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In the frame: A Remainder of One

2 June 2008

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By Cherri Moseleyprimary teacher

Soldier Joe keeps being a remainder of one when his squadron lines up for parade. Can the children help him out?

A Remainder of One by Elinor J Pinczes, illustrated by Bonnie Mackain (Houghton Mifflin, ISBN 0395694558) is a fabulous book. Perfectly pitched for Key Stage 1 children, the mathematical content is intrinsic to the story and not simply an add-on. The main focus of the activities is on problem solving using multiplication and division, and division with remainders, but there are some useful data-handling activities too.

A remainder of one cover


The queen bug likes things tidy when her bug troops parade before her. But poor soldier Joe keeps messing things up by being a remainder of one. He tries various solutions to keep the squadron of 25 in equal lines and is a very happy bug when he solves the problem.

Read and enjoy the story with the children the day before you intend to use it for a mathematical focus. Have fun with the narrative, getting the children to join in on the obvious chorus and marching on the spot to:

'Hup, two, three, four!

We're in the 25th Army Corps.

Queen's count! Two, three!

We are the marching infantry.'

Bug activities

  • Reread the story, focusing on the division facts generated by dividing 25 by 2, 3, 4 and 5. Write the calculations in a column on the board, leaving space alongside for the calculations you will generate with your class. Show the children how to write the remainder. Invite the children to predict whether or not there will be a remainder if they transform themselves into bugs and group themselves in twos, threes, fours or fives, as in the story. Will any remainder always be one, as it was for poor soldier Joe? Test out your predictions!
  • For a challenging activity, put the children into pairs and give each pair 25 insect counters or cubes. Ask them to replicate soldier Joe’s calculations and check if there are other solutions to his problem by dividing 25 by 6, 7, 8, 9, 10, 11 and 12. Some children will find a table to record their results useful. Alternatively, give each pair an appropriate number of cubes and ask them to check if that number divides exactly by 2, 3, 4 and 5. Can they make up a story to give a context to their results?
  • For an oral and mental starter, ask the children to become bugs and walk quietly and carefully around the room, listening for you to call out a number. When a number is called, the children should immediately get into groups of that number. Talk through what has happened and record the calculation on the board. For example, if there are 28 ‘bugs’ (children) and you called out ‘three’, then there will be nine groups of three and one left over. Repeat this activity on other days when a different number of children are present. Remember to verbalise the story too, for instance: ‘There are 28 bugs in Class 1B today. When they got into groups of three, there were nine groups of three and one left over.’
  • When the class divides exactly into groups, make sure they are arranged in an array, and ask them to sit down where they are. Use PE ropes to separate out the rows and columns to emphasis the groups. Walk around the array and talk about the different arrangements you can see – the two multiplication and two division calculations. Write the calculations on the board as one family of calculations.
  • The bugs in A Remainder of One are colourful with very varied patterns. Use bug template below for a sorting activity. Ask the children to restrict the number of colours and patterns used, perhaps no more than two colours and two patterns on each bug. Sort for one criterion such as red/not red or striped/not striped on a simple two-space Carroll diagram. Then move on to sorting for two criteria. Challenge the children to find a way of sorting that leaves one of the spaces empty. Try sorting for two criteria using a Venn diagram.Invite the children to comment on the different methods of sorting. Does one give you a clearer picture of the information than the other? When would it be best to use each type? Take photographs of the different arrangements then print and bind the pictures to form a class sorting book.
  • Dramatise A Remainder of One for an assembly. Include the chorus a few extra times and change the number in the troop to match the number of children present. There are lots of additional parts to be played if you have enough children. But be warned: there was some competition to be soldier Joe when my class did this!
  • A Remainder of One is a very useful book to help you bring some mathematics into a minibeast topic. Cross-curricular opportunities include writing character profiles for one of the bugs in the story (or for your own bug), writing the nomination for Joe’s medal (perhaps Sergeant Steven deserves one too?), describing the food and habitat of your bug, and much more. Enjoy!

Linking Primary Framework objectives

Another book by Elinor J Pinczes was the focus of January’s ‘In the frame’. Read it here.

The above activities relate to the following blocks and units of the Renewed Framework, but are particularly relevant for Blocks C and E.

Year 1

Block A Unit 1-3; Block C Units 1-3

Describe ways of solving puzzles and problems, explaining choices and decisions orally or using pictures.

Block B Unit 3; Block C Units 1-3

Use diagrams to sort objects into groups according to a given criterion; suggest a different criterion for grouping the same objects.

Block C Units 1-3

Answer a question by selecting and using suitable equipment, and sorting information, shapes or objects; display results using tables and pictures.

Answer a question by recording information in lists and tables; present outcomes using practical resources, pictures, block graphs or pictograms.

Block E Units 1-3

Describe a puzzle or problem using numbers, practical materials and diagrams; use these to solve the problem and set the solution in the original context.

Block E Unit 1-3

Count on or back in ones, twos, fives and tens and use this knowledge to derive the multiples of two, five and ten to the tenth multiple.

Block E Unit 2 and 3

Solve practical problems that involve combining groups of two, five or ten, or sharing into equal groups.

Year 2

Block A Units 1-3

Present solutions to puzzles and problems in an organised way; explain decisions, methods and results in pictorial, spoken or written form, using mathematical language and number sentences.

Block B Units 1-3; Block D Units 1-3; Block E Units 2 and 3

Solve problems involving addition, subtraction, multiplication or division in contexts of numbers.

Block B Units 1-3; Block E Units 1-3

Derive and recall multiplication facts for the two-, five- and ten-times tables and the related division facts; recognise multiples of two, five and ten.

Block C Units 1-3

Follow a line of enquiry; answer questions by choosing and using suitable equipment and selecting, organising and presenting information in lists, tables and simple diagrams.

Use lists, tables and diagrams to sort objects; explain choices using appropriate language, including ‘not’.

Block E Units 1-3

Identify and record the information or calculation needed to solve a puzzle or problem; carry out the steps or calculations and check the solution in the context of the problem.

Represent repeated addition and arrays as multiplication, and sharing and repeated subtraction (grouping) as division; use practical and informal written methods and related vocabulary to support multiplication and division, including calculations with remainders.

Block E Unit 3

Present solutions to puzzles and problems in an organised way; explain decisions, methods and results in pictorial, spoken or written form, using mathematical language and number sentences.