Published almost 2 years ago by Ann Baker
Use this 'Does it Matter' addition question to initiate student conversation about whether it matters what order numbers are added.
This first post in the 'Does it Matter' series explores the commutative property of addition: numbers can be added in any order and the total will remain the same.
Use this 'Does it Matter' as a warm up, mini-lesson or reflection after an addition problematized situation.
This 'Does it Matter' deals with the commonly held student view that numbers have to be added in the order in which they are presented. It also highlights which students know the commutative properly for addition but just don't stop and think about efficient strategies they use in order to work smart not hard and so 'save brain space'.
Teacher Notes: The first pair of numbers has been selected not just as an easy entry point but also to ensure that students can articulate and explain why it is that we turn those numbers around and count on from the largest number (if we don't have automaticity with 2+5). 20+50 is a related fact and is also best performed as a turnaround count on 20: 50,60, 70 rather than with tricks, such as, take of the zeroes add 5+2 then 'add zero'.
For 7+6+3 it may not be necessary to change the order, if for instance 7+6 is a known fact and the computation is straight forward. Alternatively seeing the rainbow pair 7+3 which makes the friendly number 10 makes it easy to carry out 10+6. In this case it is the automaticity with the number facts that will determine whether it matters if the order is changed or not.
Finally a slightly harder one, but for students who are familiar with landmark numbers changing the order from 26+33+26 to 26+26+33 will result in recall of 25+25, plus 2+33. The alternative of adding 26+33 then 26 is cumbersome. Adding 20+30+20 is slightly less so, but the number 70 has to be stored in memory while 6+3+6 are computed and finally added to 70.
Note: as students share as a class, remember to be respectful of student thinking, this is not about one way only, it is about deepening understanding.
As students share you may want to make their thinking visible to all by recording. For instance,
Stay in touch for Does it Matter 2 to 10 in weeks to come! Learn about teaching with Probemalized Situations here.
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