← 2-2 · Read a mirrored clock, then find elapsed time · Elapsed Time and Base-Sixty Regrouping

Read a mirrored clock, then find elapsed time · 8 practice problems

2.MD.C.73.MD.A.1

Generated variants — 8

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

Variant 1 answer: 45 minutes (0 hours 45 minutes)

Noah took an afternoon nap and then woke up. The pictures below show his clock as seen in a mirror when he fell asleep and when he woke up. For how many hours and minutes did Noah nap?

There are two mirror-image clocks side by side. The left one, labeled "fell asleep," is a clock seen in a mirror (left and right are reversed); once read correctly as a normal clock it shows $4{:}52$ . The right one, labeled "woke up," is also seen in a mirror and read correctly shows $5{:}37$ . Because both clocks are mirror reflections, their left and right sides are swapped.

Show solution

Understand

Two clocks are shown as seen in a mirror. Read correctly, the 'fell asleep' clock is 4:52 and the 'woke up' clock is 5:37. Find how long Noah napped, in hours and minutes.

Givens

The two pictures are mirror images (left and right reversed).
The 'fell asleep' mirrored clock reads as 4:52 once flipped back to normal.
The 'woke up' mirrored clock reads as 5:37 once flipped back to normal.
From the figure, after un-mirroring, the hour hand and minute hand give 4:52 (asleep) and 5:37 (awake).

Unknowns

The nap duration from 4:52 to 5:37 in hours and minutes.

Constraints

Waking time is later than falling-asleep time the same afternoon.

Plan

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems

First mentally flip each mirrored clock to read the true time, then find the elapsed time between the two real times by adding a jump to the next o'clock plus the leftover minutes.

Execute

#17 Visualize Spatial Relationships 2.MD.C.7

Flipping the mirror images back to normal reads the true times: fell asleep at 4:52, woke up at 5:37.

\text{asleep } 4{:}52,\ \text{awake } 5{:}37

A mirror swaps left and right, so picturing the flip restores the real clock face.

#7 Identify Subproblems 3.MD.A.1

From 4:52 it takes 8 minutes to reach 5:00.

60 - 52 = 8 \Rightarrow 4{:}52 + 8 = 5{:}00

Stepping up to the whole hour first makes the rest of the count easy.

#7 Identify Subproblems 3.MD.A.1

From 5:00 to 5:37 is another 37 minutes. The total nap is 8 + 37 minutes.

8 + 37 = 45 \text{ minutes} = 45 minutes

Adding the hop to the hour and the remaining minutes gives the full nap.

Answer: 45 minutes (0 hours 45 minutes)

Review

Check by adding: 4:52 + 45 minutes = 5:37, which matches the wake-up time.

Count the minutes from 4:52 to the next hour, then from there to 5:37, and add the parts.

Standards · min grade 3

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the true clock times after un-mirroring the reflected clock faces.
3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding the elapsed nap time between 4:52 and 5:37.

💡 Flip the mirror clock in your head, then count the minutes to the next time: Grade 3 clock-reading plus a spatial flip!

Variant 2 answer: 50 minutes (0 hours 50 minutes)

Noah took an afternoon nap and then woke up. The pictures below show his clock as seen in a mirror when he fell asleep and when he woke up. For how many hours and minutes did Noah nap?

There are two mirror-image clocks side by side. The left one, labeled "fell asleep," is a clock seen in a mirror (left and right are reversed); once read correctly as a normal clock it shows $2{:}15$ . The right one, labeled "woke up," is also seen in a mirror and read correctly shows $3{:}05$ . Because both clocks are mirror reflections, their left and right sides are swapped.

Show solution

Understand

Two clocks are shown as seen in a mirror. Read correctly, the 'fell asleep' clock is 2:15 and the 'woke up' clock is 3:05. Find how long Noah napped, in hours and minutes.

Givens

The two pictures are mirror images (left and right reversed).
The 'fell asleep' mirrored clock reads as 2:15 once flipped back to normal.
The 'woke up' mirrored clock reads as 3:05 once flipped back to normal.
From the figure, after un-mirroring, the hour hand and minute hand give 2:15 (asleep) and 3:05 (awake).

Unknowns

The nap duration from 2:15 to 3:05 in hours and minutes.

Constraints

Waking time is later than falling-asleep time the same afternoon.

Plan

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems

First mentally flip each mirrored clock to read the true time, then find the elapsed time between the two real times by adding a jump to the next o'clock plus the leftover minutes.

