Timetables and Itineraries: a week of ready-to-teach maths

Five days of lessons for Year 6 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet with its own timetable or itinerary, plus duration match cards, day-out activity cards, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the duration match cards and the day-out activity cards once, one set per pair.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.

No maths background needed

This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: a duration is the time between two clock times, and because an hour has 60 minutes, not 100, it is found by counting on through the hour rather than by subtracting the numbers. A timetable lists the choices; an itinerary is the plan you choose from them. Planning often runs backwards, from the time you must arrive to the time you must leave.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.

Words to watch

All times in this pack are in 24-hour time, as on the board: 8:15 is a quarter past eight in the morning and 13:45 is a quarter to two in the afternoon. A service is one bus or train trip; departs means leaves and arrives means gets in. A connection is the next service you must catch after you get off, and a wait is the time between the two.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 reads a timetable; Day 2 works out durations; Day 3 follows and completes an itinerary; Day 4 joins two timetables with a connection; and Day 5 plans backwards from a deadline and builds an itinerary of its own. It builds on the Year 5 work of 12- and 24-hour time (AC9M5M03). The same reading of tables and planning carries into later work with data tables and rates, and into real journeys outside school.

Materials for the week (one trip)

• From the classroom: pencils, scissors and this pack printed; an analogue clock with moving hands helps on Day 2.
• If you can, print a real local bus or train timetable for Day 4 as an extra challenge.
• Cut out once: the duration match cards and the day-out activity cards, one set of each per pair.

Words for the word wall

timetable, itinerary, service, depart, arrive, duration, elapsed time, connection, wait, 24-hour time, schedule, deadline, plan

Dear families

This week in maths, Year 6 reads timetables, works out how long journeys and events take, and plans trips with itineraries, including catching a connection and working back from the time we must arrive.

Try this at home

• Look at a real bus, train or ferry timetable together and plan a trip you might take.
• Before an outing, work out when to leave so you arrive on time, then check how close you were.
• Find how long a favourite show, a sports game or a car trip lasts from its start and end times.
• Write tomorrow morning as an itinerary: each stage with its time, from waking to arriving at school.

Times this week

Fill one row a day. Write an event or a trip, when it started and finished, and how long it took.

Printed from the free seegongsik Timetables and Itineraries teaching pack · seegongsik.com/au/y6/measurement/AC9M6M03/pack

Read the timetable

A timetable sets times out in a grid. In most bus and train timetables each column is one service and each row is one stop, so you find your stop’s row and read across, or follow one bus down its column. Children read a timetable, find trip times and waits, choose a bus that arrives by a set time, and add a new service.

We are learning to

• find a time in a timetable from its row and column,
• work out a trip time and a wait from a timetable,
• choose the service that arrives by a given time.

Success criteria

• I can find when the 8:10 bus reaches the Library.
• I can choose the latest bus from Main Street that reaches Beach Terminal by 9:00.

You need

The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the first three questions in Part A; start Session B with the fourth.

Watch for these ideas

• Reading along the wrong row or down the wrong column.
• Choosing a bus by the time it leaves when the question is about when it arrives.
• Expecting the next bus to come at the usual gap when the gaps are not all the same.

Answers

• Part A: (1) 8:25; (2) 40 min; (3) 8:48, a wait of 18 min; (4) bus B, leaving Main Street at 8:33 and arriving 8:50; (5) 25 min; (6) 45 min.
• Part B: 10:00, 10:08, 10:15, 10:23, 10:40.
• Part C: (1) true, (2) false, (3) true, (4) false.

Read the timetable

Route 42, Monday to Friday. Times are in 24-hour time.

A. Find it

1. When does the 8:10 bus from Hilltop Station reach the Library?  ______________

2. How long does the whole trip from Hilltop Station to Beach Terminal take?  ______________

3. You reach Park Road at 8:30. When does the next bus come, and how long do you wait?  ______________

4. You must be at Beach Terminal by 9:00. Which is the latest bus you can catch from Main Street?  ______________

5. How long is the ride from the Library to Beach Terminal?  ______________

6. How long is the gap between the last two buses leaving Hilltop Station?  ______________

B. Add a bus

Bus E leaves Hilltop Station at 10:00 and takes the same time between stops. Write its times.

C. True or false?

1. Every bus takes 40 min from Hilltop Station to Beach Terminal.  ______

2. Bus C reaches Main Street at 9:13.  ______

3. Two buses leave Hilltop Station between 8:00 and 9:00.  ______

4. A bus leaves Park Road every 30 min all morning.  ______

How long?

A duration is the time from a start to an end. An hour has 60 minutes, not 100, so durations are found by jumping along a time line: to the next o’clock, then whole hours, then the minutes left. Subtracting clock times like ordinary numbers only works when no hour is crossed. Children jump along time lines, find the durations in a school day, and explain the slip.

