule at Mia's school is shown below. Find the time that the 4th period starts.

Period	Start time	Class length	Break
1st period	8:50	40 min	10 min
2nd period		40 min	10 min
3rd period		40 min	10 min
4th period

The 1st period starts at 8:50. Each period lasts 40 minutes and is followed by a 10-minute break.

Show solution

1 · Understandwhat's really being asked

Periods at Mia's school each last 40 minutes and are followed by a 10-minute break. The 1st period starts at 8:50. I need to find what time the 4th period begins.

Givens

1st period starts at 8:50.
Each period is 40 minutes long.
After each period there is a 10-minute break.

Unknowns

The start time of the 4th period.

Constraints

60 minutes = 1 hour (regroup when minutes reach 60).
Between the start of one period and the start of the next is 40 + 10 = 50 minutes.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Each period-then-break repeats the same 50-minute block, so the gap from one start to the next is constant. Finding that pattern lets me add 3 of these blocks to reach the 4th period, regrouping minutes into hours as needed.

3 · Execute4 carry out the plan

1Find the gap between consecutive period starts

#5 Look for a Pattern 3.MD.A.1

A period is 40 minutes and the following break is 10 minutes, so the next period starts 40 + 10 = 50 minutes after the previous one started.

40 + 10 = 50 \text{ min}

The same 'class then break' chunk repeats, so each start is one fixed step after the last.

2Count how many gaps to the 4th period

#7 Identify Subproblems 3.OA.A.3

From the 1st period to the 4th period there are 3 gaps. Each gap is 50 minutes.

3 \times 50 = 150 \text{ min}

3 equal 50-minute jumps gets you from the 1st start to the 4th start.

3Convert 150 minutes to hours and minutes

#7 Identify Subproblems 3.MD.A.1

Regroup 150 minutes using 60 minutes = 1 hour: 150 = 120 + 30, so 150 minutes is 2 hour(s) 30 minute(s).

150 \text{ min} = 2 \text{ h } 30 \text{ min}

Trading every 60 minutes for an hour is the base-sixty regrouping kids use for clocks.

4Add the elapsed time to the start time

#7 Identify Subproblems 3.MD.A.1

Add 2 h 30 min to 8:50. Carry an hour whenever the minutes pass 60 to land on 11:20.

8:50 + 2{:}30 = 11:20

When the minutes pass 60 you carry an hour, just like reading the clock forward.

Answer: 11:20

4 · Reviewdoes it hold up?

Each period plus break is 50 minutes, so 4 periods span about 2 h 30 min; starting at 8:50 and reaching 11:20 is a sensible school schedule.

Another way: Make a systematic list: 1st 8:50, 2nd 9:40, 3rd 10:30, 4th 11:20 - adding 50 minutes each line gives the same 11:20.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Adding elapsed minutes to a start time and regrouping minutes into hours.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying 3 gaps x 50 minutes to find the total elapsed time.

💡Takeaway. Spot the repeating 50-minute 'class + break' chunk, multiply by 3, and add - that's all Grade 3 time sense!

Variant 8 hard answer: 11:30

The class schedule at Mia's school is shown below. Find the time that the 5th period starts.

Period	Start time	Class length	Break
1st period	8:30	40 min	5 min
2nd period		40 min	5 min
3rd period		40 min	5 min
4th period		40 min	5 min
5th period

The 1st period starts at 8:30. Each period lasts 40 minutes and is followed by a 5-minute break.

Show solution

1 · Understandwhat's really being asked

Periods at Mia's school each last 40 minutes and are followed by a 5-minute break. The 1st period starts at 8:30. I need to find what time the 5th period begins.

Givens

1st period starts at 8:30.
Each period is 40 minutes long.
After each period there is a 5-minute break.

Unknowns

The start time of the 5th period.

Constraints

60 minutes = 1 hour (regroup when minutes reach 60).
Between the start of one period and the start of the next is 40 + 5 = 45 minutes.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Each period-then-break repeats the same 45-minute block, so the gap from one start to the next is constant. Finding that pattern lets me add 4 of these blocks to reach the 5th period, regrouping minutes into hours as needed.

