math links on mastery vs. spiral

This is for myself to but also for anyone interested in the topic of mastery vs. spiral discussion and also about MEP.

It all started with a post by A Peaceful day about Is MEP compatible with CM? I first read her first post on MEP when I joined the MEP yahoo group.

Then there is discussion of spiral vs. mastery by Silvia in Homeschooling in a Bilingual Home which I was really intrigued.
part I
part II
part III

which led me to Living Math! and

more about literature based math books and mathemagic

and to Susan Lemon's book on Homepreschool and Beyond

and to the post of "Math, MEP Charlotte Mason and Mastery"on Science of Relations

and to Liping Ma's book of Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (studies in Mathematical Thinking and Learning Series)
(It's interesting since she also have a Chinese language study program for children which J used in her Chinese school)
*Silvia summarized the chapter in Ma's about regarding teaching to mastery in China in part II of her post on mastery vs spiral.

Productive day

I have no pictures today and considering the kids didn't get up until 10am and Prime had few incidents of nosebleeds, we had a really productive day.

We did quite a bit of cleaning this morning. I rally the kids and we got it presentable together in a decent amount of time. I feel calm returning when the house is in order.

We also did our normal stuff: reading of bible stories and bible. J is making improvements on retelling the stories. Prime has been listening to fairy tales and has been enjoying them. The two favorite currently is Rumpelstitskin and Puss in the Boots. He always manage to find humor in the stories and giggles so much.

J practiced her math. But today I'm happy to say that she actually wanted to do it, again and again. The sand timer must plays a role as the motivating factor. We used double dominoes and she have to do subtraction and put the same answers in the same pile. Finally, she finished before the sand ran out. :)

For lunch, Prime learned to make scramble eggs as that is one his favorite dish.

In the afternoon, J surprised me today by doing a TON (approx: 1 hour) of dance all by herself. I borrowed a dance music CD from the library and she did free dance. She keep saying she was hot, hot but when the next song came on, she was up and dancing again. She uses some of the moves her teacher taught her but also put a lot of her own spin on to it. I felt she was really expressing herself through the music and interpreting what she felt the music was saying to her so it was very nice to see that.

We also tried a Chinese language course called "After School Chinese", borrowed from the library today. It works well for what I'm looking for. Right off the bat, the kids learned to introduce themselves in Chinese- what their names are, how old they are this year, and what they like to do. It has a very realistic clip of what actually happens in Chinese classroom, like when the teacher comes, students would be asked to stand up to greet the teacher and then sit down. only when the teacher gives permission. Also, the kids how to introduce others (like your mom to your classmates/friends and vice versa) when they are in a non-classroom setting. The kids liked it very much, esp Prime. I can see he really wanted to learn and absorb the info. It came as no surprise that J wanted to be the teacher and have Prime and I be the students. :)

Later, we even managed to make it to the splash park and the kids had fun there too.

Fun with dominoes and wheelbarrow

Prime asked to work on "mini minus" today since he believes he knows how to do "paddy plus" so that's what we did. (These names are from Enki education) Of course, then J joined us.

Later, we also took out the dominoes. First it was just to see if they can tell me the sum on the double dominoes. Prime had a little trouble with the 5, always thinking it was 4.

Then they did this individually. They loved to quiz each other and had a lot of fun with that. Then I asked them to put the dominoes in order and they did that with a lot of enthusiasm. That was also good for some team building.



The love with beanies continues but today we took them out for a ride in the wheelbarrow. Toward the end of our walk, it was starting to rain so we ran for cover for the beanies.



The kids ran back and changed into their rain gear but when they came back outside, it already stopped raining so we continued to walk a little more.

1st week of vacation (theme: play)

Let the fun begin! Today, we kick off our first week of vacation. J says the theme for this week is "play".

The day started with "science"... talking about how the balloon is loosing its air, and is coming down and down, and finally, it just lands on the floor right before our eyes. J drew the face on the pink balloon days ago.

Then we explored fractions using cuisinaire rods since we read a bible story related to tithing 10%. Later, I showed them the Geo boards I brought in Florida and that was a big hit with the kids.

For lunch, J made scrambled egg all by herself. She cracked the eggs, whip the eggs, poured into the frying pan, turned on the fire, put in oil, stir-fried the egg and even scooped the egg out into a bowl all by herself.

The kids also had a play date with their friends in the afternoon. We even shared a dinner together. It was a very full and fun day.

Having fun with the descending balloon.

J is working on the Geo Boards

Prime ties the rubber bands around his finger

J's pattern on the Geo board

Having fun with friends.

math and ice cream

Today, while doing our math, we play this little game and the kids were really excited about it. They are loving math time.

J has previously made a whole bunch of origami people along with Prime so for the game I used those, but you can use anything. The key is to have them close their eyes while I put out the the origami people. And then I say, open your eyes. Then after like 2-3 seconds, I say, "now!" and they put up their fingers to show me how many people they see.

Prime was always counting so when the # gets higher, it was challenge as I covered up the origami and he haven't finished counting. But he got better as the game went on. Even if I kept the # same but made different patterns, he would know fast it was the same #. :)

J for the most part, looked and perhaps counted silently, but she was able to tell me correctly how many people there are. But in the beginning, I think she was also counting but later, she counted by 2's.

