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# Top Drawer Teachers: Further divisibility patterns

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Top Drawer Teachers
The Australian Association of Mathematics Teachers (AAMT) Inc.
http://topdrawer.aamt.edu.au

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### Top Drawer Teachers: Further divisibility patterns

1. 1. Further divisibility patternsfor students to investigate
2. 2. Without doing any calculations whatother numbers do you think might divideequally by 5 or 10. Why?Encourage students to list their ideas andreasoning (e.g. if the last digit of a numberis a 5 or 0 then it will divide equally by 5;if the last digit of a number is a 0 then itwill divide equally by 10).Pose the following question:Further divisibility patterns
3. 3. How would you decide whether a number isdivisible (a number that divides equally with noremainder) by 4? Where would you start?Possible student responses: colour in the fours pattern on a 100 chart;look at the final digit; look at where the pattern repeats.In pairs, students work out a theory for knowingwhich numbers are divisible by 4, and why.Have a 100 chart or multiplication facts table available forstudents to use if they so choose.Going furtherFurther divisibility patterns
4. 4. Teaching tipsNote: As every 100 is divisible by 4 onlythe numbers formed by the tens and onesdigits need to be considered.Alternatively, present a conjecture forstudents to prove or disprove, such as:If the number formed by the last two digits ofa number is divisible by four, then the wholenumber is divisible by four.Further divisibility patterns
5. 5. Going furtherAs a class, students can share their reasoning and testout their theories using randomly generated numbersfrom the learning object, L2006 The divider: with orwithout remainders.Without doing any calculations, do you think each ofthese numbers are divisible by 4 and why?Follow up investigation: What numbers are divisibleby 3, by 6, by 9, and why?Further divisibility patterns
6. 6. Going furtherAs a class, students can share their reasoning and testout their theories using randomly generated numbersfrom the learning object, L2006 The divider: with orwithout remainders.Without doing any calculations, do you think each ofthese numbers are divisible by 4 and why?Follow up investigation: What numbers are divisibleby 3, by 6, by 9, and why?Further divisibility patterns