3 · Execute4 carry out the plan

1Find the gap between consecutive period starts

#5 Look for a Pattern 3.MD.A.1

A period is 40 minutes and the following break is 5 minutes, so the next period starts 40 + 5 = 45 minutes after the previous one started.

40 + 5 = 45 \text{ min}

The same 'class then break' chunk repeats, so each start is one fixed step after the last.

2Count how many gaps to the 5th period

#7 Identify Subproblems 3.OA.A.3

From the 1st period to the 5th period there are 4 gaps. Each gap is 45 minutes.

4 \times 45 = 180 \text{ min}

4 equal 45-minute jumps gets you from the 1st start to the 5th start.

3Convert 180 minutes to hours and minutes

#7 Identify Subproblems 3.MD.A.1

Regroup 180 minutes using 60 minutes = 1 hour: 180 = 180 + 0, so 180 minutes is 3 hour(s) 0 minute(s).

180 \text{ min} = 3 \text{ h } 0 \text{ min}

Trading every 60 minutes for an hour is the base-sixty regrouping kids use for clocks.

4Add the elapsed time to the start time

#7 Identify Subproblems 3.MD.A.1

Add 3 h 0 min to 8:30. Carry an hour whenever the minutes pass 60 to land on 11:30.

8:30 + 3{:}00 = 11:30

When the minutes pass 60 you carry an hour, just like reading the clock forward.

Answer: 11:30

4 · Reviewdoes it hold up?

Each period plus break is 45 minutes, so 5 periods span about 3 h 0 min; starting at 8:30 and reaching 11:30 is a sensible school schedule.

Another way: Make a systematic list: 1st 8:30, 2nd 9:15, 3rd 10:00, 4th 10:45, 5th 11:30 - adding 45 minutes each line gives the same 11:30.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Adding elapsed minutes to a start time and regrouping minutes into hours.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying 4 gaps x 45 minutes to find the total elapsed time.

💡Takeaway. Spot the repeating 45-minute 'class + break' chunk, multiply by 4, and add - that's all Grade 3 time sense!

Variant 9 hard answer: 11:45

The class schedule at Mia's school is shown below. Find the time that the 5th period starts.

Period	Start time	Class length	Break
1st period	8:45	35 min	10 min
2nd period		35 min	10 min
3rd period		35 min	10 min
4th period		35 min	10 min
5th period

The 1st period starts at 8:45. Each period lasts 35 minutes and is followed by a 10-minute break.

Show solution

1 · Understandwhat's really being asked

Periods at Mia's school each last 35 minutes and are followed by a 10-minute break. The 1st period starts at 8:45. I need to find what time the 5th period begins.

Givens

1st period starts at 8:45.
Each period is 35 minutes long.
After each period there is a 10-minute break.

Unknowns

The start time of the 5th period.

Constraints

60 minutes = 1 hour (regroup when minutes reach 60).
Between the start of one period and the start of the next is 35 + 10 = 45 minutes.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

3 · Execute4 carry out the plan

1Find the gap between consecutive period starts

#5 Look for a Pattern 3.MD.A.1

A period is 35 minutes and the following break is 10 minutes, so the next period starts 35 + 10 = 45 minutes after the previous one started.

35 + 10 = 45 \text{ min}

The same 'class then break' chunk repeats, so each start is one fixed step after the last.

2Count how many gaps to the 5th period

#7 Identify Subproblems 3.OA.A.3

From the 1st period to the 5th period there are 4 gaps. Each gap is 45 minutes.

4 \times 45 = 180 \text{ min}

4 equal 45-minute jumps gets you from the 1st start to the 5th start.

3Convert 180 minutes to hours and minutes

#7 Identify Subproblems 3.MD.A.1

Regroup 180 minutes using 60 minutes = 1 hour: 180 = 180 + 0, so 180 minutes is 3 hour(s) 0 minute(s).

180 \text{ min} = 3 \text{ h } 0 \text{ min}

Trading every 60 minutes for an hour is the base-sixty regrouping kids use for clocks.