I used the pink origami person whenever it is an odd # and J caught on that.



We also worked on # ladder. 0-9 would be first row, 10-19 would be 2nd row, going up. This was a little challenge for both kids as I give them only some #s on the bottom row and each subsequent row, I only gave them one # on the row.

For Prime, I asked him to fill the # straight up, like 10, 20, 30, etc or 6, 26, 36, etc.

For J, I asked her to do it diagonally, like 51, 42, 33, 24, 15, 6 and asked her to start at the top, getting 51 because it is next to 50 and filling the blank # I circled. She was really trying to count to come up with the #s but later, I asked her if she sees a trick, she started to see the pattern.

On a totally separate note... since we have been eating pretty healthy, raw veggies and fruits and nuts, I said they can have some ice cream. But they scoop themselves. This also proved to be a good challenge for both of them as well as squeezing the organic chocolate syrup. :)


Scooping, licking, squeezing, mixing, eating. J says after the vigorous mixing, it was like a smoothie.

J also sewed today but she wanted to blog about that.

new math program

Today is a better day than yesterday. Still feeling the effects of cold/allergy/sinus, but w/o Benedrayl, at least I feel more alive than yesterday. :)

The kids had a great day. I started them on a new math program and the kids seem to really enjoy it. I'm keeping my fingers crossed that this will become our official math program. J especially enjoy playing school. She loves that I "act" like the teacher and write some stuff on the chalk board. Does that mean she miss school? Hm... Prime is also happy to go along as long as he can get it right and especially when he gets it before J. LOL. And when they both get it, they get excited and want to do it again and again. Honestly, I was quite surprised how long the kids did math. Normally, J is only willing to spend about 5-10 minutes on math and hurries to finish it up. So this is a HUGE thanks to a special someone whom I won't disclose just yet.

Anyway, I'm still just trying to take it easy. I'm starting to really appreciate and understand that "teacher's health is most important." :-)

My first math gnome

I'm feeling under the weather but I still want to do something, so I tried to make a math gnome today. I'd say it was a success as I'm not crafty but I can copy. If I can make it, you all can make it. You can find the tutorial here on Elizabeth Foss's webiste. Her instructions are also very clear as I need easy, clear instruction with lots of photos to be able to understand.

J tells me to make 2 and leave her 2 to make herself so check out her blog for gnome updates if you like at a later date. In Enki, he is called "Paddy Plus".


I had a hard time taking a good photo more than anything else. If you don't want to do much sewing, you can also get ideas by taking a look at other gnomes Elizabeth Foss made. Those, the signs are made with markers.

I also want to post our little science experiment with the white carnations, after our celery experiment fell flat. As many of you have wisely told me, the white carnations (I almost typed wise carnation) :-P worked so much better. The result can seen in about less than 1 minute, especially the green one. And even the red, you can't see it on the petals, but you can tell as the whole flowers changing color and it's a pink hue. It was really pretty. J did this in her kinder class so she knew how it would turn out and wasn't too excited. Prime didn't care much about flowers. Is that a boy thing? He will later though, I think. :) So I am the one who was most excited. LOL!


Just playing with my camera, seeing if I need the flash.

Math fun

Many of you probably read this, but this was really fun for my daughter so I thought I will put it up if any of you like to try.

This is from Learning all the Time by John Holt.

A: Think of a number. Don't tell me what it is, but be sure to remember it."

B: got it.

A: Make sure you don't forget it.

B: Okay.

A: Now add 3 to it -- and don't tell me the answer.

B: Got it.

A: Now add 10 to it.

B: Okay.

A: Now take away 7 from it.

B: Okay.

A: Now add 5 to it.

B: okay.

A: Now take away the number you started with.
B: okay.

A: The answer is eleven!

Later, J made her own little math problem and was just amazed the answer always worked out except one time where she started with 90 and had math errors. J also tried this game on Prime, and she said, Prime says, "My answer is 11 too!". :)

We did this for her copy work as well. I changed our routine a little bit and I think it worked better. Previously, I would let her choose what she wanted to copy and she picked few sentences to copy but she did the work by herself. But today, I put up a piece of paper on my wall with scotch tape and wrote it on the paper to demonstrate. (WOW, do I feel like a teacher now!) I wrote one sentence at a time and J copied. This is a lot more hands on but I can tell J liked it better. She is people person and enjoyed the interaction. I also wanted to make sure she had no problem copying from a black board as I read some children have that problem. Luckily, J did fine.

I also did few minutes of beads work with Prime. I was surprised that he can tell by the bead, any number 10 and below really fast, like 9 for example. But if I give him a row of 10 and a row of 9, he would say that's 10 and then he would count the 9 beads one by one. And it didn't matter if I give him 1 row of 10 with another 3 or 5 beads, or pretty much any beads, he would start counting the beads which did not add up to 10. If however, I gave him 2 rows of 10, he would say 20 w/o counting. It was an interesting observation for me. I'm sure daddy can write more about this as daddy is the one who works with Prime on the math and says he loves to do math and always asks for more and that in turn gets J going on too.

What does $1 trillion dollars look like?

Here is the link, check it out. (very good visual, for kids and adult alike). :)