A Remainder of One

Teacher's notes for Remainder of One and One Hundred Hungry Ants

by Cherri Moseley, Bignold Infants School, Norwich

Synopsis
Learning outcomes
Extension learning outcomes
Vocabulary
Prior knowledge
Divisibility rules

These teachers' notes have been written as part of my research with the St John's Gatsby Teacher Associate programme into resources to support the teaching of multiplication and division. The programme is aimed at the production of materials and programmes of development to improve the teaching of mathematics. My research led to a book on using stories to develop children's understanding of multiplication and division, Number and Calculating, published by Belair (http://www.amazon.co.uk/exec/obidos/ASIN/0947882758/ref=br_lf_b_5/202-8253026-0323833). Any comments or suggestions about these notes would be welcomed. Please contact me at cherri.moseley@btopenworld.com.

Synopsis

Remainder of One: The queen bug likes thing tidy when her bug troops parade before her. 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.

One Hundred Hungry Ants: A soft breeze carries the suggestion of a picnic to one hundred hungry ants. The littlest ant tells them that marching in single file will take to long and organises them into lines of 50, then 25, then 20, then 10. Will they get there before all the food is eaten?

The activities suggested can be used in the literacy, numeracy (division/multiplication ,sorting and fractions) and PSHE areas of the curriculum. If you have ideas of your own on how you can use either Remainder of One or One Hundred Hungry Ants, please follow them and tell us about them in the second videoconference.

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Learning outcomes

• Understand the operation of division and the associated vocabulary.
• Understand the idea of a remainder.
• Solve simple word problems set in 'real life' contexts and explain how the problem has been solved.
• Develop and refine written methods for division.
• Recognise multiples and know some tests of divisibility.

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Extension learning outcomes

• Check by doing the inverse operation.
• Use the relationship between multiplication and addition, or multiplication and division.
• Find out about the divisibility rules.
• Carry out simple sorting activities, using Carroll and Venn diagrams.
• Explore simple fractions and find equivalents.
• Recognise that fractions are about division.
• Compare simple fractions in a practical situation.
• Recognise the equivalence between fractions, decimals and percentages.
• Understand percentages as the number of parts in every 100.

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Vocabulary

Share, group, divide, divided by, divided into, divisible by, times, multiply, multiplied by, product, multiple, factor, quotient, left over, remainder, inverse.

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Prior knowledge

Division as equal sharing and grouping without remainders has been explored and understood.

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Divisibility rules - simplified versions for numbers up to 100

1. All whole numbers are divisible by one.
2. A number is divisible by two if it is even.
3. A number is divisible by three if the sum of the last two digits is divisible by 3, e.g. for 27, 2 + 7 = 9, which is divisible by 3, so 27 is too.
4. A number is divisible by 4 if the number of tens is odd and the unit digit is 2 or 6, or the number of tens is even and the unit digit is 4, 8 or 0. Alternatively, a number is divisible by 4 if you can halve it twice without a remainder.
5. A number is divisible by 5 if the unit digit is either 0 or 5.
6. A number is divisible by 6 if it is divisible by both 2 and 3.
7. There is no simple divisibility rule for 7.
8. A number is divisible by 8 if you can halve it three times without a remainder.
9. A number is divisible by 9 if the sum of the digits is 9 or a multiple of 9, e.g. 99 is divisible by 9 because 9 + 9 + 18, which is divisible by 9.
10. A number is divisible by 10 if the unit digit is 0.

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