Execute

#17 Visualize Spatial Relationships 2.MD.C.7

Flipping the mirror images back to normal reads the true times: fell asleep at 2:15, woke up at 3:05.

\text{asleep } 2{:}15,\ \text{awake } 3{:}05

A mirror swaps left and right, so picturing the flip restores the real clock face.

#7 Identify Subproblems 3.MD.A.1

From 2:15 it takes 45 minutes to reach 3:00.

60 - 15 = 45 \Rightarrow 2{:}15 + 45 = 3{:}00

Stepping up to the whole hour first makes the rest of the count easy.

#7 Identify Subproblems 3.MD.A.1

From 3:00 to 3:05 is another 5 minutes. The total nap is 45 + 5 minutes.

45 + 5 = 50 \text{ minutes} = 50 minutes

Adding the hop to the hour and the remaining minutes gives the full nap.

Answer: 50 minutes (0 hours 50 minutes)

Review

Check by adding: 2:15 + 50 minutes = 3:05, which matches the wake-up time.

Count the minutes from 2:15 to the next hour, then from there to 3:05, and add the parts.

Standards · min grade 3

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the true clock times after un-mirroring the reflected clock faces.
3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding the elapsed nap time between 2:15 and 3:05.

💡 Flip the mirror clock in your head, then count the minutes to the next time: Grade 3 clock-reading plus a spatial flip!

Variant 3 answer: 45 minutes (0 hours 45 minutes)

Noah took an afternoon nap and then woke up. The pictures below show his clock as seen in a mirror when he fell asleep and when he woke up. For how many hours and minutes did Noah nap?

There are two mirror-image clocks side by side. The left one, labeled "fell asleep," is a clock seen in a mirror (left and right are reversed); once read correctly as a normal clock it shows $3{:}05$ . The right one, labeled "woke up," is also seen in a mirror and read correctly shows $3{:}50$ . Because both clocks are mirror reflections, their left and right sides are swapped.

Show solution

Understand

Two clocks are shown as seen in a mirror. Read correctly, the 'fell asleep' clock is 3:05 and the 'woke up' clock is 3:50. Find how long Noah napped, in hours and minutes.

Givens

The two pictures are mirror images (left and right reversed).
The 'fell asleep' mirrored clock reads as 3:05 once flipped back to normal.
The 'woke up' mirrored clock reads as 3:50 once flipped back to normal.
From the figure, after un-mirroring, the hour hand and minute hand give 3:05 (asleep) and 3:50 (awake).

Unknowns

The nap duration from 3:05 to 3:50 in hours and minutes.

Constraints

Waking time is later than falling-asleep time the same afternoon.

Plan

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems

First mentally flip each mirrored clock to read the true time, then find the elapsed time between the two real times by adding a jump to the next o'clock plus the leftover minutes.

Execute

#17 Visualize Spatial Relationships 2.MD.C.7

Flipping the mirror images back to normal reads the true times: fell asleep at 3:05, woke up at 3:50.

\text{asleep } 3{:}05,\ \text{awake } 3{:}50

A mirror swaps left and right, so picturing the flip restores the real clock face.

#7 Identify Subproblems 3.MD.A.1

From 3:05 it takes 55 minutes to reach 4:00.

60 - 5 = 55 \Rightarrow 3{:}05 + 55 = 4{:}00

Stepping up to the whole hour first makes the rest of the count easy.

#7 Identify Subproblems 3.MD.A.1

From 4:00 to 3:50 is another -1 hours 50 minutes. The total nap is 55 + -10 minutes.

55 + -10 = 45 \text{ minutes} = 45 minutes

Adding the hop to the hour and the remaining minutes gives the full nap.

Answer: 45 minutes (0 hours 45 minutes)

Review

Check by adding: 3:05 + 45 minutes = 3:50, which matches the wake-up time.

Count the minutes from 3:05 to the next hour, then from there to 3:50, and add the parts.

Standards · min grade 3

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the true clock times after un-mirroring the reflected clock faces.
3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding the elapsed nap time between 3:05 and 3:50.

💡 Flip the mirror clock in your head, then count the minutes to the next time: Grade 3 clock-reading plus a spatial flip!

Variant 4 answer: 45 minutes (0 hours 45 minutes)

Noah took an afternoon nap and then woke up. The pictures below show his clock as seen in a mirror when he fell asleep and when he woke up. For how many hours and minutes did Noah nap?

There are two mirror-image clocks side by side. The left one, labeled "fell asleep," is a clock seen in a mirror (left and right are reversed); once read correctly as a normal clock it shows $1{:}40$ . The right one, labeled "woke up," is also seen in a mirror and read correctly shows $2{:}25$ . Because both clocks are mirror reflections, their left and right sides are swapped.

