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# Maths Year 4 Autumn Measures and Data

Each unit has everything you need to teach a set of related skills and concepts. 'Teaching for Understanding' provides whole-class teaching and fully differentiated adult-led group activities. ‘Problem-solving and Reasoning’ develops these skills, and includes questions to enable you to assess mastery. Practice sheets ensure procedural fluency. Extra support activities enable targeted work with children who are well below ARE.

‘UNIT PLAN’ gives you a text version of all parts of the unit to use in your school planning documentation. ‘DOWNLOAD ALL FILES’ gives you that unit plan plus all of associated documents. These bulk downloads are available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

## Unit 1 Tell time to nearest minute: am/pm (suggested as 3 days)

### Objectives

Telling time to nearest minute; am and pm
Unit 1: ID# 4261

National Curriculum
Meas (i) (v)

Hamilton Objectives
37. Convert between units of time, analogue/digital times, and between 12-hour and 24-hour times.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Launch ITP Tell the time. Recap telling the time by moving the minute hand around clock at 5-minute intervals. Establish that there are 5 divisions between the numbers, each of which represents 1 minute. Count marks with children to tell time to the minute. Distinguish am and pm as morning and afternoon/evening.
Group Activities
-- Suggest start and finish times to the nearest minute for a day of given holiday camp activities.
-- Make and match analogue and digital times to personal activities.

Day 2 Teaching
Imagine school started 40 mins later. Find all the activity times, now 40 mins later, crossing the hour as necessary. Record times in both analogue and digital times, and work out time intervals.
Group Activities
-- Calculate the times of films that are showing late at a cinema.
-- Solve word problems that add various time intervals to go through the hour.

Day 3 Teaching
Show children that to calculate time intervals, we can use Frog to find the difference between times like finding a difference between 2 numbers on a number line. Model finding time intervals using Frog, crossing the hour, using both analogue and digital clocks.
Group Activities
Use the ‘Palindromic Time Intervals’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Create and challenge one another with time problems that add various time intervals to go through the hour.
-- Identify start times, finish times and the length of programmes and activities from TV guides and swimming timetables.

### You Will Need

• ITP: Tell the Time
• Holiday camp sheet (see resources)
• Small analogue clocks
• Cinema times sheet (see resources)
• Internet access (required for Day 2)
• Children’s TV programme guide
• Local swimming pool timetable

### Mental/Oral Maths Starters

Day 1
Pairs that make 60 (pre-requisite skills)

Day 2
Roman numeral clock (pre-requisite skills)

Suggested for Day 3
Order months (simmering skills)
OR
Units of time (simmering skills)

### Procedural Fluency

Day 1
What’s the time? Show analogue and digital forms of a given time.

Day 2
Find the finish time. Calculate the finish time of activities at a sports centre, based on start times and length of activity.

Day 3
Calculate times.

### Mastery: Reasoning and Problem-Solving

• Write the times for breakfast, lunch and tea on a Saturday in digital and analogue format. Make sure you use am and pm correctly.
• How long to the next hour from:
(i) 4:54
(ii) quarter to 12
(iii) twenty past 9
• Complete each sentence.
4:35 + ☐ minutes = 5:05
11:30 – ☐ minutes = 10:40
6:14 + ☐ minutes = 7:00
8:45 + 18 minutes = ☐
• How long was each film?
(a) started at 6:15pm and ended at 7:05pm
(b) started at 11:20am and ended at 1:15pm
(c) started at 9:00pm and ended at ten to eleven.

In-depth Investigation: Palindromic Time Intervals
Children systematically find palindromic digital times and list them in an ordered way. They convert these to analogue times and calculate the intervals between them.

### Extra Support

Stop the Clock
Telling the time to the ¼ hour on analogue and digital clocks

Match the Times
Telling the time to 5 minutes on analogue and digital clocks

## Unit 2 Calculate time intervals; 24 hour clock (suggested as 3 days)

### Objectives

Tell time and calculate time intervals; 24 hour clock
Unit 2: ID# 4271

National Curriculum
Meas (i) (v)

Hamilton Objectives
33. Convert between units of measurement, e.g. units of time.
37. Convert between units of time, analogue/digital times, and between 12-hour and 24-hour times.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use ITP Tell the time and show several times. Match digital to analogue times and ensure children understand ‘to’ as well as ‘past’ the hour times. Introduce 24-hour clock, explaining that for pm times we add 12 hours.
Group Activities
-- Order various times presented in 24-hour format.
-- Match am/pm times to 24-hour clock equivalents in a game of bingo.

Day 2 Teaching
Ask why we use a 24-hour clock. Say it helps to differentiate between am and pm times. Explain that we don’t say 13 o’clock but 13 hundred hours and 16:45 as sixteen forty-five. Practise saying different 24-hour times by writing them on the board and asking children to read them out. Write 24-hour times in a 2 × 3 grid and ask children to convert them to 12-hour am/pm times in their own grids.
Group Activities
-- Creating and playing pairs or snap games with analogue and digital times using am/pm and 24-hour clock formats.

