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## Time problems

This problem solving activity has a number focus.

These students are to sit an exam that begins at 9:30 pm sharp. Which of them will get there i n time for the start of the exam?

Derek’s watch is 15 minutes fast but he thinks that it is 10 minutes fast.

Marilyn’s watch is 15 minutes fast but she thinks it is 20 minutes fast.

Sara’s watch is 15 minutes slow but she thinks it is 10 minutes fast.

Tim’s watch is 15 minutes slow but he thinks that it is 10 minutes slow.

- Understand how positive and negative numbers can be used in an unusual practical problem.
- Devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, look for patterns, draw a diagram, make a table, use algebra).

This logic problem, involving positive and negative numbers in a practical situation, may challenge students and generate interesting discussion. Students need to possess knowledge of time to work successfully with this problem.

- Copymaster of the problem (English)
- Copymaster of the problem (Māori)
- A clock (a digital version could be used)

## The Problem

These students are to sit an exam that begins at 9:30 pm sharp. Which of them will get there in time for the start of the exam?

## Teaching Sequence

- Pose the problem for students to work on in their groups. Allow discussion.
- When groups believe they know about at least one of the examinees, pause for discussion.
- Take a vote on which of the four people get to the exam late and have students give reasons for their choices.
- Reach a consensus.
- Give time for the students finish the problem and begin on the extension as appropriate.
- Have students share their results with reference to their written solutions. Encourage them to use the clock to model their solutions.

There are other possibilities for people’s watches. They could be fast but they think they’re slow; they could be slow but they think they’re fast; they could be slow and their owners think that they are slower than that, and so on. Investigate the other possibilities.

There are many ways of solving this problem. Here is one approach, using a table for each examinee. Derek.

If it was 9:30, Derek’s watch would show 9:45 because it is 15 minutes fast. But Derek thinks it is 10 minutes fast. So he thinks that the actual time is 9:35. That gives the first row of the table.

But Derek wants to be at the exam at 9:30. So he will go there when he thinks that it is 9:30. But when he thinks that it is 9:30, his watch will be showing 9:40. However, the actual time then is 9:25. So Derek gets there in time.

Marilyn will be 5 minutes late.

Sara, who will very very late.

Tim. There are a lot of people coming late to this exam!

## Solution to the Extension

The possibilities are:

- watch fast by x; person thinks it is fast by y with y > x;
- watch fast by x; person thinks it is fast by y with y < x;
- watch fast by x; person thinks it is fast by y with y = x;
- watch fast by x; person thinks it is slow by y with y > x;
- watch fast by x; person thinks it is slow by y with y < x;
- watch fast by x; person thinks it is slow by y with y = x;
- watch slow by x; person thinks it is fast by y with y > x;
- watch slow by x; person thinks it is fast by y with y < x;
- watch slow by x; person thinks it is fast by y with y = x;
- watch slow by x; person thinks it is slow by y with y > x;
- watch slow by x; person thinks it is slow by y with y < x;
- watch fast by x; person thinks it is slow by y with y = x.

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## 25 Time Word Problems for Year 2 to Year 6 With Tips On Supporting Pupils’ Progress

Emma johnson.

Time word problems are an important element of teaching children how to tell the time. Children are introduced to the concept of time in Year 1. At this early stage, they learn the basics of analogue time; reading to the hour and half past and learn how to draw hands on the clocks to show these times.

As they move through primary school, pupils progress onto reading the time in analogue, digital and 24 hour clocks and being able to compare the duration of events. By the time children reach upper Key Stage 2, they should be confident in reading the time in all formats and solving problems involving converting between units of time.

## Time in Year 1

Time in year 2, time in year 3, time in year 4, time in year 5 & 6, why are word problems important for children’s understanding of time, how to teach time word problem solving in primary school, time word problems for year 2, time word problems for year 3, time word problems for year 4, time word problems for year 5, time word problems for year 6, more time and word problems resources, let's practice telling the time.

Download this free printable worksheet to let your students practice telling the time.

When students are first introduced to time and time word problems , it is important for them to have physical clocks, to hold and manipulate the hands. Pictures on worksheets are helpful, but physical clocks enable them to work out what is happening with the hands and to solve word problems involving addition word problems and subtraction word problems .

Time word problems are important for helping children to understand how time is used in the real-world. We have put together a collection of 25 time word problems, which can be used with pupils from Year 2 to Year 6.