Show solution

Understand

Two clocks are shown as seen in a mirror. Read correctly, the 'fell asleep' clock is 1:40 and the 'woke up' clock is 2:25. Find how long Noah napped, in hours and minutes.

Givens

The two pictures are mirror images (left and right reversed).
The 'fell asleep' mirrored clock reads as 1:40 once flipped back to normal.
The 'woke up' mirrored clock reads as 2:25 once flipped back to normal.
From the figure, after un-mirroring, the hour hand and minute hand give 1:40 (asleep) and 2:25 (awake).

Unknowns

The nap duration from 1:40 to 2:25 in hours and minutes.

Constraints

Waking time is later than falling-asleep time the same afternoon.

Plan

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems

First mentally flip each mirrored clock to read the true time, then find the elapsed time between the two real times by adding a jump to the next o'clock plus the leftover minutes.

Execute

#17 Visualize Spatial Relationships 2.MD.C.7

Flipping the mirror images back to normal reads the true times: fell asleep at 1:40, woke up at 2:25.

\text{asleep } 1{:}40,\ \text{awake } 2{:}25

A mirror swaps left and right, so picturing the flip restores the real clock face.

#7 Identify Subproblems 3.MD.A.1

From 1:40 it takes 20 minutes to reach 2:00.

60 - 40 = 20 \Rightarrow 1{:}40 + 20 = 2{:}00

Stepping up to the whole hour first makes the rest of the count easy.

#7 Identify Subproblems 3.MD.A.1

From 2:00 to 2:25 is another 25 minutes. The total nap is 20 + 25 minutes.

20 + 25 = 45 \text{ minutes} = 45 minutes

Adding the hop to the hour and the remaining minutes gives the full nap.

Answer: 45 minutes (0 hours 45 minutes)

Review

Check by adding: 1:40 + 45 minutes = 2:25, which matches the wake-up time.

Count the minutes from 1:40 to the next hour, then from there to 2:25, and add the parts.

Standards · min grade 3

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the true clock times after un-mirroring the reflected clock faces.
3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding the elapsed nap time between 1:40 and 2:25.

💡 Flip the mirror clock in your head, then count the minutes to the next time: Grade 3 clock-reading plus a spatial flip!

Variant 5 answer: 50 minutes (0 hours 50 minutes)

Noah took an afternoon nap and then woke up. The pictures below show his clock as seen in a mirror when he fell asleep and when he woke up. For how many hours and minutes did Noah nap?

There are two mirror-image clocks side by side. The left one, labeled "fell asleep," is a clock seen in a mirror (left and right are reversed); once read correctly as a normal clock it shows $12{:}10$ . The right one, labeled "woke up," is also seen in a mirror and read correctly shows $1{:}00$ . Because both clocks are mirror reflections, their left and right sides are swapped.

Show solution

Understand

Two clocks are shown as seen in a mirror. Read correctly, the 'fell asleep' clock is 12:10 and the 'woke up' clock is 1:00. Find how long Noah napped, in hours and minutes.

Givens

The two pictures are mirror images (left and right reversed).
The 'fell asleep' mirrored clock reads as 12:10 once flipped back to normal.
The 'woke up' mirrored clock reads as 1:00 once flipped back to normal.
From the figure, after un-mirroring, the hour hand and minute hand give 12:10 (asleep) and 1:00 (awake).

Unknowns

The nap duration from 12:10 to 1:00 in hours and minutes.

Constraints

Waking time is later than falling-asleep time the same afternoon.

Plan

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems

First mentally flip each mirrored clock to read the true time, then find the elapsed time between the two real times by adding a jump to the next o'clock plus the leftover minutes.

Execute

#17 Visualize Spatial Relationships 2.MD.C.7

Flipping the mirror images back to normal reads the true times: fell asleep at 12:10, woke up at 1:00.

\text{asleep } 12{:}10,\ \text{awake } 1{:}00

A mirror swaps left and right, so picturing the flip restores the real clock face.

#7 Identify Subproblems 3.MD.A.1

From 12:10 it takes 50 minutes to reach 1:00.

60 - 10 = 50 \Rightarrow 12{:}10 + 50 = 1{:}00

Stepping up to the whole hour first makes the rest of the count easy.

#7 Identify Subproblems 3.MD.A.1

From 1:00 to 1:00 is another 0 minutes. The total nap is 50 + 0 minutes.

