6 ms·

If he's seven, he was probably coloring in ten frames, which are used to build a stronger conceptual understanding of our base-10 number system. The model start

by pflats 10y ago

If he's seven, he was probably coloring in ten frames, which are used to build a stronger conceptual understanding of our base-10 number system. The model starts out with physical objects, moves to visual representations of those objects ("coloring in"), then to abstraction. From there, students use those techniques to move away from the to develop good mental math strategies. If you were doing 17 + 35 on a ten frame, you'd fill in 1 full 10 for the 17 and have 7 left over. You'd then fill in 3 full 10s for the 35, and have 5 left over. You can take 3 of those 5 and fill in the missing spots on the 7 out of 10 ten frame, making a 5th full ten frame, and leaving 2 lonely chips/colored squares in sixth. The goal is to eventually get students to do all that mentally. 17 + 35 = 10 + 7 + 30 + 5 = 10 + 30 + 7 + 5 = 10 + 30 + 7 + 3 + 2 = 10 + 30 + 10 + 2 = 50 + 2 = 52. You might have figured out that kind of mental math trick on your own. If so, the lesson's not there for you. It's for all the people out in the real world who didn't develop it on their own and will readily tell you that they're "not math people". The same technique will be revisited to work with fractions, first with the same denominator and then dissimilar denominators, and similar techniques will be used for multiplication, the distributive property, etc.

tropo 10y ago
That is a horribly complicated way to do 17 + 35. The sane way is to try matching against a pattern, then if that fails you fall back to the traditional algorithm with the numbers lined up one over the other and doing the carries. Yes, you can run the traditional algorithm in your head, for this and for much larger things. Fully in memory, 4-digit plus 4-digit is quite doable. (can your method handle that?) While staring at the numbers on paper to avoid forgetting, and writing down the answer as you go, arbitrary sizes are doable. It so happens that I do see a pattern I can fit, but this shouldn't be expected. I convert to 17+(172+1) and then to 173+1 and I know 17*3 is 51 so the answer is 52. It's forgivable to not spot this shortcut.
- deleted 10y ago
  [deleted]
- pflats 10y ago
  >(can your method handle that?) It's not "my" method. I'm not quite sure what I did to merit attitude and hostility, but to answer your question: Yes. Third-graders are expected to do it with 3-digit numbers. You'll have to take my word for it that I'm capable of adding 4-digit numbers. http://www.corestandards.org/Math/Content/3/NBT/#CCSS.Math.Content.3.NBT.A.2 http://www.corestandards.org/Math/Content/3/NBT/#CCSS.Math.C...
  - tropo 10y ago
    What hostility? Come on, you have to admit that a procedure which expands the problem out to the sum of 5 numbers is pretty insane. BTW, my shortcut got mangled by Hacker News. Multiplication turned into italics. I did 17 times 3, which is great, but I don't think that anybody should be expected to see that path to a solution.
branchless 10y ago
yep I know about the "drawing as math" - it's often not that. I am not a happy bunny with their school work!
michaelbuddy 10y ago
Or you could teach somebody how to 'carry the 1' and get this done in a less mentally taxing way, being faster and still understandable. This looks like a brain dump of how 'somebody somewhere' conceptualizes math and now we're all supposed to put it in play en masse because it 'shows the work'. I look at this math and if I was in 3rd grade, I would know in my gut this is BS. Does anyone actually think that more written steps will remove mistakes, because less moves = less mistakes.
- hdctambien 10y ago
  I'm not impressed when my students can add two numbers together. I want to know if they understand the math behind the algorithm. You like "the old way" because that is how you learned it. But when push comes to shove, I bet you actually use pflats method to do math in your head. http://www.patheos.com/blogs/friendlyatheist/2014/03/07/about-that-common-core-math-problem-making-the-rounds-on-facebook/ http://www.patheos.com/blogs/friendlyatheist/2014/03/07/abou...
  - tropo 10y ago
    Really I don't. I do "the old way" unless I happen to spot a nice pattern. (in this case the pattern involves knowing that 17 times 2 is 34 and that 17 times 3 is 51) My speed and reliability allowed me to focus on understanding higher-level math. With little effort, I easily blew past my peers for years afterward. Using pflat's method, my reliability would drop. There are too many extra numbers to account for.
woliveirajr 10y ago
Oh my. I used to do 17 + 35 = 35 + 17 = 35 + 20 + (20-17) = 55 - 3 = 52. And then I found out that my father used to think the same way, but not my mother, who was a teacher a long time ago and just for few years. And my breakthrough for that didn't happen when using all those squares (for 1s and 100s) or rows (for 10s).

