Divisibility Rules
Thursday, August 15, 2019
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In the concluding lesson of term my students played a few rounds of a Countdown type game, as well as were specially stumped past times this problem:
I managed to produce it pretty rapidly as well as briefly experienced 1 of those lovely moments of appearing, to my students at least, to move a maths genius. Of class all I did was location that 531 divides past times 9, as well as thus it was straightforward. Have a go.
Influenza A virus subtype H5N1 colleague asked me how I'd done it thus rapidly as well as I told her that I'd used divisibility rules. She said that she'd never taught divisibility rules because she'd never seen it specified on a system of work. It strikes me that this is a helpful fighting of mathematical noesis that many secondary maths teachers don't teach. Do you lot learn it? In what year? Most resources for this theme are aimed at master copy children but I intend nosotros should in all probability revisit it at Key Stage 3.
I was aware that my Year 10s didn't know the divisibility rules, thus I covered them every bit business office of the 'Factors as well as Multiples' theme this twelvemonth (ie amongst prime number factorisation, highest mutual component etc). It's a skillful agency to review the fundamentals of multiplication as well as to prepare fluency as well as efficiency with numbers. To my Year 10s the rules seemed similar 'new' maths that they'd non seen earlier (or if they had, they couldn't hollo upward it), thus it made an interesting as well as suitably challenging lesson.
I also ran a session on divisibility rules with merely about smart Year 3s as well as 4s at a local master copy schoolhouse this year. They picked it upward well, as well as over again I saw it every bit a skillful agency to prepare their agreement of multiplication as well as their divulge fluency.
So it's a theme that industrial plant good with whatsoever historic menstruation group, from Key Stage 2 to Key Stage 4. Let's accept a quick expect at the rules as well as resources.
The Rules
Most children volition easily move able to create upward one's heed whether a divulge is divisible past times 2, v or 10. The neat 'tricks' are for 3 (the digit amount is divisible past times 3) as well as nine (the digit amount is divisible past times 9). Once nosotros know whether a divulge divides past times 3, nosotros know whether it divides past times 6 (ie all even multiples of 3 are multiples of 6). For divisibility past times 4 in that location are 2 alternatives: either banking concern gibe whether the concluding 2 digits split upward past times 4, or halve the divulge as well as run into if your respond is fifty-fifty (the iv times tabular array beingness double the 2 times table). The 7 key tests are shown inwards the graphic below (there are loads of prissy graphics for this on google images).
I didn't bother instruction the dominion for divisibility past times 7 because it's non straightforward. Rather as well as thus memorise this dominion I idea my students would move amend off merely checking for divisibility past times 7 with long division.
If you're interested inwards all the rules, from 1 - xxx as well as beyond, banking concern gibe out the Wikipedia page Divisibility rule.
Resources
I constitute a mixture of uninspiring worksheets as well as bizarre activities when I searched for resources online (the to a greater extent than odd activities included Divisibility Rock n' Rule, NFL divisibility dance and I'll take, you lot take...).
For the interactive whiteboard nosotros direct maintain Vectorkids: divisibility rules, Divisibility Test as well as Delightfully Divisible.
If you're looking for a good structured worksheet pack, this is quite good.
This Don Steward.
Don Steward also has slides on divisibility rules, total of lovely challenging problems.
Dan Walker has a nifty laid upward of slides as well as activities on divisibility rules too, including this lovely Venn activity.
Why produce the rules work?
The ancient Greeks knew rules for divisibility past times 2, 3, v as well as nine inwards the 3rd century BC.
So why does the digit amount of multiples of 3 split upward past times three? Sal Khan explains here...
He has a similar video for divisibility past times 9.
Do allow me know virtually your experiences of instruction divisibility rules as well as whatsoever resources recommendations. If you've non taught it before, direct maintain a become adjacent year. It's useful noesis as well as good worth teaching.
Influenza A virus subtype H5N1 colleague asked me how I'd done it thus rapidly as well as I told her that I'd used divisibility rules. She said that she'd never taught divisibility rules because she'd never seen it specified on a system of work. It strikes me that this is a helpful fighting of mathematical noesis that many secondary maths teachers don't teach. Do you lot learn it? In what year? Most resources for this theme are aimed at master copy children but I intend nosotros should in all probability revisit it at Key Stage 3.
I was aware that my Year 10s didn't know the divisibility rules, thus I covered them every bit business office of the 'Factors as well as Multiples' theme this twelvemonth (ie amongst prime number factorisation, highest mutual component etc). It's a skillful agency to review the fundamentals of multiplication as well as to prepare fluency as well as efficiency with numbers. To my Year 10s the rules seemed similar 'new' maths that they'd non seen earlier (or if they had, they couldn't hollo upward it), thus it made an interesting as well as suitably challenging lesson.
I also ran a session on divisibility rules with merely about smart Year 3s as well as 4s at a local master copy schoolhouse this year. They picked it upward well, as well as over again I saw it every bit a skillful agency to prepare their agreement of multiplication as well as their divulge fluency.
So it's a theme that industrial plant good with whatsoever historic menstruation group, from Key Stage 2 to Key Stage 4. Let's accept a quick expect at the rules as well as resources.
The Rules
Most children volition easily move able to create upward one's heed whether a divulge is divisible past times 2, v or 10. The neat 'tricks' are for 3 (the digit amount is divisible past times 3) as well as nine (the digit amount is divisible past times 9). Once nosotros know whether a divulge divides past times 3, nosotros know whether it divides past times 6 (ie all even multiples of 3 are multiples of 6). For divisibility past times 4 in that location are 2 alternatives: either banking concern gibe whether the concluding 2 digits split upward past times 4, or halve the divulge as well as run into if your respond is fifty-fifty (the iv times tabular array beingness double the 2 times table). The 7 key tests are shown inwards the graphic below (there are loads of prissy graphics for this on google images).
I didn't bother instruction the dominion for divisibility past times 7 because it's non straightforward. Rather as well as thus memorise this dominion I idea my students would move amend off merely checking for divisibility past times 7 with long division.
If you're interested inwards all the rules, from 1 - xxx as well as beyond, banking concern gibe out the Wikipedia page Divisibility rule.
Resources
I constitute a mixture of uninspiring worksheets as well as bizarre activities when I searched for resources online (the to a greater extent than odd activities included Divisibility Rock n' Rule, NFL divisibility dance and I'll take, you lot take...).
For the interactive whiteboard nosotros direct maintain Vectorkids: divisibility rules, Divisibility Test as well as Delightfully Divisible.
If you're looking for a good structured worksheet pack, this is quite good.
This Don Steward.
Dan Walker has a nifty laid upward of slides as well as activities on divisibility rules too, including this lovely Venn activity.
The ancient Greeks knew rules for divisibility past times 2, 3, v as well as nine inwards the 3rd century BC.
So why does the digit amount of multiples of 3 split upward past times three? Sal Khan explains here...
He has a similar video for divisibility past times 9.
Do allow me know virtually your experiences of instruction divisibility rules as well as whatsoever resources recommendations. If you've non taught it before, direct maintain a become adjacent year. It's useful noesis as well as good worth teaching.