All Kinds of Addition

Dragon has been doing a lot of good counting in both English and Japanese, and I felt like it was time to introduce addition. It's not really a new concept; he has naturally picked up on it, and regularly asks, "What is 10+9?" But he hasn't been working with the rods very long, so we've been working with just counting exercises, laying the groundwork by attaching meaning to the rods and making sure that his counting is good in both English and Japanese. He's been doing great, so today we started doing addition.

The lady over at Education Unboxed is so good at teaching math, and I was using a different program when Hero learned this stuff, so I popped over to see what she suggests for doing addition. I'm glad I did. Not only did she have a fantastic way of showing the concepts, but there is a lot of it that's vocabulary I know in Japanese, so we went ahead and did the lesson bilingually.



 He doesn't write numbers, so the little bit of that I ascribed for him, but he did great with figuring everything out. I only gave him 6 problems, and just enough rods for what we were doing because the whole bin is overwhelming. I also made up a short 1-5 staircase for reference. 

It doesn't look like much, only six problems, but it was just right. Between the various new concepts and working in both languages, he had a lot of stuff to keep track of. It was just right to get him working, and to stretch his abilities, but not so much as to over do it. I love it when I judge things nicely and it turns out like that!

Hero did some self-checking double-digit addition. I picked this sheet mostly because I knew he would enjoy the hero on the page, and the puzzle. It was actually a little on the easy side for him, since there wasn't any regrouping. When he did it perfectly the first time, it was a great opportunity to praise him for doing careful work. I liked that both because I like to give a well-earned thumbs-up, and also because his last several pages of math had several errors in math facts that he should have known. So the timing for an opportunity to praise careful work was just right. We're really working on addition with carrying, which is frustrating for him (so many places you can put numbers!), so it's nice to have a moment to say, "Hey! You're doing good!" He's been needing that.

Switchable Multiplication

Today's math project was pattern discovery. Yesterday, we did a worksheet that was intended to help the kids discover the communitive principle of multiplication. He did the work reasonably well, but it seemed clear that he had not noticed the pattern. So today we got out the completed worksheet and the rods, and we went after the pattern. 

First, we built rod trains for yesterday's problems. And I made a new train, following the same pattern. 

At this point, he thought he had this figured out, and he didn't like my train; he wanted to build his own. I knew he didn't have the pattern figured out yet, but I also knew that he'd learn more being more active, so he built his train. It was wrong. Now I had his attention. We looked closer at the patterns in the other trains, and he was able to figure his out. 

Once his train was following the pattern, we grabbed a new sheet of paper and started looking at yesterday's problems as a model for problems he would. 

This was tricky at first, but soon he was really understanding what he was looking at, and the hardest part was writing small enough to fit on the page. At that point, I helped with the writing again. 

Then, we looked at a new problem, and how we could use this idea of "switchable" numbers in addition & multiplication to solve easier problems. 

Altogether, I feel like it was a very successful lesson!

Scrapping Again

It's been a tough couple weeks. Tigress got pneumonia again, and Dragon had surgery (he's fine), plus there's the usual life stuff that always has to happen. Pleasant things like scrapbooking got crowded out. Then, I discovered that my favorite scrapbooking site -really the only one I visit- is closing down. Bummer. But they've got a sister site, and there was a sketch challenge, and I did it. I'm glad I did. It feels so good to make a page again. I need to figure out where I'm going to get some of these printed. I need to make actual physical books out of some of these pages I've been making.

Tasty Math and Other Number Fun

These cookies that Vihart and her friends made look like so much fun, but I'm thinking it's a bit involved for us, just yet. We did something a little simpler for our math lesson today.

Hero's 2nd rocket.

However, we tried this idea for teaching fractions with pattern blocks today, and it worked out really well. We didn't do the activity quite as outlined, since Hero(7) is still somewhat new to fractions (we're going to be spending the next couple weeks working with them), but we did have a good time.

The first rocket he made didn't work because I forgot to tell him that we'd be working with only a limited number of shapes - the ones that can make a hexagon. The second one did much more nicely.  But it became clear as we tried to do the worksheet that he needed some of the foundational ideas still, so that's what we mainly worked on.

First, we looked at the number of each shape he'd used. Hexagons were our "whole," the shape we called "one." The rest of them, we looked at in terms of how many hexagons could we make. This worked out nicely, since he chose to count the hexagon first. Next, we looked at the trapezoids. Since Dragon(3) was (kind of) also playing with the shapes, he got some exposure to the names of the shapes as well. We decided that each trapezoid is half of a hexagon, and that 4 trapezoids make 2 hexagons. This gave us a chance to write a couple of fractions: 1/2, 1/2, and 2/2. I forgot to show him the 4/2, which is probably ok. But things got really interesting when we got to the rhombuses (rhombi??). This posed a challenge: figuring out the denominator. We've talked about the denominator several times, but it hasn't really stuck, and he needed more help with the concept. At this point, we pretty much abandoned the worksheet to work on the concepts he needed to solidify.


First, we more firmly established our base:

A yellow hexagon = 1. Surprisingly, this took a moment to establish. It didn't click into place until I started talking about how we can trade the other shapes for a hexagon, the way we trade with our Cuisenaire Rods. Then he had the ah-ha! moment and things were much more clear.

