Finding subtraction

Sometimes I have to go to work on days when I don’t have coverage for L – so she gets to come to meetings with me! What a lucky little duck huh?

Last week, I was going to an open writing support time for my college. I suspected that perhaps I would be the only one in the room at the time, but I wanted to be sure that if that wasn’t the case, I could have some things prepared for L that she could complete independently. I brought along some play-doh, some books she hasn’t seen in awhile, coloring, and I printed off a few Halloween-based pages for her. One of them was a math pyramid, which led to my realization that her math knowledge is really growing quickly!

A few months ago, we used a free trial of the Dreambox math app. While we loved the interface, she was frustrated by the concept she was working on, which was to build numbers through subtraction. In other words, to build 57, the app wanted her to move all 100 beads over, then subtract 4 tens, then subtract 3 ones. She wasn’t quite ready to think of numbers this way and we couldn’t get around that topic, so we didn’t extend our free trial.

Since that time, we’ve worked with single-digit subtraction, but have not talked about number building through subtraction. We have done lots of number building through the hundreds with number cards, base ten blocks, and base ten stamps.

In any case, we were using the fourth page of this pdf. I thought she could independently complete the first few rows. I packed up four tens of snap cubes and brought them along.

As I expected, she completed the first few rows independently. She’s got a good memory for addition facts and many of these were within her memory. She added 8 + 9 and 9 + 7 through counting on and correctly figured 17 and 16 as the answers. When it came to adding 17 and 16, though, she paused.

I had pulled out the snap cubes when she began her work and she eyed them at this point. She said, “I think I need to use my cubes.” I said ok, handed them to her, and sat back.

As I mentioned, the cubes were in lines of 10. She took two tens and put them in front of her. She stared at them for a minute and then said, “Three!”. She snapped three off of one of the tens and then placed the ten and the seven next to the number 17 on her paper. She then repeated the process with the other two tens, saying, “Four!” and making 16. Wow! I didn’t expect at all that she would work backwards from the number 20!!

She then took the ten from 17 and the ten from 16 and put them together. She held the 7 and the 6 and looked at them. “This makes more than a ten.” As I watched, she snapped three off of the 6 and added them onto the 7. She then moved the new ten over to the first two tens. I then heard, “Ten, twenty, thirty, thirty-one, thirty-two, thirty-three! It is 33!”

Ta da!

Ta da!

Yes, baby girl, it sure is.

Tic Tac math

So, we’re “those” people. You know: we don’t use plastic. We are vegan. We compost. We’re really quite difficult to take seriously.

One of the indulgences I partake in is (wait for it…) the tic-tac! Seriously. I love a white tic-tac. And when L asks for one, I give it to her. I don’t know if I “should” but I do.

In any case, she asked me for a tic-tac the other day. I reported back that we didn’t have any and needed to get them the next time we were at the store. She wanted to know how many tic-tacs came in a box. Great question! I have no idea, but we can count them… which led to today:

6 groups of ten!

6 groups of ten!

We revisited the question of the tic-tacs. We framed our question and took guesses from L, mommy, and daddy. L’s favorite number right now appears to be 100, so it wasn’t a surprise that it was her guess.

We then used a cupcake pan to hold our tic-tacs as we counted. We placed 1-10 in the first cupcake spot, then repeated until we’d counted all the tic-tacs. L counted by tens (“10, 20, 30, 40, 50, 60! There are 60 tic-tacs!”) to arrive at her answer, which I recorded for her.

Then, we moved onto three more boxes of tic-tacs. On the advice of a very wise friend, I’d purchased the value pack (all in the same color, nonetheless, so if there was a difference in quantity it wasn’t incorrectly attributed to the color). We repeated the process. She guessed the second box would have 100… but it had 60. By the time we got to the third box, she guessed 60 (which was correct). Finally, when counting the fourth box, we practiced counting by two’s as we dropped the tic-tacs into the cupcake pan. We arrived at 60 once again. L generated our rule about tic-tacs: There are 60 tic-tacs in a box.

Daddy then raised an interesting question – how do they know there are 60 in the box? Do you think someone at the factory counts them? Sounds like an inquiry question for another day… =)

Tomorrow is her first day at play school (a Waldorf-inspired two-day a week solution to allow me to, you know, do the work that I get paid for). We will school again on Wednesday.