4Add the elapsed time to the start time

#7 Identify Subproblems 3.MD.A.1

Add 3 h 0 min to 8:45. Carry an hour whenever the minutes pass 60 to land on 11:45.

8:45 + 3{:}00 = 11:45

When the minutes pass 60 you carry an hour, just like reading the clock forward.

Answer: 11:45

4 · Reviewdoes it hold up?

Each period plus break is 45 minutes, so 5 periods span about 3 h 0 min; starting at 8:45 and reaching 11:45 is a sensible school schedule.

Another way: Make a systematic list: 1st 8:45, 2nd 9:30, 3rd 10:15, 4th 11:00, 5th 11:45 - adding 45 minutes each line gives the same 11:45.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Adding elapsed minutes to a start time and regrouping minutes into hours.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying 4 gaps x 45 minutes to find the total elapsed time.

💡Takeaway. Spot the repeating 45-minute 'class + break' chunk, multiply by 4, and add - that's all Grade 3 time sense!

Variant 10 hard answer: 11:40

The class schedule at Mia's school is shown below. Find the time that the 6th period starts.

Period	Start time	Class length	Break
1st period	7:30	45 min	5 min
2nd period		45 min	5 min
3rd period		45 min	5 min
4th period		45 min	5 min
5th period		45 min	5 min
6th period

The 1st period starts at 7:30. Each period lasts 45 minutes and is followed by a 5-minute break.

Show solution

1 · Understandwhat's really being asked

Periods at Mia's school each last 45 minutes and are followed by a 5-minute break. The 1st period starts at 7:30. I need to find what time the 6th period begins.

Givens

1st period starts at 7:30.
Each period is 45 minutes long.
After each period there is a 5-minute break.

Unknowns

The start time of the 6th period.

Constraints

60 minutes = 1 hour (regroup when minutes reach 60).
Between the start of one period and the start of the next is 45 + 5 = 50 minutes.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Each period-then-break repeats the same 50-minute block, so the gap from one start to the next is constant. Finding that pattern lets me add 5 of these blocks to reach the 6th period, regrouping minutes into hours as needed.

3 · Execute4 carry out the plan

1Find the gap between consecutive period starts

#5 Look for a Pattern 3.MD.A.1

A period is 45 minutes and the following break is 5 minutes, so the next period starts 45 + 5 = 50 minutes after the previous one started.

45 + 5 = 50 \text{ min}

The same 'class then break' chunk repeats, so each start is one fixed step after the last.

2Count how many gaps to the 6th period

#7 Identify Subproblems 3.OA.A.3

From the 1st period to the 6th period there are 5 gaps. Each gap is 50 minutes.

5 \times 50 = 250 \text{ min}

5 equal 50-minute jumps gets you from the 1st start to the 6th start.

3Convert 250 minutes to hours and minutes

#7 Identify Subproblems 3.MD.A.1

Regroup 250 minutes using 60 minutes = 1 hour: 250 = 240 + 10, so 250 minutes is 4 hour(s) 10 minute(s).

250 \text{ min} = 4 \text{ h } 10 \text{ min}

Trading every 60 minutes for an hour is the base-sixty regrouping kids use for clocks.

4Add the elapsed time to the start time

#7 Identify Subproblems 3.MD.A.1

Add 4 h 10 min to 7:30. Carry an hour whenever the minutes pass 60 to land on 11:40.

7:30 + 4{:}10 = 11:40

When the minutes pass 60 you carry an hour, just like reading the clock forward.

Answer: 11:40

4 · Reviewdoes it hold up?

Each period plus break is 50 minutes, so 6 periods span about 4 h 10 min; starting at 7:30 and reaching 11:40 is a sensible school schedule.

Another way: Make a systematic list: 1st 7:30, 2nd 8:20, 3rd 9:10, 4th 10:00, 5th 10:50, 6th 11:40 - adding 50 minutes each line gives the same 11:40.

Standardsmin grade 3

3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Adding elapsed minutes to a start time and regrouping minutes into hours.
3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying 5 gaps x 50 minutes to find the total elapsed time.

💡Takeaway. Spot the repeating 50-minute 'class + break' chunk, multiply by 5, and add - that's all Grade 3 time sense!