## Time word problems in the National Curriculum

In Year 1, students are introduced to the basics of time. They learn to recognise the hour and minute hand and use this to help read the time to the hour and half past the hour. They also draw hands on clock faces to represent these times.

By the end of Year 2, pupils should be able to tell the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times. They should also know the number of minutes in an hour and the number of hours in a day.

In Year 3, children read the time in analogue (including using Roman Numerals). By this stage they are also learning to read digital time in 12 and 24 hour clock, using the AM and PM suffixes. Pupils record and compare time in terms of seconds, minutes and hours; know the number of seconds in a minute, days in a month and year and compare durations of events.

By Year 4, pupils should be confident telling the time in analogue to the nearest minute, digital and 24 hour clock. They also need to be able to read, write and convert time between analogue and digital 12 and 24 hour clocks and solve problems involving converting from hours to minutes; minutes to seconds; years to months and weeks to days.

By Year 5 and 6, there is only limited mention of time in the curriculum. Pupils continue to build on the knowledge they have picked up so far and should be confident telling the time and solving a range of problems, including: converting units of time; elapsed time word problems, working with timetables and tackling multi-step word problems .

Time word problems have been known to appear on Year 6 SATs tests. Third Space Learning’s online one-to-one SATs revision programme incorporates a wide range of word problems to develop students’ problem solving skills and prepare them the SATs tests. Available for all primary year groups as well as Year 7 and GCSE, our online tuition programmes are personalised to suit the needs of each individual student, fill learning gaps and build confidence in maths.

Word problems are important for helping children to develop their understanding of time and the different ways time is used on an every-day basis. Confidence in telling the time and solving a range of time problems is a key life skill. Time word problems provide children with the opportunity to build on the skills they have picked up and apply them to real-world situations.

It’s important children learn the skills needed to solve word problems. Key things they need to remember are: to make sure they read the question carefully; to think whether they have fully understood what is being asked and then identify what they will need to do to solve the problem and whether there are any concrete resources or pictorial representations which will help them.

Here is an example:

Mr Arrowsmith drives to Birmingham. He sets off at 3:15pm. He stops for a break of 15 minutes at 4:50 and arrives in Birmingham at 6:15pm.

How long did Mr Arrowsmith spend driving?

How to solve:

What do you already know?

- We know that he set off at 3:15pm and stopped for a break at 4:50. We can calculate how long the first part of his journey was, by counting on from 3:15 to 4:50.
- He had a break at 4:50pm for 15 minutes, so we won’t include that in our driving time calculation.
- He then must have set off again at 5:05pm, before arriving at 6:15pm. We can use this information to work out the length of the second part of his journey.
- We can then add the 2 journey times together, to calculate the total amount of time spent driving.

How can this be represented pictorially?

- We can use a number line to calculate the length of time each journey takes.
- If we start by adding on an hour, we can then calculate how many more minutes for each section of the journey.
- Once we have calculated the journey time for each part of the journey, we can add these together to calculate the total journey time.

Time word problems in Year 2 require students to read the time to o’clock and half past the hour and compare and sequence time intervals.

Oliver went for a bike ride with his friend.

He left home at 2 o’clock and came home at 4 o’clock.

How long was he out on his bike for?

Answer: 2 hours

Count on from 2 o’ clock to 4 o’clock or subtract 2 from 4.

Mum went shopping at 3 o’clock and got home an hour later.

Draw the time she got home on the clock below.

Tom baked a cake.

The cake was in the oven for one hour.

If he took the cake out at half past 11, what time did he put the cake in?

Answer: Half past 10

Use an hour from half past 11.

Arlo starts school at 9 o’clock and has his first break at half past 10.

How long does he have to wait for his first break?

Answer: One and a half hours.

(Use a number line to count on from 9 to half past 10)

The Smith family are going to the beach.

They plan to leave home at 10 o’clock and the journey take two hours.

What time will they arrive at the beach?

Answer: 12 o’clock

(Use a number line to count on 2 hours from 10 o’clock)

With time word problems for year 3 , students build on their understanding of analogue time from Year 2 and also begin to read the time in digital (12 and 24 hour clock). Children also need to be able to compare time and durations of events.

Chloe is walking to football training.

She sets off at 8:40am and takes 17 minutes to get there.

What time does she arrive?

