A Remainder of One

Division activities

Simply read and enjoy the story the first time. Accept comments on the mathematics but avoid going into too much detail.
Re-read the story, focusing (verbally only to start with) on the division facts generated by dividing 25 by 2,3, and 4 with a remainder of one, then on 25 divided by 5 leaving no remainder.
Physically do the same division with the class. Can they be divided by 2,3,4,5, etc. Are there any remainders? Is the remainder always 1? (Warning - this is a noisy, fun activity!).
Individually or in pairs, the children can divide 25 (or the class number or another appropriate number) by 2,3,4,5, etc. Some children are likely to need concrete apparatus when they try this.
Discuss how to record what they have found out, either using the children's own method or by using the appropriate symbols. Some children can extend the activity by checking their calculation with an inverse calculation. They can then record it alongside their work as a check. Each pair or individual can compare their work with another pair or individual and discuss what they notice. Can they see a pattern in the remainders?
Revisit the calculations to discuss their meaning. For example, if 26 divided by 3 is 8 remainder 2, What does that actually mean in terms of lines of children (or bugs)?

100 hungry ants Use the suggestions for activities above, but dividing 100 by 2, 4, 5, and 10. What happens if you divide 100 by other numbers?

Use a pack of 0-100 cards (with 0-10 removed, or more as appropriate) and a pack of playing cards with the picture cards removed to investigate numbers to 100. Give each child one card from each pack and ask them to find out if the playing card number will divide exactly into the larger number. Some children will need concrete apparatus for support. Known multiplication facts can be a useful starting point.
Although most simple calculators do not have a constant button, you can create a sequence with the following key presses (e.g.) 6 + + =. Each time = is pressed, another 6 is added. For subtraction, use 6 - - =. If you want to start with a number other than zero, you need to enter the jump size, then + +, then the start number. So 8 + + 3 =,=,=,=,etc will generate the sequence 11, 19, 27 etc. 6 - - 100 =,=,=, etc will generate the sequence 94, 88,82 etc. So to find out if 8 will divide exactly into 100, enter 8 - - 100 = = etc. Remember that what is shown on the screen is what is 'left over'. As the display approaches zero, is the last number shown 8 or something else?
This is a useful activity to build up information on numbers, recognise patterns and to begin to develop divisibility rules (see Divisibility rules in the Teachers' Notes).