We are learning to

• find a duration by jumping along a time line through the hour,
• write durations in hours and minutes,
• explain why subtracting clock times like ordinary numbers can fail.

Success criteria

• I can find the time from 10:50 to 12:15 with jumps.
• I can explain why 11:50 to 12:35 is not 85 minutes.

You need

The worksheet, one per child, the duration match cards (cut-outs), one set per pair, and a clock with hands if you have one.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the school day in Part B.

Watch for these ideas

• Subtracting the times as if an hour had 100 minutes.
• Counting the jump to the next hour wrongly, such as 10:50 to 11:00 as 50 minutes.
• Writing 1 h 25 min as 1.25 h, as if the minutes were a decimal part of an hour.

Answers

• Part A: 45 min, 1 h 25 min, 1 h 45 min, 1 h 15 min.
• Part B: assembly 20 min, maths 1 h 15 min, recess 25 min, science 1 h 10 min, lunch 50 min, sport 1 h 15 min, library 45 min; the whole day is 6 h; Maths and Sport are longest (1 h 15 min); Maths is 5 min longer than Science.
• Part C: (1) 45 min; (2) 1 h 25 min; (3) 1 h 35 min; (4) right, 35 min, as no hour is crossed.

How long?

A. Jump along the time line

Draw your jumps above each line: to the next o’clock, then whole hours, then the minutes left.

B. A school day

How long is the whole school day? ______   Which sessions are longest? ______________________

How much longer is Maths than Science? ______

C. Spot the slip

Alex worked out each duration by subtracting the times like ordinary numbers. Tick the right ones and fix the others.

1. 11:50 to 12:35: 1235 − 1150 = 85 minutes.  ______________________

2. 9:45 to 11:10: 1110 − 945 = 165 minutes.  ______________________

3. 14:40 to 16:15: 1615 − 1440 = 175 minutes.  ______________________

4. 8:15 to 8:50: 850 − 815 = 35 minutes.  ______________________

Itineraries

An itinerary is a plan of stages in order, each with its times. Where a timetable lists the choices, an itinerary is the plan that was chosen. Children follow a class excursion itinerary, fill in its missing start times, end times and durations, find the total time and the time spent travelling, and see what one delay does to every later time.

We are learning to

• follow an itinerary stage by stage,
• find a missing start, end or duration from the other two,
• work out how a delay changes the rest of a plan.

Success criteria

• I can fill in a missing end time from a start time and a duration.
• I can work out when the class gets back if the bus leaves 15 min late.

You need

The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the questions in Part B.

Watch for these ideas

• Adding a duration to the end time instead of the start time.
• Leaving out the gaps between stages, such as the walk from the bus to the koala talk.
• Adding durations across the hour as if an hour had 100 minutes.

Answers

• Part A, the missing cells in order: 9:35, 30 min, 10:15, 11:20, 45 min, 12:05, 13:55.
• Part B: (1) 5 h 10 min, from 8:45 to 13:55; (2) 1 h 40 min; (3) 14:10; (4) 1 h 5 min after getting back on time.
• Part C: itineraries vary; check that each end is its start plus its duration.

Itineraries

Year 6 excursion to the wildlife park. Times are in 24-hour time.

A. Fill the gaps

B. What if?

1. How long is the class away from school?  ______________

2. How much of that time is spent on the bus?  ______________

3. The bus back leaves 15 min late. When does the class get back to school?  ______________

4. School finishes at 15:00. If the bus is on time, how long is left after the class gets back?  ______________

C. Your own itinerary

Plan a morning with four stages. Give each a start, an end and how long it takes.

Connections

A journey often joins two services: you get off one and catch the next. A connection works only if the next service leaves after you arrive, with enough time to change. Children read a train timetable and a bus timetable together, allow 5 min to walk between them, and choose the services that reach the zoo on time.

We are learning to

• read two timetables together to plan a journey,
• allow time to change between services,
• choose the latest services that still arrive on time.

Success criteria

• I can plan a journey from Riverton to the zoo with one change.
• I can say whether a connection works when I need 5 min to change.

You need

The worksheet, one per child, and a real local timetable for an extra challenge if you have one.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the changes in Part B.

Watch for these ideas

• Forgetting the time needed to change, so a gap of 2 minutes looks like a connection.
• Reading the train’s leaving time when the question needs its arrival at the change.
• Choosing the earliest service when the question asks for the latest that still arrives on time.

Answers

• Part A: (1) 9:13, the 9:20 bus, at the zoo 9:45, 1 h 10 min in all; (2) the 9:05 train, then the 9:50 bus; (3) 10:23, the 10:50 bus, at the zoo 11:15; (4) 7 min.
• Part B: (1) make it, (2) miss it, (3) make it, just, (4) miss it.
• Part C: the 9:47 train from Fairfield, in at 10:13, then the 10:20 bus, at the zoo 10:45.