So, a yellow hexagon = 2 red trapezoids = 3 blue rhombuses = 6 green triangles.

We wrote this out like this:

1/1  2/2   3/3   6/6

And at the end, I went through and did this:

1 = 1/1 = 2/2 = 3/3 = 6/6

And we kind of lined the numbers up with the shapes so he could see it was true.



We've done work with "Names of a Number" before, so when I told him these are all different names for one, he understood, and at that point I felt like he had the concept, so we went back to his rocket again. He'd used 2 rhombuses, and that now made sense to him as 2/3 of a hexagon, so I asked him to make the same shape in triangles, and we figured out the name of that as well.

2/3 = 4/6.

At this point, I mentioned the terms "equivalent fractions" and "improper fractions," though I don't really expect them to stick. We did, however, note that the root of equivalent is "equal" and that's really what we're saying: equivalent fractions are equal.




I could tell that we were close to time to be done, but I wanted to try going one step further, and I gave him 7 triangles and asked him to figure out the name of the fraction they represented. It took a few minutes, but he figured it out.

 Pattern blocks are so much fun. Hero has made some beautiful and intricate pictures with them in the past, and today when we were done working, he made this one again. It's one of my favorites. The more of math that I re-learn, the more that I believe that playing around with shapes and patterns like this is immensely valuable. I hope that in the next while as we're messing around with fractions and pattern blocks that he makes some more pictures that I can share.

And, browsing around through comments and links, I found this amazing list of picture books with math in them. I could spend so much $$$ on books! There's a couple in the fractions section that are sounding pretty interesting. I need to order more pattern blocks and Cuisenaire Rods anyway, now that there are usually at least 2 kids playing with them during math time.

I love it when math is play. I think I need to make me some "math cards" and just keep them. I'd play these games with the kids more often if I didn't have to go through and sort the cards before we could start every time.

Subtraction Race

Hero asked for one of these race sheets again, so I made one to practice subtraction to 20. If your kids like it, "like" Baby Steps Blog on facebook to be notified when I make him more games and sheets.

Math Race! Subtraction to 20

Names of 11 and 16

This is what we'll be doing for math the next two days. These are some of my favorite ones; I may print an extra to do myself! I think I might have gotten the original idea for this exercise from Education Unboxed, but I can't find it on there this afternoon, so I could be remembering the wrong website. Who knows. In any case, it's a great activity. We'll be getting out our rods and playing around with them to see how many different ways we can make the numbers.

Names of 16 Math Worksheet

Names of 11 Math Worksheet

Addition Practice

We worked on sheet C-19 from our Miquon books this morning. By the end Hero was doing pretty well, but he needed more practice, and I needed to be sure he really understood. I made up this page to double-check the concepts. Gotta brag just a bit on the owls; those are my own original creation!

Miquon c-19a: make 10s & add

Practicing Reading Clocks

We're practicing reading clocks now. We've fooled around with it before, but this time it's more serious, and I'm thinking that it's going to take better than last time. Since I didn't buy the workbooks that go with our Math Expressions books and I didn't really love the ones in our Miquon books, I generally just make up something similar to what the book shows. Generally this works very well, since he's testing out of a ton of the work (I give unit tests as pretests). We don't do every page, and we usually don't do as many problems as they offer on a page either. But clocks are harder to fake it, and I couldn't find a worksheet that made me happy, so I made one. Feel free to use it now or to pin it for later!

Blank Clocks by

Fun With Triangles

I woke up this morning so excited to do math, because I had this awesome idea: build triangles to practice subtraction. Monkey's been exploring two-digit addition and subtraction, and we do usually do these problems with rods. He calls them "tricky math." Today, I threw in a twist by showing him about degrees and building a triangle as he subtracted from 180, which I had previously given him. He could choose any numbers that made him happy as he was subtracting, and I drew the triangle that went with them.

I did the writing because (A)I was drawing the triangles, and (B)that kind of "tricky math" still requires a lot of concentration for him to do, just counting the rods. But, he liked it well enough to do again; he wants to do rectangles tomorrow. That's going to challenge our set of rods! And, not so incidentally, he got some exposure to geometry concepts this morning, in a fun way.

I looked up the sum of the angles here, and I'm sure that I'll be back to that page as we play with more shapes; they have quite a few. I think that building pentagons would be fun, but we'll have to work our way up to that.

Placevalue and Writing

I've discovered that 10 + 3 = 13 is a relatively difficult problem for Monkey at this point; he hasn't caught the concept of placevalue yet. Which isn't very surprising, since it's a pretty new idea, this writing of numbers and matching them with their correct meanings. I realized this as we were doing some problems at Khan Academy. I like a lot of things about Khan, but there isn't much explanation or practice in the arithmetic section. It jumps from single digit problems to triple digit with no in between, and relies heavily on number lines. But as a supplement, to see how he's doing, and what happens when I sit back and let him do his thing, it's wonderful. So now, we're working a bit on some of the ideas that I've realized are weak. I thought that I might share the lab sheet I made up for him. To use it, copy, then paste into your word processor. Let me know how it goes for you!