Digit sum Y4
Mathematics
Year 4
Digit sum
Information
Objectives

to solve mathematical problems, recognise and explain patterns and
relationships, generalise and predict

to suggest extensions by asking ‘What if …?’
Prior learning
To benefit from this lesson, children should have had experience of listing all
possibilities systematically.
Vocabulary
digit, digit sum, systematic
Resources

interactive whiteboard or data projector linked to a laptop

software that allows the generation of random numbers according to
specific rules and then allows these numbers to be arranged in numerical
order

a resource file with the appropriate number generation capacity (in this
example, the spreadsheet ‘Digit sum Y4’)
ICT skills needed by teachers
To teach this unit, teachers need to know how to manipulate a spreadsheet file.
Preparation for this lesson
Before the lesson, set up the relevant software and resources on the shared area
of the network, or on the computers that the children are to use. Prepare the
software on your own computer ready for display.
Lesson extract
Mental oral starter
Launch the appropriate resource file (in this example, ‘Digit sum Y4’ worksheet 1 ‘4
digits’). Ask children to read aloud the four-digit number displayed.
Q. What is ten more … ten less … than this number?
Discuss answers and the impact on the digits of adding and subtracting ten.
Click on the upwards arrow on the spinner to display another four-digit number and
repeat.
Q. What is 100 more … 100 less … than this number?
Page 1 of 4 | Keys to learning | Problem solving | Year 4
From Learning and teaching using ICT: Example materials from Foundation Stage to Year 6. Ref: 0315-2004
Ref: 0360-2006DVD-EN
© Crown copyright 2006
Digit sum Y4
Continue, discussing the impact on the digits. Incorporate the addition and
subtraction of 1 and 1000. Use children’s answers to compare the impact on the
digits with the impact on the whole number: for example, subtracting 100 from 4382
changes the hundreds digit three to a two, and changes the number 4382 to 4282.
Main activity
Launch worksheet 2 (‘3 digits’), to display a three-digit number. Ask children to
read this number aloud. Click on the spinner to increase or decrease the number,
and ask children to read this new number aloud. Repeat.
Q. What do you notice about all these three-digit numbers?
Collect children’s observations. Generate new numbers to test their observations.
Establish that the sum of the three digits in each number is seven. Say that you will
call the sum of the digits the ‘digit sum’. Ask children to work in pairs and record
four three-digit numbers whose digit sum is seven.
Q. What numbers did you use for the hundreds digit?
Collect answers, and for each hundreds digit suggested, ask for a three-digit
number whose digit sum is seven. Record these on the board.
Q. Could the hundreds number be an eight or nine?
Confirm that it could not, and why not, so children understand that the largest
possible hundreds digit is seven. Establish that 700 is the largest three-digit
number as it is the only three-digit number in the 700s with digit sum seven.
Q. Could the hundreds digit be zero?
Record 016 to establish that while its digit sum is seven, 016 is really 16, a twodigit number.
Confirm that 1 is the smallest possible hundreds digit. Establish that 106 is the
smallest three-digit number in the hundreds with the digit sum seven.
Say that you want the children to work in pairs and list all the three-digit numbers in
the hundreds with a digit sum of seven.
Open a blank sheet, and enter the number 106. Collect and discuss children’s
answers, and record their numbers in the spreadsheet. Make sure 115 is recorded.
Q. Have we got all the hundreds numbers? How can we check to see
whether there are any we have missed?
Discuss suggestions.
Q. How will putting these numbers in order help us to see which numbers
are missing?
Page 2 of 4 | Keys to learning | Problem solving | Year 4
From Learning and teaching using ICT: Example materials from Foundation Stage to Year 6. Ref: 0315-2004
Ref: 0360-2006DVD-EN
© Crown copyright 2006
Digit sum Y4
Use the spreadsheet to put the hundreds numbers in order, and ask children
whether they can identify any that are missing. Establish that it is easier to identify
missing numbers when the list is ordered.
With the children, analyse the numbers in the list. Identify the first number as 106
and ask:
Q. What is the next biggest hundreds number we have found?
Establish that the number is 115. Emphasise the decreasing of the units digit from
six to five and the increasing of the tens digit from zero to one. The digit sum has
stayed at seven because you have subtracted one and added one, keeping the
total at seven.
Q. What can we do to get the next biggest hundreds number?
Invite children to demonstrate the decrease in the units digit and the increase in the
tens digit to get 124.
Continue this process to generate the full list:
106, 115, 124, 133, 142, 151, 160
Explain that by being systematic we have made all the hundreds numbers with a
digit sum of seven.
Q. How many hundreds numbers have a digit sum of seven?
Agree that there are seven.
Q. If the three-digit numbers had a digit sum of seven, what would the
smallest 200s number be this time?
Agree that it is 205, and enter 205 on the spreadsheet.
Say that you want the children to work in pairs and list all the other three-digit
numbers that have a digit sum of seven.
Plenary
Collect answers and ask the children for three-digit numbers whose digit sum is
seven. Record these under 205 to generate the list:
205, 214, 223, 232, 241, 250
Q. Have we listed all the 200s numbers? How can we check to see whether
there are any we have missed?
Discuss suggestions.
Ask children to explain the strategies they used to list all the three-digit numbers
with a digit sum of seven.
Q. Can we predict how many hundreds numbers have a digit sum of nine?
Page 3 of 4 | Keys to learning | Problem solving | Year 4
From Learning and teaching using ICT: Example materials from Foundation Stage to Year 6. Ref: 0315-2004
Ref: 0360-2006DVD-EN
© Crown copyright 2006
Digit sum Y4
Collect responses.
Enter 108. Ask children to use the strategies you have looked at during this lesson
to list all the possible numbers. Take responses and enter these into the
spreadsheet under the starting number of 108:
108, 117, 126, 135, 144, 153, 162, 171, 180
Q. Was our prediction correct? Can we see a pattern in the numbers we
have listed that will help us to predict?
Discuss the strategy of starting with the smallest possible three-digit number and
increasing one digit and decreasing another to generate the pattern. Say that this
is an example of working systematically. Track the units digit, which decreases
from eight to zero. This covers a range of nine digits, so there are nine hundreds
numbers with a digit sum of nine.
Q. If the three-digit numbers had a digit sum of eight, how many hundreds
numbers are there?
Collect answers and ask children to check for homework.
Notes
Links to the Framework for teaching mathematics
The lesson links to units on properties of numbers and reasoning about numbers.
Why use ICT?
The advantages of using ICT are as follows.

ICT allows teachers to project enlarged visual images for whole-class
demonstration and discussion.

The interactivity of the software is motivating and stimulating.

The sorting facility in a spreadsheet can be used to arrange the numbers
in ascending or descending order, helping children to see a systematic
way of ordering the solutions they have found. The workbook can be
saved and used at a later date.
Useful resources
There are further problems in the publication ‘Mathematical challenges for able
pupils in Key stages 1 and 2’ (DfEE 0083/2000) and in the ‘problem solving’
publications available on the DfES Standards Site (www.standards.dfes.gov.uk).
There are ICT-based resources to support the effective classroom use of these
problems available on the National Whiteboard Network website
(www.nwnet.org.uk).
Page 4 of 4 | Keys to learning | Problem solving | Year 4
From Learning and teaching using ICT: Example materials from Foundation Stage to Year 6. Ref: 0315-2004
Ref: 0360-2006DVD-EN
© Crown copyright 2006