Day 3 Teaching
Show a 24-hour train timetable (see resources). Ask how we know if the times are am/pm? Why do train timetables use 24-hour time? Establish that it helps travellers make sure they turn up at the right time of day! Use a train timetable to calculate intervals.
Group Activities
Use the ‘Time to Reflect’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Explore and answer a series of questions about bus timetables, then create their own.

### You Will Need

• ITP: Tell the time (see resources)
• ‘24-hour time’ sheet (see resources)
• scissors and glue
• Additional activity sheets (see resources)
• Small pieces of card
• Small analogue clocks

### Mental/Oral Maths Starters

Day 1
Tell Time on an analogue clock (pre-requisite skills)

Day 2
Convert analogue times to digital (pre-requisite skills)

Day 3
Find the time a number of minutes later (pre-requisite skills)

### Procedural Fluency

Day 1
Children match 12-hour and 24-hour time formats.

Day 2
Children match 12-hour and 24-hour time formats, showing times to the minute.

Day 3
Children solve a timetable conundrum in 24-hour format.

### Mastery: Reasoning and Problem-Solving

• Each of these train times is given using 24-hour clock. How will they appear when shown on the station analogue clock?
13:40 to London
14:45 to Bristol
15:13 to Newcastle
16:05 to Birmingham
17:35 to Chester
• True or false?
Half an hour after 4:45 is quarter past 5.
16:30 is 4:30pm.
00:30 is half past midday.
Quarter of an hour after 13 minutes to 6pm is 18:02
• Write the missing times.
☐ minutes past 2:50 is quarter past 3.
35 minutes before 7:10 is ☐ minutes to 7.
☐ minutes to ten past midnight is 23:45.

In-depth Investigation: Time to Reflect
Children apply their knowledge of 24 hour digital clocks and look at their reflections in a mirror.

### Extra Support

Pinks and Blues
Telling the time to 5 minutes on analogue and digital clocks

## Unit 3 Units of time, record data and interpret (suggested as 2 days)

### Objectives

Units of time; timing events and recording data; interpret results
Unit 2: ID# 4283

National Curriculum
Meas (i) (vi)
Stats (i)

Hamilton Objectives
37. Convert between units of time, analogue/digital times, and between 12-hour and 24-hour times.
38. Interpret and present discreet data using bar charts, pictograms and tables, and continuous data on time graphs; answer questions re: data.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Four children write their name 20 times and four others time them. Record times in a table. Discuss how we can draw a bar chart to represent this data. What scale shall we have? Try 1 step = 5 or 10 seconds. Which will fit on the page but not look too small? Discuss and draw a bar chart. Discuss questions that could be asked about the data. Children then write their name 10 times and record the time.
Group Activities
-- Use self-generated data to draw bar charts.

Day 2 Teaching
Show children the table showing the number of children that were born in the first 7 months of the year. Discuss this. Say that we will represent this information in a pictogram – one picture represents four units. Draw this together.
Group Activities
Use the in-depth problem-solving investigation ‘Real Statistics’ from NRICH as today’s group activity.
Or, use these activities:
-- Use given data to devise and create pictograms.

### You Will Need

• IWB stopwatch (see resources)
• Computer data-handling package
• Pre-prepared bar chart
• Creating pictograms’ (see resources)
• Sunshine data from projectbritain.com

### Mental/Oral Maths Starters

Suggested for Day 1
4 times table (simmering skills)

Day 2
Convert units of time (pre-requisite skills)

### Procedural Fluency

Day 1
Children draw bar charts from collected data.

Day 2
Children create pictograms from given data.

### Mastery: Reasoning and Problem-Solving

• Estimate how long it will take you and a friend to write ‘The quick brown fox jumps over the lazy dog.’ 3 times. Write your estimates in seconds. Try it. How close were you?
• Complete each equivalence:
☐ seconds = 2 minutes
24 hours = ☐
2½ hours = ☐ minutes
☐ days = a fortnight
☐ months = 2 years
• This bar chart shows the number of texts sent each day by one family. (The vertical axis is marked in 5s.)

 // // // // // // // // // // // // // // // // Mum Dad Me Tom Nana

How many texts are sent in total each day?
Which two people send 40 between them?

In-depth Investigation: Real Statistics
Analyse a table of data showing how children travel to school. How does it compare with children in your class? Real Statistics from nrich.maths.org.

### Extra Support

This unit has no separate Extra Support activities.

## Unit 4 Rehearse 24 hour clock; time intervals (suggested as 2 days)

### Objectives

Rehearse 24 hour clock; time intervals
Unit 4: ID# 4289

National Curriculum
Meas (i) (v)

Hamilton Objectives
33. Convert between units of measurement, e.g. units of time
37. Convert between units of time, analogue/digital times, and between 12-hour and 24-hour times.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Revise 24-hr clock using a train timetable and relating times to the school day. Convert 24-hour clock times to am and pm times and vice versa. Count in steps of 1 hour on a counting stick from different starting times, through midday and midnight.
Group Activities
-- Work out start times of TV programmes; convert 24-hour clock times to 12-hour times (and vice versa) and into analogue format.