Answer: 8:57

(Count on 17 minutes from 8:40 – use a number line if needed)

(Picture of analogue clock with 2:30 showing here)

Maisie says that in 1 hour and 48 minutes it will be 4:28.

Do you agree? Explain how you worked out your answer.

Answer: Maisie is wrong. It will be 4:18.

This can be worked out by counting on an hour from 2:30 to 3:30 and then another 48 minutes to 4:18.

The Baker family are driving to their campsite.

They set off at 8:30 am, drive for 2 hours and 15 minutes, then had a 30 minute break.

If they drive for another 1 hour and 45 minutes, what time do they arrive at the campsite?

Answer: 12:45pm

Use a number line to show what time they arrive at the break. From 8:30, count on 2 hours and 15 minutes to get to 10:45. Add on the 30 minute break. It is now 11:15. They count on another hour and a half to 12:45

Ahmed looks at his watch and says ‘it is half past 4 in the afternoon’

Jude says that it is 17:30 in a 24 hour clock.

Is Jude correct? Explain your answer.

Answer: Jude is not correct. Half past 4 in the afternoon is 16:30 not 17:30

How many minutes are there in 2 hours and 30 minutes?

Answer: 150 minutes

60 + 60 + 30 = 150

When solving time word problems for year 4 , pupils need to be confident telling time in analogue, and digital, as well as converting between analogue, 12 hour and 24 hour clock. They also begin to solve more challenging problems involving duration of time and converting time.

If there are 60 seconds in 1 minute. How many seconds are there in 8 minutes?

Answer: 480 seconds

60 x 8 = 480 seconds (calculate 6 x 8, then multiply by 10)

Mason played on his VR from 3:35 to 5:25.

How long did he play on his VR?

Answer: 1 hour and 50 minutes.

Count on from 3:35 (using a numberline if needed)

Jamie started his homework at 3:45pm. He finished 43 minutes later.

What time did Jamie finish? Give your answer in 24 hour clock.

Answer: 16:28

Count on 43 minutes from 3:45 (use a number line, if needed) = 4:28. Convert to 24 hour clock.

Chloe and Freya went to the cinema to watch a film. The film started at 2:05pm and lasted for 1 hour and 43 minutes.

What time did the film end?

Answer: 3:48pm

Count on one hour from 2:05 pm to 3:05pm, then add another 43 minutes – 3:48pm

A family is driving on their holiday.

They drive for 2 hours and 28 minutes, stop for 28 minutes and then drive a further 1 hour and 52 minutes.

If they left at 8:30am, what time did they arrive?

Answer: 1:18pm

2 hours and 28 minutes from 8:30am = 10:58am

10:58am with a 28 minute break = 11:26am

1 hour 52 minute drive from 11:26 am = 1:18pm

With word problems for year 5 , pupils should be confident telling the time in analogue and digital and solving a wider range of time problems including: converting units of time; interpreting and answering questions on timetables and elapsed time.

The sun set at 19:31 and rose again at 6:28.

How many hours passed between the sun setting and rising again?

Answer: 10 hours and 57 minutes

Count on from 19:31 to 5:31 (10 hours)

Then count on from 5:31 to 6:28 (57 minutes)

A play started at 14:45 and finished at 16:58.

How long was the play?

Answer: 2 hours and 13 minutes

Count on 2 hours from 14:45 to 16:45, then add another 13 minutes to get to 16:58

How many seconds are there in 23 minutes?

Answer: 1380 seconds

Show as column method: 60 x 23 = 1380

Max ran a race in 2 minutes 13 seconds, Oscar ran it in 125 seconds.

What was the difference in time between Max and Oscar?

Answer: Oscar was 8 seconds faster.

Max – 2 minutes 13 seconds, Oscar – 2 minutes 5 seconds (difference of 8 seconds)

4 children take part in a freestyle swimming relay.

There times were:

Maisie: 42.8 seconds

Amber 36.3 seconds

Megan 48.7 seconds

Zymal 45.6 seconds

What was the final time for the relay in minutes and seconds?

Answer: 2:53.4

(Show as column method) 42.8 + 36.3 + 48.7 + 45.6 = 173.4 seconds

173.4 seconds = 2:53.4

No new time concepts are taught to pupils in word problems for year 6 . By this stage they are continuing to build confidence and develop skills within the concepts already taught.

Chess: 25 minutes

Basketball: 40 minutes.