50 + 0 = 50 \text{ minutes} = 50 minutes

Adding the hop to the hour and the remaining minutes gives the full nap.

Answer: 50 minutes (0 hours 50 minutes)

Review

Check by adding: 12:10 + 50 minutes = 1:00, which matches the wake-up time.

Count the minutes from 12:10 to the next hour, then from there to 1:00, and add the parts.

Standards · min grade 3

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the true clock times after un-mirroring the reflected clock faces.
3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding the elapsed nap time between 12:10 and 1:00.

💡 Flip the mirror clock in your head, then count the minutes to the next time: Grade 3 clock-reading plus a spatial flip!

Variant 6 answer: 45 minutes (0 hours 45 minutes)

Noah took an afternoon nap and then woke up. The pictures below show his clock as seen in a mirror when he fell asleep and when he woke up. For how many hours and minutes did Noah nap?

There are two mirror-image clocks side by side. The left one, labeled "fell asleep," is a clock seen in a mirror (left and right are reversed); once read correctly as a normal clock it shows $9{:}45$ . The right one, labeled "woke up," is also seen in a mirror and read correctly shows $10{:}30$ . Because both clocks are mirror reflections, their left and right sides are swapped.

Show solution

Understand

Two clocks are shown as seen in a mirror. Read correctly, the 'fell asleep' clock is 9:45 and the 'woke up' clock is 10:30. Find how long Noah napped, in hours and minutes.

Givens

The two pictures are mirror images (left and right reversed).
The 'fell asleep' mirrored clock reads as 9:45 once flipped back to normal.
The 'woke up' mirrored clock reads as 10:30 once flipped back to normal.
From the figure, after un-mirroring, the hour hand and minute hand give 9:45 (asleep) and 10:30 (awake).

Unknowns

The nap duration from 9:45 to 10:30 in hours and minutes.

Constraints

Waking time is later than falling-asleep time the same afternoon.

Plan

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems

First mentally flip each mirrored clock to read the true time, then find the elapsed time between the two real times by adding a jump to the next o'clock plus the leftover minutes.

Execute

#17 Visualize Spatial Relationships 2.MD.C.7

Flipping the mirror images back to normal reads the true times: fell asleep at 9:45, woke up at 10:30.

\text{asleep } 9{:}45,\ \text{awake } 10{:}30

A mirror swaps left and right, so picturing the flip restores the real clock face.

#7 Identify Subproblems 3.MD.A.1

From 9:45 it takes 15 minutes to reach 10:00.

60 - 45 = 15 \Rightarrow 9{:}45 + 15 = 10{:}00

Stepping up to the whole hour first makes the rest of the count easy.

#7 Identify Subproblems 3.MD.A.1

From 10:00 to 10:30 is another 30 minutes. The total nap is 15 + 30 minutes.

15 + 30 = 45 \text{ minutes} = 45 minutes

Adding the hop to the hour and the remaining minutes gives the full nap.

Answer: 45 minutes (0 hours 45 minutes)

Review

Check by adding: 9:45 + 45 minutes = 10:30, which matches the wake-up time.

Count the minutes from 9:45 to the next hour, then from there to 10:30, and add the parts.

Standards · min grade 3

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the true clock times after un-mirroring the reflected clock faces.
3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding the elapsed nap time between 9:45 and 10:30.

💡 Flip the mirror clock in your head, then count the minutes to the next time: Grade 3 clock-reading plus a spatial flip!

Variant 7 answer: 45 minutes (0 hours 45 minutes)

Noah took an afternoon nap and then woke up. The pictures below show his clock as seen in a mirror when he fell asleep and when he woke up. For how many hours and minutes did Noah nap?

There are two mirror-image clocks side by side. The left one, labeled "fell asleep," is a clock seen in a mirror (left and right are reversed); once read correctly as a normal clock it shows $10{:}50$ . The right one, labeled "woke up," is also seen in a mirror and read correctly shows $11{:}35$ . Because both clocks are mirror reflections, their left and right sides are swapped.

Show solution

Understand

Two clocks are shown as seen in a mirror. Read correctly, the 'fell asleep' clock is 10:50 and the 'woke up' clock is 11:35. Find how long Noah napped, in hours and minutes.

Givens

The two pictures are mirror images (left and right reversed).
The 'fell asleep' mirrored clock reads as 10:50 once flipped back to normal.
The 'woke up' mirrored clock reads as 11:35 once flipped back to normal.
From the figure, after un-mirroring, the hour hand and minute hand give 10:50 (asleep) and 11:35 (awake).