Also, last week was back-to-school here – my husband was in meetings all Monday and Tuesday and school started for his students on Wednesday. I was in meetings all week, and L spent the week luxuriating at a Cincinnati Zoo camp. Seriously, I could preach the greatness of the Cincinnati Zoo. LOVE THEM.

Math is fun!

We’ve had a blast today working on math!

No, really, we have!

We get lots of funny looks when we talk with others about how excited we all get about learning together, but I swear to you, this is a snark-free blog entry. As much as I can make one, I suppose. =)

We started off our morning working with place value. L still inverts the ones and tens places when reading and writing numbers (15 is likely to be read 51, etc). We have worked hard on visualizing the numbers themselves (What does 15 look like? What does 51 look like?) and I decided today to link it explicitly to written notation.

Rolling place value, writing it out, and stamping the base ten blocks, too

Rolling place value, decomposing, and stamping the base ten blocks

We have place value dice (the dark green ones say “hundreds” under the numerals, the blue “tens”, and the purples “ones”). We have thousands and ten-thousands, too, but I didn’t want to be overwhelming. I think she has a pretty solid grasp of 10 tens being 1 hundred, so I decided to stop there. I also grabbed our one, ten, and hundred base ten stamps and our decomposition templates (100, 200, 300, etc through 900 on green tagboard; 10, 20, 30 through 90 on blue; the numerals 1-9 on purple).

She rolled the dice and worked on putting the hundreds on the far left, the tens in the middle, and the ones on the far right. She then read the number aloud (six hundred fifteen in this picture) and I transcribed it for her. I asked if her she wanted to stamp it or decompose it first. She chose decompose, so she separated this number into 600+10+5. She then stamped out 6 hundreds, 1 ten, and 5 ones. We repeated this for a few numbers and I could tell she was growing bored…

So I pulled out another concept! We took the two numbers she’d rolled most recently and I told her about the hungry alligator. We agreed that given the choice, the alligator would always eat the bigger snack. We giggled about how the alligator would eat me, not L, and the dog, not the cat. Silly! Anyway, I showed her the alligator sign with its open mouth toward the bigger number:

Introducing greater than/less than signs

Introducing greater than/less than signs

I did not introduce the idea that one sign was called “greater than” and the other was called “less than” because it seemed to me that if she grasped the idea that the mouth was eating the bigger number, we were good to go at this point. We played with this for awhile (you can see that at the top of the paper, we inverted our example to show how the mouth opened the opposite way).

Whew! Math is fun!

We then decided to play with our new magnet kit. After we both built a few shapes for fun, she noted that I’d built a hexagon. I promptly decided that a geometry construction lesson was in order! I pulled off the “names of the polygons” chart we’d made a few weeks ago and challenged her to build a triangle. Easy! A quadrilateral? Surprisingly challenging.

Construction of polygons with magnets

Construction of polygons with magnets

She spent some time struggling with adding line segments onto a vertex but it never transformed into a quadrilateral. We stopped for a minute and looked at the hexagon to notice how many line segments and vertices there were, and how many line segments touched each vertex. We then pulled apart the attempt at a quadrilateral and started from scratch. Slowly, narrating her way through it, she built it! I then challenged her to transform her quadrilateral into a pentagon. She grinned, opened a vertex/line segment, and added another line segment and vertex. Easy peasy! So fun.

Mindware's pattern play

Fun with patterns

We ended our “school time” with Pattern Play (which we LOVE!) She found an error on card 19 – if you look closely at the card in the picture, you can see it. In the triangle facing us, there are two yellow segments and there are none on the triangle against the edge of the picture, while there ought to be one yellow per triangle. She found the error but decided to replicate it (see her example) since she was creating the pattern on the card. Funny girl!

In addition to this, we’ve spent some quality time over the past few days (too much time!) watching They Might Be Giants videos on YouTube – her current favorites include The Sun is a Mass of Incandescent Gas, I am a Paleontologist, The Bloodmobile, and How Many Planets? (especially when it says “Jupiter” in the deep, deep voice!).

We may be creating a monster. =)