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This problem encourages students to consider a range of alternative methods of calculation. There is an opportunity for students to appreciate the importance of the quotient and the remainder when using division to solve a problem. When using calculators, students can explore the relationship between the remainder and the decimal part of the
How can I use what I know (small multiples of 7, 12, 360...) to generate number facts that are not at my fingertips (large multiples of 7, 12, 360...)?
Colour Wheels provides a simple context for exploring repeating patterns.
Days and Dates begins in the same way as this problem, but then encourages exploration of the algebra behind modular arithmetic.
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.