Unknowns

The nap duration from 10:50 to 11:35 in hours and minutes.

Constraints

Waking time is later than falling-asleep time the same afternoon.

Plan

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems

First mentally flip each mirrored clock to read the true time, then find the elapsed time between the two real times by adding a jump to the next o'clock plus the leftover minutes.

Execute

#17 Visualize Spatial Relationships 2.MD.C.7

Flipping the mirror images back to normal reads the true times: fell asleep at 10:50, woke up at 11:35.

\text{asleep } 10{:}50,\ \text{awake } 11{:}35

A mirror swaps left and right, so picturing the flip restores the real clock face.

#7 Identify Subproblems 3.MD.A.1

From 10:50 it takes 10 minutes to reach 11:00.

60 - 50 = 10 \Rightarrow 10{:}50 + 10 = 11{:}00

Stepping up to the whole hour first makes the rest of the count easy.

#7 Identify Subproblems 3.MD.A.1

From 11:00 to 11:35 is another 35 minutes. The total nap is 10 + 35 minutes.

10 + 35 = 45 \text{ minutes} = 45 minutes

Adding the hop to the hour and the remaining minutes gives the full nap.

Answer: 45 minutes (0 hours 45 minutes)

Review

Check by adding: 10:50 + 45 minutes = 11:35, which matches the wake-up time.

Count the minutes from 10:50 to the next hour, then from there to 11:35, and add the parts.

Standards · min grade 3

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the true clock times after un-mirroring the reflected clock faces.
3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding the elapsed nap time between 10:50 and 11:35.

💡 Flip the mirror clock in your head, then count the minutes to the next time: Grade 3 clock-reading plus a spatial flip!

Variant 8 answer: 40 minutes (0 hours 40 minutes)

Noah took an afternoon nap and then woke up. The pictures below show his clock as seen in a mirror when he fell asleep and when he woke up. For how many hours and minutes did Noah nap?

There are two mirror-image clocks side by side. The left one, labeled "fell asleep," is a clock seen in a mirror (left and right are reversed); once read correctly as a normal clock it shows $7{:}20$ . The right one, labeled "woke up," is also seen in a mirror and read correctly shows $8{:}00$ . Because both clocks are mirror reflections, their left and right sides are swapped.

Show solution

Understand

Two clocks are shown as seen in a mirror. Read correctly, the 'fell asleep' clock is 7:20 and the 'woke up' clock is 8:00. Find how long Noah napped, in hours and minutes.

Givens

The two pictures are mirror images (left and right reversed).
The 'fell asleep' mirrored clock reads as 7:20 once flipped back to normal.
The 'woke up' mirrored clock reads as 8:00 once flipped back to normal.
From the figure, after un-mirroring, the hour hand and minute hand give 7:20 (asleep) and 8:00 (awake).

Unknowns

The nap duration from 7:20 to 8:00 in hours and minutes.

Constraints

Waking time is later than falling-asleep time the same afternoon.

Plan

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems

First mentally flip each mirrored clock to read the true time, then find the elapsed time between the two real times by adding a jump to the next o'clock plus the leftover minutes.

Execute

#17 Visualize Spatial Relationships 2.MD.C.7

Flipping the mirror images back to normal reads the true times: fell asleep at 7:20, woke up at 8:00.

\text{asleep } 7{:}20,\ \text{awake } 8{:}00

A mirror swaps left and right, so picturing the flip restores the real clock face.

#7 Identify Subproblems 3.MD.A.1

From 7:20 it takes 40 minutes to reach 8:00.

60 - 20 = 40 \Rightarrow 7{:}20 + 40 = 8{:}00

Stepping up to the whole hour first makes the rest of the count easy.

#7 Identify Subproblems 3.MD.A.1

From 8:00 to 8:00 is another 0 minutes. The total nap is 40 + 0 minutes.

40 + 0 = 40 \text{ minutes} = 40 minutes

Adding the hop to the hour and the remaining minutes gives the full nap.

Answer: 40 minutes (0 hours 40 minutes)

Review

Check by adding: 7:20 + 40 minutes = 8:00, which matches the wake-up time.

Count the minutes from 7:20 to the next hour, then from there to 8:00, and add the parts.

Standards · min grade 3

2.MD.C.7 Tell and write time from analog and digital clocks to nearest five minutes — Reading the true clock times after un-mirroring the reflected clock faces.
3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding the elapsed nap time between 7:20 and 8:00.

💡 Flip the mirror clock in your head, then count the minutes to the next time: Grade 3 clock-reading plus a spatial flip!