Connections

Times are in 24-hour time. It takes 5 min to walk from the train to the bus stop at City Station.

A. Plan the trip

B. Make it or miss it?

You need 5 min to change. Write make it or miss it.

C. From Fairfield

You get on the train at Fairfield and must be at the zoo by 11:00. Which train and which bus do you catch? ______________________________

Plan backwards

Planning often runs backwards: you know when you must arrive and work out when to start by taking each step away from the deadline, the last step first. Children work back from deadlines, then plan a class day out from activity cards so that every stage fits between leaving school and the time to be back.

We are learning to

• work back from a deadline to a start time,
• take several durations away in order,
• plan an itinerary that fits a time limit.

Success criteria

• I can work out when to start getting changed for 17:30 training.
• I can plan a day out that gets back by 14:45.

You need

The worksheet, one per child, and the day-out activity cards (cut-outs), one set per pair.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the day out in Part B.

Watch for these ideas

• Adding the durations to the deadline instead of taking them away.
• Taking minutes away like ordinary numbers, so 9:00 take away 40 minutes becomes 860, written 8:60.
• Fitting the activities but forgetting the bus ride back.

Answers

• Part A: (1) 16:45, (2) 13:37, (3) 14:55, (4) 7:55.
• Part B: plans vary. The bus takes 1 h 20 min of the 5 h 30 min, so the activities must fit in 4 h 10 min. One plan that fits is on the activity card sheet.

Plan backwards

A. Work back from the deadline

B. Plan a day out

The class leaves school at 9:15 and must be back by 14:45. The bus takes 40 min each way. Choose activity cards and write the itinerary.

Back at school at ______   Minutes to spare ______   Do you fit? ______

Duration match

Cut out the twelve time cards and the twelve duration cards once, one set for each pair.

Duration match (Day 2)

1. Shuffle all twenty-four cards and lay them face down in rows.
2. Take turns to turn over two cards. A time card and the duration card that matches it make a pair.
3. Say your jumps aloud to keep a pair. If you are wrong, or the cards do not match, turn them back. Most pairs wins.

Teacher note, each time and its duration: 9:35 to 9:50, 15 min; 10:50 to 11:10, 20 min; 7:45 to 8:10, 25 min; 12:40 to 13:15, 35 min; 15:30 to 16:10, 40 min; 8:25 to 9:10, 45 min; 14:35 to 15:25, 50 min; 11:20 to 12:15, 55 min; 16:50 to 17:55, 1 h 5 min; 6:40 to 7:55, 1 h 15 min; 18:45 to 20:10, 1 h 25 min; 13:30 to 15:10, 1 h 40 min.

Day-out activity cards

Cut out the activity cards and the two bus cards once, one set for each pair.

Plan a day out (Day 5)

1. Start with the bus to the city at 9:15 and end with the bus back to school, which must arrive by 14:45.
2. Lay activity cards in order between the two bus cards. Write each start and end time on the worksheet.
3. Check that you are back in time. Swap a card for a shorter one if you run over, or add a short one if there is time left.

Teacher note: the activities must fit in 4 h 10 min. One plan that fits: bus to the city 9:15 to 9:55, museum tour 9:55 to 11:10, lunch in the park 11:10 to 11:50, science show 11:50 to 12:35, botanic garden walk 12:35 to 13:45, ice-cream stop 13:45 to 14:00, bus back to school 14:00 to 14:40, with 5 min to spare.

What we know: Timetables and Itineraries

Work on your own. Show your thinking if you can. Times are in 24-hour time.

1. A bus departs 7:55 and arrives 8:40. How long is the trip? ______
2. A train leaves at 10:45 and the trip takes 1 h 20 min. When does it arrive? ______
3. How long is it from 13:50 to 15:25? ______
4. Explain why 10:40 to 11:15 is not 75 minutes. How long is it? ______________________
5. A morning plan: swimming 9:00 to 9:45, morning tea 9:45 to 10:05, art 10:05 to 11:00. How long is the plan altogether? ______
6. Your train arrives at 11:52 and you need 5 min to reach the bus stop. Buses leave at 11:55 and 12:10. Which bus do you catch? ______
7. A trip of 35 min must arrive by 13:10. What is the latest time you can leave? ______
8. School starts at 8:50. The walk takes 20 min and breakfast takes 15 min. When do you start breakfast? ______

Answers and marking guide

Answers

1. 45 min.
2. 12:05.
3. 1 h 35 min.
4. 35 min: an hour has 60 minutes, so the jump is 20 min to 11:00 and 15 min more.
5. 2 h.
6. The 12:10 bus: you reach the stop at 11:57, after the 11:55 bus has gone.
7. 12:35.
8. 8:15.

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and counts on through the hour rather than subtracting the clock numbers.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: reading timetables, duration, itineraries, connections, and planning backwards.