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# Maths Year 5 Summer 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 added value for Hamilton Friends and School Subscribers.

## Unit 1 24-hr timetables; calculate time intervals (suggested as 4 days)

### Objectives

Read timetables using 24 hour clock; calculate time intervals
Unit 1: ID# 5903

National Curriculum
Meas (vi)
Stats (ii)

Hamilton Objectives
40. Solve problems involving converting between units of time; use 12- and 24-hour times, find time intervals and tell the time with confidence.
43. Complete, read and interpret information in tables, including timetables.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Revise 24-hour clock times. Revise counting up on a time number line to calculate time intervals in the context of school lessons, e.g. from 10:45 to 11:35, 13:30 to 14:45, 11:50 to 12:35.
Group Activities
-- Calculate time intervals on the class timetable.
-- Calculate time intervals on the class timetable, then compare with lesson durations in a younger class.

Day 2 Teaching
Ask questions requiring simple interpretation of the Hogwarts Train Timetable, e.g. What time does the 08:45 reach Ottery St Catchpole? Convert 24-hour to 12-hour times and vice versa. Then ask questions requiring calculation of time intervals, e.g. How long does the 08:45 from Diagon Alley take to reach Ottery St Catchpole? Which is the fastest train between Kings Cross and Hogwarts?
Group Activities
-- Investigate journey times by interpreting a train timetable.

Day 3 Teaching
Use and interpret the timetable for the North Yorkshire Steam Railway. Practise writing 24-hour times as 12-hour times. Calculate time intervals and solve reasoning problems.
Group Activities
-- Plan itineraries using a real railway timetable.

Day 4 Teaching
Give fictitious train delay announcements, e.g. The 14:48 to Birmingham New Street is running approximately 37 minutes late as a result of sheep on the line near Worcester. Model counting up on a number line to find the new departure time. Repeat.
Group Activities
-- Use counting on on a number line as a strategy for adding a time duration to a start time.

### You Will Need

• Mini-whiteboards and pens
• Class timetable from Y1 (or other class with a different timetable)
• ‘Hogwarts Train Timetable’ (see resources)
• ‘North Yorkshire Moors Steam Railway timetable’ (see resources)

### Mental/Oral Maths Starters

Day 1
Read the 24-hour clock (pre-requisite skills)

Day 2
Converting between the 12- hour and the 24- hour clock (pre-requisite skills)

Suggested for Day 3
Pairs to 60 (simmering skills)

Suggested for Day 4
Units of time (simmering skills)

### Procedural Fluency

Day 1
Calculate elapsed times.
Create a schedule for DIY tasks.

Day 2
Interpret a fictional timetable, including reading times and calculating durations.

Day 3
Interpret a fictional timetable, including calculating elapsed times.

Day 4
Given start times and an elapsed time, find journey end times.

### Mastery: Reasoning and Problem-Solving

• True or false?
13:40 is twenty to two in the afternoon.
Midnight is 00:00.
Midday is 12:00 on the 24- hour clock.
19:15 is quarter past 7 in the morning.
1 hour after 15:00 is six o’clock pm.
• Calculate how long it is between:
13:40 and five to 5 in the afternoon.
Quarter to midday and 17:23.
Five past midnight and ten to midday.
• If each bus is 40 minutes late, write its new arrival time.
(i) Number 31 bus due at 12:55.
(ii) Number 22 bus due at 13:04.
(iii) Number 15 bus due at 14:44.
• The number 4A bus arrived 27 minutes late at 00:14. What time was it due?

In-depth Investigation
Use the investigation described in the group activities for Day 3.

### Extra Support

Two Clocks
Consolidate children’s understanding of telling the time on analogue clocks. Two Clocks from nrich.maths.org.

## Unit 2 Draw line graphs and conversion graphs (suggested as 2 days)

### Objectives

Draw line graphs and conversion graphs
Unit 2: ID# 5923

National Curriculum
Meas (vii)
Stats (i) (ii)

Hamilton Objectives
44. Create and interpret line graphs, solving comparison, sum and difference problems.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Draw a vertical axis from 0 to 75 labelled ‘product’ in steps of 5 and a horizontal axis from 0 to 15 labelled ‘multiplier’. Write the title ‘A line graph to show multiples of 5’. Complete the graph, plotting the multiples of 5. How could we use the graph to find 14 × 5? Show how intermediate points on this line can be used to find 2.5 × 5. If we were to sketch a graph for the 3 times table what might look similar? What would look different? Take children’s suggestions.
Group Activities
-- Draw line graphs of multiplication tables; read off whole number and intermediate values.
-- Draw line graphs of multiplication tables; read off whole number and intermediate values; use to solve problems.

Day 2 Teaching
Show a table of approximate conversions from kilograms to ounces and pounds and ounces. Point out that pounds and ounces are often used to give the weight of born baby. Model how to draw a conversion line graph for these measures, with kg on the horizontal axis and ounces on the vertical.
Group Activities
Use the in-depth problem-solving investigation ‘Graphing number patterns’ from NRICH as today’s group activity.
Or, use this activities:
-- Plot a graph for converting cm to inches; and use it to convert measurements.
-- Adjust two different recipes by scaling measurements up and down and converting between grams and ounces.

