Description
Here’s the problem with teaching any kind of technique in mathematics: once you have kids practice it, they discard all the other techniques they know, even if the ones they discard are faster, more efficient and more accurate. Such is the case with teaching “stacking” of addition problems. Sure, it’s a great skill to have, but is it always necessary? I say this: based on some statistic I ran, between 70 - 80% of all addition problems with two addends don’t need to be stacked. Yet we act as if stacking is the default; it should not. It should be the option that we use when we see that the problem requires it.
Take a look at the randomly generated sheet of 10 problems on the next page. As you can see, almost all of these can be solved without stacking. Of course, stacking can be a useful techinque, especially when there are more than 3 numbers, but at the same time, shouldn’t we be building on the intuition that students already have? Or are we just resigned to letting students do computation without any actual thinking, like some kind of calculating poultry?
Below each problem I explained the strategy I used (a “mental math”) but in real life, students wouldn’t need to do this. The reason you should have your students do this on at least some of the problems is so they can show their thinking using techniques like place value, compensation (for example, changing 699 to 700 and then subtracting 1 from the answer) and other strategies which may not be apparent.
The point is this: our students should be critical users of math. They should not be sheep just blindly doing whatever they were told to do. When they use techniques like these, not only are they doing math more efficiently and accurately, but they’re also reinforcing the conceptual knowledge that underpin mathematics. So encourage them to do it!
The important thing to also know is that these are randomly generated problems! That is, they were not “made up” problems from a teacher or some drone creating it for a textbook or an algorithm that is specifically programmed only to make “tough” math problems. These actually are representative of what your students will encounter in “real life” (unless you consider some cruddy set of problems pulled out of a textbook or worksheet generator “real life.”) Therefore, it is safe to say that roughly 80 - 90% of the actually addition problems with 1 - 3 digits your students may ever encounter in their life will NOT require regrouping! And for this we make them slave over hundreds of examples until they want to scream “uncle?”
How to use these activities: This activity is designed as a “fishbowl,” rather than a traditional set of problems. This are over 2,500 different addition and subtraction problems that you can cut out, put into a fish bowl (or a hat, or whatever you have to hold them), give each student a “recording sheet” and then leave the bowl o’ problems out for your students to randomly select and solve over the next 10 - 20 weeks. Because what your students need is ongoing practice with this skill. It makes NO SENSE to practice a skill for 2 - 3 weeks and never do it again. With this activity, your students can practice adding multi-digit numbers with and without stacking for as long as they are ready, willing and able. And all you have to do is keep the fishbowl around to do so!
But there’s a bonus! The final “recording sheets” can be customized with your own instructions. I’ve put in two samples, one involved estimation and the other about the need for stacking. The point here is that you can target certain problems that are found in the fishbowl, so kids are developing critical thinking skills in evaluating what kind of problem it is before actually solving it.
To Stack or Not To Stack: 2,500+ Critical Thinking: Addition/Subtraction
Highlights
Description
Here’s the problem with teaching any kind of technique in mathematics: once you have kids practice it, they discard all the other techniques they know, even if the ones they discard are faster, more efficient and more accurate. Such is the case with teaching “stacking” of addition problems. Sure, it’s a great skill to have, but is it always necessary? I say this: based on some statistic I ran, between 70 - 80% of all addition problems with two addends don’t need to be stacked. Yet we act as if stacking is the default; it should not. It should be the option that we use when we see that the problem requires it.
Take a look at the randomly generated sheet of 10 problems on the next page. As you can see, almost all of these can be solved without stacking. Of course, stacking can be a useful techinque, especially when there are more than 3 numbers, but at the same time, shouldn’t we be building on the intuition that students already have? Or are we just resigned to letting students do computation without any actual thinking, like some kind of calculating poultry?
Below each problem I explained the strategy I used (a “mental math”) but in real life, students wouldn’t need to do this. The reason you should have your students do this on at least some of the problems is so they can show their thinking using techniques like place value, compensation (for example, changing 699 to 700 and then subtracting 1 from the answer) and other strategies which may not be apparent.
The point is this: our students should be critical users of math. They should not be sheep just blindly doing whatever they were told to do. When they use techniques like these, not only are they doing math more efficiently and accurately, but they’re also reinforcing the conceptual knowledge that underpin mathematics. So encourage them to do it!
The important thing to also know is that these are randomly generated problems! That is, they were not “made up” problems from a teacher or some drone creating it for a textbook or an algorithm that is specifically programmed only to make “tough” math problems. These actually are representative of what your students will encounter in “real life” (unless you consider some cruddy set of problems pulled out of a textbook or worksheet generator “real life.”) Therefore, it is safe to say that roughly 80 - 90% of the actually addition problems with 1 - 3 digits your students may ever encounter in their life will NOT require regrouping! And for this we make them slave over hundreds of examples until they want to scream “uncle?”
How to use these activities: This activity is designed as a “fishbowl,” rather than a traditional set of problems. This are over 2,500 different addition and subtraction problems that you can cut out, put into a fish bowl (or a hat, or whatever you have to hold them), give each student a “recording sheet” and then leave the bowl o’ problems out for your students to randomly select and solve over the next 10 - 20 weeks. Because what your students need is ongoing practice with this skill. It makes NO SENSE to practice a skill for 2 - 3 weeks and never do it again. With this activity, your students can practice adding multi-digit numbers with and without stacking for as long as they are ready, willing and able. And all you have to do is keep the fishbowl around to do so!
But there’s a bonus! The final “recording sheets” can be customized with your own instructions. I’ve put in two samples, one involved estimation and the other about the need for stacking. The point here is that you can target certain problems that are found in the fishbowl, so kids are developing critical thinking skills in evaluating what kind of problem it is before actually solving it.