Trampolining: 30 minutes

Gymnastics: 50 minutes

Tennis 40 minutes

Tri golf – 45 minutes

Hamza is choosing activities to take part in at his holiday club.

The activities can’t add up to more than 2 hours.

Which 3 activities could he do, which add up to exactly 2 hours?

Answer: Trampolining, gymnastics and tennis: Trampolining: 30 minutes, gymnastics: 50 minutes, tennis: 40 minutes.

5 children took part in a sponsored swim. The children swam for the following lengths of time:

Sam: 27 minutes 37 seconds

Jemma: 33 minutes 29 seconds.

Ben: 23 minutes 18 seconds

Lucy: 41 minutes 57 seconds

Oliver: 39 minutes 21 seconds

Answer: 18 minutes 30 seconds

Longest: Lucy: 41 minutes 57 seconds

Shortest: Ben: 23 minutes 18 seconds.

Difference – count up from 23 minutes 18 seconds to 41 minutes 57 seconds = 18 minutes 39 seconds

What is 6 minutes 47 seconds in seconds?

Answer: 407 minutes

60 x 6 = 360

360 + 47 = 407 minutes

Bethany’s goal is to run round her school running track in under 8 minutes.

She runs it in 440 seconds. Does she achieve her goal? How far above or below the target is she?

Answer: Bethany beats her target by 40 seconds

8 minutes = 8 x 60 = 480 minutes

Lucy’s favourite programme is on TV twice a week for 35 minutes.

In 6 weeks, how many hours does Lucy spend watching her favourite programme?

Answer: 7 hours

420 minutes = 7 hours

(Show as column method) 35 x 12 = 420 minutes

420 ÷ 60 = 7

For more time resources, take a look at our collection of printable time worksheets. Third Space Learning also offers a wide collection of word problems covering a range of topics such as place value, decimals and fractions word problems , percentages word problems , division word problems , ratio word problems , addition and subtraction word problems , multiplication word problems , money word problems and other word problem challenge cards.

Do you have pupils who need extra support in maths? Every week Third Space Learning’s maths specialist tutors support thousands of pupils across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to plug gaps and boost progress. Since 2013 we’ve helped over 150,000 primary and secondary school pupils become more confident, able mathematicians. Learn more or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

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## Worksheet on Word Problems on Measurement of Time

Practice the questions given in the worksheet on word problems on measurement of time. The questions are based on addition and subtraction of hours, minutes and seconds separately.

1. A bus leaves for Rampur at 4:30 p.m. It takes 1 hr. 25 min. to reach there. At what time will it reach at Rampur?

2. Shelly sleeps for 7 hours 30 minutes in a day. Foe how many hours did she sleep in the month of January?

3. The duration of a film show is 3 hr. 15 min. It starts at 6:30 p.m. When will it end?

4. The Punjab Mail arrived at Lucknow at 11:55 a.m. It reached at Lucknow 1 hr. 25 min. late. What is the scheduled arrival time of the train at Lucknow?

5. Rex visited a fashion show. He stayed there for 2 hr. 30 min. and came back at home. If he reached in the fashion show at 8:45 p.m. when did he leave for his home?

6. It takes Jon 16 hours 45 minutes to reach his home town from the city. If he starts his journey at 9:30 p.m. at what time will he reach his home town?

7. Max travelled 2 hr. 45 min. by bus and 4 hr. 45 min. by train. Calculate the time he spent in travelling.

8. David left home at 4:30 p.m. to meet his friend. He came back after 3 hr. 25 min. At what time did he came back?

9. Sharon was to board a flight at 0845 hours. Her flight was to take 5 hours 20 minutes to reach the destination, but her flight got delayed by 50 minutes. At what time will Sharon reach her destination now if there is no further delay?

10. Mary reached her school at 7:30 a.m. and left for home at 12:45 p.m. How long did she stay in school?

11. It takes Aaron 3 hour 15 minutes to travel from A City to B City and 5 hours 25 minutes to reach C City from B City. If Aaron travels from A City to C City via B City, How much time will he take?

12. A circus show started at 6:15 p.m. and ended at 9:30 p.m. What was the duration of the show?

13. Sara started her homework at 5:30 p.m. and finished it at 9:15 p.m. How much time did she take to finish her homework?