by pflats 10y ago

tropo 10y ago

That is a horribly complicated way to do 17 + 35. The sane way is to try matching against a pattern, then if that fails you fall back to the traditional algorithm with the numbers lined up one over the other and doing the carries. Yes, you can run the traditional algorithm in your head, for this and for much larger things. Fully in memory, 4-digit plus 4-digit is quite doable. (can your method handle that?) While staring at the numbers on paper to avoid forgetting, and writing down the answer as you go, arbitrary sizes are doable. It so happens that I do see a pattern I can fit, but this shouldn't be expected. I convert to 17+(172+1) and then to 173+1 and I know 17*3 is 51 so the answer is 52. It's forgivable to not spot this shortcut.

deleted 10y ago
[deleted]
pflats 10y ago
>(can your method handle that?) It's not "my" method. I'm not quite sure what I did to merit attitude and hostility, but to answer your question: Yes. Third-graders are expected to do it with 3-digit numbers. You'll have to take my word for it that I'm capable of adding 4-digit numbers. http://www.corestandards.org/Math/Content/3/NBT/#CCSS.Math.Content.3.NBT.A.2 http://www.corestandards.org/Math/Content/3/NBT/#CCSS.Math.C...
- tropo 10y ago
  What hostility? Come on, you have to admit that a procedure which expands the problem out to the sum of 5 numbers is pretty insane. BTW, my shortcut got mangled by Hacker News. Multiplication turned into italics. I did 17 times 3, which is great, but I don't think that anybody should be expected to see that path to a solution.

branchless 10y ago

yep I know about the "drawing as math" - it's often not that. I am not a happy bunny with their school work!

michaelbuddy 10y ago

Or you could teach somebody how to 'carry the 1' and get this done in a less mentally taxing way, being faster and still understandable. This looks like a brain dump of how 'somebody somewhere' conceptualizes math and now we're all supposed to put it in play en masse because it 'shows the work'. I look at this math and if I was in 3rd grade, I would know in my gut this is BS. Does anyone actually think that more written steps will remove mistakes, because less moves = less mistakes.

hdctambien 10y ago
I'm not impressed when my students can add two numbers together. I want to know if they understand the math behind the algorithm. You like "the old way" because that is how you learned it. But when push comes to shove, I bet you actually use pflats method to do math in your head. http://www.patheos.com/blogs/friendlyatheist/2014/03/07/about-that-common-core-math-problem-making-the-rounds-on-facebook/ http://www.patheos.com/blogs/friendlyatheist/2014/03/07/abou...
- tropo 10y ago
  Really I don't. I do "the old way" unless I happen to spot a nice pattern. (in this case the pattern involves knowing that 17 times 2 is 34 and that 17 times 3 is 51) My speed and reliability allowed me to focus on understanding higher-level math. With little effort, I easily blew past my peers for years afterward. Using pflat's method, my reliability would drop. There are too many extra numbers to account for.

woliveirajr 10y ago

Oh my. I used to do 17 + 35 = 35 + 17 = 35 + 20 + (20-17) = 55 - 3 = 52. And then I found out that my father used to think the same way, but not my mother, who was a teacher a long time ago and just for few years. And my breakthrough for that didn't happen when using all those squares (for 1s and 100s) or rows (for 10s).