Day 2 Teaching
Visit an online TV guide. Children write start times using 12-hour format (they are in 24-hour format on the website). Children find programmes lasting less than half an hour, then those lasting more than half an hour. Scroll for a programme crossing an hour. Sketch a time line jotting to show how to find the length of this programme. Repeat.
Group Activities
Use the in-depth problem-solving investigation ‘Slow Coach’ from NRICH as today’s group activity.
Or, use these activities:
-- Find as many pairs of times either side of 18:00 with a given difference.
-- Find the time interval between sunrise and sunset at different UK locations.

### You Will Need

• Counting stick
• ‘Table of times’ sheet (see resources)
• ‘TV guide’ sheet (see resources)
• ’12-hour and 24-hour times from midday’ sheet (see resources)
• Analogue clock face with movable hands
• An online TV guide from e.g. bbc.co.uk
• The National Schools’ Observatory website

### Mental/Oral Maths Starters

Day 1
Convert pm times to 24-hr times (pre-requisite skills)

Day 2
Convert time on analogue clocks to digital format and written analogue times (pre-requisite skills)

### Procedural Fluency

Day 1
Children convert between Roman numeral, analogue, 12-hour digital and 24-hour digital times.

Day 2
Children add various time intervals to given start times.

### Mastery: Reasoning and Problem-Solving

• Create start and end times for these programmes, so that they start before an o’clock time and end after it.
(a) The Cool – 25 minutes
(b) Big Matt – 32 minutes
(c) Cucumber Cat – 49 mins
(d) Don’t go there – 55 mins
Write the times as pm times and then as 24-hour clock times.
• Calculate the length of Fred’s journey in total. (Don’t count his coffee and shopping time!)
He catches his train at 9:30am. His train arrives at ten to 11.
He goes and has a coffee and does a bit of shopping. Then he re-starts his journey. He waits 20 minutes for a bus, which then arrives at 12:12. It reaches its destination at 13:30. His Nan picks him up and they get to her house at 14:05.

In-depth Investigation: Slow Coach
Calculate time intervals to investigate return journeys on a coach timetable. Slow Coach from nrich.maths.org.

### Extra Support

This unit has no separate Extra Support activities.

## Unit 5 Units of time; draw line graphs (suggested as 3 days)

### Objectives

Use units of time in collecting data; draw line graphs
Unit 5: ID# 4297

National Curriculum
Meas (i) (vi)
Stats (i)

Hamilton Objectives
33. Convert between units of measurement, e.g. units of time
38. Interpret and present discreet data using bar charts, pictograms and tables, and continuous data on time graphs; answer questions re-data.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use a line graph depicting children’s heights against their age on the ITP Line graph. Show how a line graph can enable us to read a child’s height for ages that are not plotted. Show a line graph of a baby’s weight to the nearest 100g during the first 12 months of its life and discuss.
Group Activities
-- Draw, interpret and describe child growth line graphs.
-- Interpret and describe line graphs that show volume of water in a filling bath.

Day 2 Teaching
Show the table of data of shadow length during the day. Sketch a line graph to show the lengths of a shadow at the different times of day, discussing an appropriate scale for both axes. Join the points with a curve. Use the graph to estimate the length of the shadow at intermediate points.
Group Activities
-- Draw, read, interpret and describe a time graph showing customers in a shop across a day.

Day 3 Teaching
Display a calendar. Ring today’s date. Show children how we can see what day of the week it is. What will be the date on this day next week? Ring the last day of term; find how many weeks (or months) and days away it is. Count the weeks and days to the last day of term. Then work out length of the holidays. Rehearse lengths of months.
Group Activities
Use the ‘Day I was Born’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Convert from weeks to days, then hours, then minutes, then seconds through various challenges.

### You Will Need

• ITP: Line Graph
• ‘Table of baby’s weight’ (see resources)
• ‘Questions about the graph’ (see resources)
• Addtional activity sheets (see resources)
• Stick, at least 60cm long
• Copy of this year’s calendar

### Mental/Oral Maths Starters

Suggested for Day 1
Convert between cm and mm (1 decimal place) (simmering skills)

Suggested for Day 2
Convert between m and cm to m (2 decimal places) (simmering skills)

Suggested for Day 3
Convert between km and m, l and ml (1 decimal place and no decimal place) (simmering skills)

### Procedural Fluency

Day 1
Children draw, interpret and describe plant growth line graphs.

Day 2
Children draw, interpret and describe a graph for classroom noise data.

Day 3
Children are challenged to convert between days, hours, minutes and seconds.

### Mastery: Reasoning and Problem-Solving

• Explain in two sentences why a line graph would be more useful than a bar chart in showing the growth of a small child over their first year.
• Use this table of data to draw a line graph to convert between £ and €.
How much is £2.50 in euros?
How many £ is 5 euros?

 € £ 1 89p 2 1.77 3 2.66 4 3.54 5 4.43 6 5.31
• Write the dates of the next 4 Saturdays.
In which year is the next February 29th?
Which two adjacent months have 62 days?

In-depth Investigation: Day I Was Born
Children calculate the day they were born on, and other birthdays of friends and family. They then investigate corresponding months.

### Extra Support

This unit has no separate Extra Support activities.