The 3rd graders and I are working hard on our class play at the moment, which has been taking up more of our morning lesson time than I’d like. I don’t typically schedule a dedicated play block — I’ve found that students get a little out of themselves if we focus entirely on the play — but it is difficult to get some hard-hitting academic work done.
(By the way, if you’re looking for a play for 1st or 2nd grade, I’ve got you covered.)
So, I’ve set aside our usual language arts/composition rhythm and instead we’re doing lots of math practice. Math practice is actually a really good complement to the outward energy of working on the play.
As we work on beefing up those arithmetic skills, some thoughts and questions are occurring to me.
Number Sense vs. Using the Algorithm
I was really careful last year to introduce addition and subtraction of large numbers without teaching them the tool of stacking the numbers. They still recognized that they were adding the place value columns (every time we solved I said, “1 ten plus 4 tens equals how many tens?” Just to reinforce the place values.) But we kept the problems horizontal so they wouldn’t be encouraged to think of 20 + 30 as 0 + 0 and 2 + 3.
This approach was recommended by Jamie York, as well as my favorite math resource. I wrote a blog post all about my approach to 2nd grade math here. (There are actually quite a few 2nd grade math posts. Check the 2nd grade archives.) I’ve also got a pretty thorough curriculum guide for that first 2nd grade math block.
But towards the end of 2nd grade, and then into 3rd grade, we’ve been stacking the numbers. I still remind them that we’re adding 10’s (not 1’s) when we’re working in that second column, but I know that many of them forget. I also occasionally slip in a problem that is WAY easier if they think about the value of the numbers, rather than using the algorithm. For example, just try solving 1000 – 999 using regrouping — it is HARD! So now whenever they stumble across a problem that is difficult, they take a step back and look at the VALUE of the numbers. That makes it SO much easier.
It’s also occurring to me that rounding off and using approximation is a handy skill for this work. If before we solve the problem, they round off the numbers and get an approximate answer, they might be able to identify if they’ve made a big mistake.
Using Pictures
I’ve got several students who draw little pictures to figure out their problems. I see little tally marks with circles around them putting them into groups. I have been really encouraging my students to use any tools that make sense to them, which I think is a good approach, but I think that some of them are overlooking other tools because they get stuck with what they know.
For example, we’ve been practicing large multiplication problems like 9824 X 2. As he goes through multiplying the 2, he draws little marks on the paper, counting them as he goes. I’ve been reminding him that he also knows how to count by 2’s, which is an easier and faster way, if you ask me, but he keeps going with the little marks.
I can’t imagine telling them not to use the tools they’ve found, but I’m pushing myself to come up with different kinds of problems or formats that will encourage them to use other tools. Also, ultimately, I want them to have those times tables memorized so it’ll just be automatic.
Enlivened Math Practice
I have to confess that the math practice we’ve been doing is pretty straightforward — without much imagination or creativity. But honestly, I think this is the best way to give them the practice that they need.
I’ve found a few resources that use the answers to the problems to give fill-in-the-blank letters that give an answer to a riddle, which my students really love and they do get a lot out of doing problems this way. But they get more out of solving problems that I have created. When I’m creating them, I can design the problems so they get increasingly difficult and practice the specific type of problem they’re ready for.
For example, yesterday my students were surprisingly baffled by the 0 in the problem 2305 X 5. So many raised their hands saying, “What do I do here? Is it 5?” I had to go back and say, “You’ve got 5 groups and there are 0 in each group. What do you have?” “Zero?” They replied, questioningly.
You can bet that there are more zeroes on today’s practice page. So, they get the right kinds of problems at the right time. But no fun riddles. Sorry kids.
(Want to download an example of our math practice? Scroll to the bottom of this page.)
Correcting Your Mistakes
We’ve been starting every math practice period by going over the page from the day before. I correct their papers and then we quickly go through each problem in class. It’s remarkable to hear them blurt out, “Oh! Ms. Floyd-Preston, I added instead of subtracted! That’s all!” Or, “I just forgot to carry the one!” Then they want me to re-correct their papers when they make the changes.
But I just love it when they discover their mistakes! I’m so convinced that this is the way to eliminate those little mistakes.
But for now, they’re still making a LOT of those little errors. Each day, I’ve got maybe one student who gets them all right, but the others have lots of little arithmetic or process mistakes.
I guess the solution is to just keep practicing, making mistakes, noticing them and learning from them. Oh gosh, math as a metaphor for life!
If you’re interested in seeing an example of the math practice pages we’ve been doing, you can download the pdf here. I’ve been loving my iPad and Apple Pencil for this. Typed math practice pages just don’t work and I love that I can save all of these pages in digital format.
I’d love to hear if you’ve got similar questions about teaching math, or if you’ve got resource suggestions. Math is not my area of expertise and though I love teaching it, I do often feel like I’m figuring it out along the way.
But then, I guess that’s the way of Waldorf teaching. I’ll let all you 3rd grade teachers of the future know when I’ve got it all figured out.
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