14. Adrian studies 3 hr. 45 min. He starts studying at 8:05 p.m. At what time does he finish?

15. Derek was 4 years 2 months old when he joined school. Today he is 11 years 1 month old. For how long has he been in school?

16. A school starts at 8:00 a.m. and closes at 12:45 a.m. How long does it work?

17. Jack left for Jaunpur at 4:30 a.m. He reached there at 11:55 a.m. How much time did he take to reach there?

18. Shelly started playing at 5:05 p.m. She played till 8: 15 p.m. How long did she play?

19. The doctor advised Peter to take the medicine after every 80 minutes. How many times did Peter take the medicine in a day?

20. Maya started to draw a picture at 2:45 p.m. She completed it at 4:35 p.m. How much time did she take to draw the picture?

21. Rachel works for 2 hours 25 minutes in the morning and 3 hours 40 minutes in the evening. For how much time did Rachel work in a fortnight?

22. Aaron watched a cricket match from 10:15 a.m. to 11:50 a.m. and again from 2:30 p.m. How long did he watch the match in all?

23. Rebecca has taken 20 days leave from her office. Her vacation will start Monday, 16 September. On which day and date will the vacation end?

Answers for the worksheet on word problems on measurement of time are given below.

1. 5:55 p.m.

2. 232 hours 30 minutes

3. 9:45 p.m.

4. 10:30 a.m.

5. 11:15 p.m.

6. 2:10 p.m. next day

7. 7 hr. 30 min.

8. 7:55 p.m.

9. 1455 hours

10. 5 hr. 15 min.

11. 8 hours 40 minutes

12. 3 hr. 15 min.

13. 3 hr. 45 min.

14. 11:50 p.m.

15. 6 years 11 months

16. 4 hr. 45 min.

17. 7 hr. 25 min.

18. 3 hr. 10 min.

19. 18 times

20. 1 hr. 50 min.

21. 85 hours 10 minutes

22. 4 hours.

23. 6 th October Friday

4th Grade Math Activities

From Worksheet on Word Problems on Measurement of Time to HOME PAGE

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This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

## Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

## How Many Times?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

## Wonky Watches

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

These clocks have been reflected in a mirror. What times do they say?

## The Time Is ...

Can you put these mixed-up times in order? You could arrange them in a circle.

## 5 on the Clock

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

These clocks have only one hand, but can you work out what time they are showing from the information?

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## Time and Work Formula and Solved Problems

- The basic formula for solving is: 1/r + 1/s = 1/h
- Let us take a case, say a person Hrithik
- Let us say that in 1 day Hrithik will do 1/20 th of the work and 1 day Dhoni will do 1/30 th of the work. Now if they are working together they will be doing 1/20 + 1/30 = 5/60 = 1/12 th of the work in 1 day. Now try to analyze, if two persons are doing 1/12 th of the work on first day, they will do 1/12 th of the work on second day, 1/12 th of the work on third day and so on. Now adding all that when they would have worked for 12 days 12/12 = 1 i.e. the whole work would have been over. Thus the concept works in direct as well as in reverse condition.
- The conclusion of the concept is if a person does a work in ‘r’ days, then in 1 day- 1/r th of the work is done and if 1/s th of the work is done in 1 day, then the work will be finished in ‘s’ days. Thus working together both can finish 1/h (1/r + 1/s = 1/h) work in 1 day & this complete the task in ’h’ hours.
- The same can also be interpreted in another manner i.e. If one person does a piece of work in x days and another person does it in y days. Then together they can finish that work in xy/(x+y) days
- In case of three persons taking x, y and z days respectively, They can finish the work together in xyz/(xy + yz + xz) days

## Time and work problems

Time and work concepts, time and work problems (easy), time and work problems (difficult).

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## Course: 4th grade > Unit 14

- Finding reasonable unit of measurement example
- Estimating time (seconds, minutes, and hours)
- Time differences example
- Time differences
- Time word problem: puzzle
- Time word problem: travel time

## Telling time word problems

- (Choice A) A
- (Choice B) B
- (Choice C) C
- (Choice D) D

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They are ideal for working towards National Curriculum aims for Maths. Time Events Problems Differentiated Worksheets – Print these worksheets in black and

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Worksheet on Word Problems on Measurement of Time · 1. A bus leaves for Rampur at 4:30 p.m. It takes 1 hr. · 2. Shelly sleeps for 7 hours 30 minutes in a day. · 3.

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