### You Will Need

• Interactive whiteboard software with squared/graph paper background
• Squared paper or graph paper
• Rulers marked in inches and cm
• ‘Recipe conversions 1 and 2’ (see resources)

### Mental/Oral Maths Starters

Day 1
Times tables (pre-requisite skills)

Suggested for Day 2
Round decimal numbers to the nearest tenth and whole (simmering skills)

### Procedural Fluency

Day 1
Plot a graph of the 6x table. Read intermediate values and use the graph to estimate larger products.
Plot a graph of the 21/2x table. Read intermediate values and use the graph to estimate larger products.

Day 2
Convert inches to cm using a graph. Convert ounces to grams using a graph.

### Mastery: Reasoning and Problem-Solving

• Sketch a line graph of the 12 times table.
• Use this to find answers to the multiplications below.
(a) 12 × 3.5
(b) 12 × 6.5
(c) 12 × 13
(d) 12 × 9.25
• Mary is drawing a graph to convert pints to litres. She has found this table of conversion facts.
 Pints Litres 1 0.57 2 1.14 3 1.7 4 2.27
1. Draw a conversion graph to represent this data.
2. Create a table showing whole numbers of litres (1 to 3) and the corresponding number of pints (accurate to 1 decimal place).

In-depth Investigation: Graphing Number Patterns
Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the six times table too? Graphing Number Patterns from nrich.maths.org.

### Extra Support

Times Table Puzzler
Finding multiples and factors

## Unit 3 Concept of rate; line graphs (suggested as 4 days)

### Objectives

Explore the concept of rate; draw and interpret line graphs
Unit 3: ID# 5939

National Curriculum
Stats (i) (ii)

Hamilton Objectives
44. Create and interpret line graphs, solving comparison, sum and difference problems.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Children measure their heart rates in beats per minute. Once everyone has located their pulse, start an Interactive Whiteboard timer while children count the number of beats in 30 seconds. Use this to discuss the concept of ‘rate’ (an amount of something that happens in a given unit of time). Discuss other examples of rate, e.g. rate of growth, rate of pay, speed.
Group Activities
-- Calculate rates involved in World Record breaking achievements.

Day 2 Teaching
Show children a bar line chart of temperatures (resources). Explain how we can join the tops of each bar to create a line graph. Do this, then ask questions about intermediate points on the line graph. Note how it is good for representing changes over time, how it ‘tells a story’.
Group Activities
-- Use real temperature data to draw a line graph.

Day 3 Teaching
Use a skydiver’s record-breaking free-fall as a context for measuring the rate of fall of temperature with height. Temperature falls at a constant rate as you ascend above the earth. Work together to draw a line graph to represent this. Ask questions about other heights, using familiar points of reference, e.g. the top of Mount Everest at about 8.8km.
Group Activities
-- Interpret scales on a graph; complete a line graph that has been started.
-- Draw a line graph, falling to zero at a constant rate, given a rate of change.

Day 4 Teaching
Discuss the idea that many things, like tablet computers, fall in price as they get older (they depreciate). Look at a table showing the rates of depreciation of a cheap tablet and an expensive tablet. Interpret the table to recognise that rates of depreciation are different.
Group Activities
Use the in-depth problem-solving investigation ‘Take your dog for a walk’ from NRICH as today’s group activity.
Or, use this activity:
-- Use a table of values to draw a depreciation graph for two tablet computers.

### You Will Need

• Guinness World Records book or online version
• Interactive Whiteboard
• Stopwatch
• ‘Rates’ sheet 1 and 2 (see resources)
• ‘Bar line chart of outside temperature during the day’ (see resources)
• Squared / graph paper
• ‘Line graph to show air temperature at increasing height above the Earth’s surface’ (see resources)
• ‘Leaving the cinema’ (see resources)
• ‘How much does your tablet computer lose in value over 5 years?’ (see resources)
• Tablet computer or an image of one

### Mental/Oral Maths Starters

Day 1
Bar charts (pre-requisite skills)

Day 2

Day 3
Matching measures (pre-requisite skills)

Suggested for Day 4
Equivalent fractions, decimals and percentages (simmering skills)

### Procedural Fluency

Day 1
Use multiplication and division to solve problems involving rate.

Day 2
Interpret a graph of temperature vs time.

Day 3
Plot a graph representing a linear rate relationship; answer questions about it.

Day 4
Use multiplication and division to solve problems involving rate.

### Mastery: Reasoning and Problem-Solving

• An ice block is melting. It loses 1mm in height every 5 minutes. If the block is 3.5cm tall when it comes out of the freezer, how long is it after half an hour? And after an hour?
• Tim has left his bedroom window open on a cold night. Here is a table showing the temperature in his room after the heating turned off.
 Time Temp 10pm 18° 11pm 16.5° 12pm 1am 2am 3am 4am 9 5am 6am
• His room continues to cool at a rate of 1.5 degrees every hour until 6am.
Complete the table.
-- If Tim does not turn the heating on, what will the temperature be at 6am?
-- What time will the temperature be 13°?

In-depth Investigation: Take Your Dog for a Walk
Use an interactivity to move Mr Pearson and his dog. Can you move him in ways to fit different types of line graph? Take Your Dog for a Walk from nrich.maths.org.

### Extra Support

This unit has no separate Extra Support activities.