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01 February 2016

More Number Squares

The MEP lesson plans suggested that our Number Square activity should take about nine minutes in a classroom setting. Hero and I have gotten a good deal more milage out of it than that so far! Because the plans said that it was a short activity, I had additional math work ready to go when we started it, but that work sat on the fridge for several days while we played and explored these squares.

The first day, I showed him how to do the activity, using a 3x3 square and the word ONE. Then, we worked together to do a 4x4 square with the word MORE. By the end of that, he had the idea, and I was just watching while he figured things out. Next, he did a 5x5 with his name. That one was more difficult, because he hadn't yet realized that working systematically will make his life much easier. I think this might be the first problem he's run into where working systematically mattered - the activity would have been a success just for that discovery, I think. (There's pictures showing our work in the first post.) For each square, we figured out an equation suggested by the book:

1+2+1=4
1+3+3+1=8
1+4+6+4+1=16

That was as far as we got the first day. I was intrigued, so I played with a 6x6 square that evening, which we talked about the next day. My own weakness with numbers had lead me to misidentify this as an activity working with square numbers, so I started out trying to show him square numbers on our Cuisenaire Rods... which didn't match up. I love the way that I get to (re)learn along with the kids. I never understood how math was related to patterns until I started doing math things with Hero, and it's pretty exciting to me to see how these things fit together. He got to watch me be confused and then work it out -- which is not a bad thing. And looking at the Rods was cool.


I don't know that I'd ever really seen an exponential relationship laid out and made touchable like that. We started out building long skinny towers, and later Hero added the blocked versions as we were starting to run out of space on the table.


Because it meant we were able to use our hundreds flats, the blocked versions allowed us to go even larger (we added another after the photo was taken) without running out of pieces. I was pleasantly surprised at how far our Rods went. That was as far as we got the second day, building the answers to the equations we'd built. I'm not sure if Hero feels like messing around with this anymore, but I am planning to play with at least one more set. We've done a 7 letter word set, which makes 32 solutions. I want to play with an 8-letter word, giving 64 solutions, and see if I can predict what the equation will be. And there's some cool patterns in how the letters fall on the graph that I'm intrigued by. I don't know if Hero's interest is strong enough to keep him engaged at a third sitting for our "9 minute" activity (that would bring us to around 1.5 hours), but if he is, there's plenty to play with still. 

Math is pretty amazing. 
How come nobody ever told me about playing with numbers?!

31 January 2016

Psalm 8: Under His Feet


I was browsing through some of the places that Psalm 8 is quoted in the BYU Citation Index, and this phrase caught my eye:


Thou madest him to have dominion over the works of thy hands; thou hast put all things under his feet. (vs. 6, emphasis added)


This phrase became even more interesting when I realized that different apostles and prophets use these verses to mean both mankind and also Christ. I love the way that the Lord layers meaning in the scriptures, and uses the same passage to teach different lessons, depending on where we are and what lessons we are in need of. Elder Monson used the Psalm to refer to mankind when he said:


David declares in one of his beautiful and moving psalms, “O Lord our Lord, how excellent is thy name in all the earth! … “When I consider thy heavens, the work of thy fingers, the moon and the stars, which thou hast ordained; “What is man, that thou art mindful of him?” (Ps. 8:1, 3–4)
Job, that righteous man of old, joined in the question when he asked, “What is man, that thou shouldest magnify him? and that thou shouldest set thine heart upon him?” (Job 7:17 )
One need not grope for answers to these penetrating questions when in your presence here in the historic Tabernacle or with you in the many meeting places throughout the world where you have assembled. “Ye are a chosen generation, a royal priesthood, an holy nation” (1 Pet. 2:9) “Ye … are … a spiritual house, an holy priesthood” (1 Peter 2:5)


On the other hand, the Apostle Paul seems to have used these verses to refer to Christ when he quotes them in his Epistle to the Hebrews:


But one in a certain place testified, saying, What is man, that thou art mindful of him? or the son of man, that thou visitest him?
Thou madest him a little lower than the angels; thou crownedst him with glory and honour, and didst set him over the works of thy hands:
Thou hast put all things in subjection under his feet. For in that he put all in subjection under him, he left nothing that is not put under him. But now we see not yet all things put under him.
But we see Jesus, who was made a little lower than the angels for the suffering of death, crowned with glory and honour; that he by the grace of God should taste death for every man.
-Hebrews 2:6-9


Looking through the various places in scriptures, it looks like this phrase is predominantly used to refer to the majesty and power of Christ. And that has been a recurring theme in the Psalms I've looked at thus far.

29 January 2016

February Watercolor Challenge



For this month's challenge, I spent a few minutes browsing through the Google Art Project's watercolor collection. There's some stuff in there that I look at and think, "Really? That got in a museum?" As well as some pieces that are incredibly beautiful. This month's logo features a painting of Conwy Castle in North Wales that I found while browsing. (That's the Welsh spelling, not a misspelling, by the way.) So the first suggestion this month is to spend a few minutes browsing their watercolor collection, and maybe pick a few paintings that catch your eye to come share in the Facebook group. There's an amazing variety of looks that the various artists have persuaded their water color paints to produce for them. As with so many things, spending time looking at copying the work of accomplished artists will give us a boost in our own work; you can't go wrong by studying excellence.

After that, spend a few minutes watching watercolor timelapse videos to see how experienced artists build their paintings. I think it's fascinating to watch how they layer their colors, and I find it helpful to watch them do it, and think about their work as I'm planning my own attempts. Here's a couple, but there are many more on YouTube.




This one is a little bit longer, but it shows the whole process, including how this artist uses the lifting technique that we practiced last month. I think it's interesting how she made the painting "loose" - which made a beautiful final picture.




Next, read chapter 3, Transparency and Opacity from our book. This chapter has more discussion of how to mix colors, and the properties of the two classes of paints, transparent and opaque. Mess around with your colors. Observe how they mix, and what they do on wet paper when placed adjacent each other, as well as what happens when you tip a damp page. Once you have figured out if your colors are transparent or opaque, try building up a few layers, working from light to dark. As with last month's blending activity, remember that this exercise is not about the final product, but rather about learning the behavior of your paint: there are no mistakes, even when the result is not what you were anticipating.

Finally, still working with the artist you selected last month, choose another painting to copy in whole or in part. Remember to bring a photo of your projects to our Facebook group and share your accomplishments so we can cheer for you!



The January challenge can be found here.

26 January 2016

Number Squares

So, I'm thinking about switching to MEP for our math (Hero's close to outgrowing Miquan) seriously enough that I printed out their lesson plans and we're taking them on a bit of a test drive this week. This was the first activity we did (level 4), and I am having so much fun with it that, after Hero(9) was finished, I did some more to see what the pattern was going to do. It starts like this, with the blue set:


So, that was pretty tricky for him (and me, too, when I was looking it over last night). But you're writing the letters, and then in the final grid, we sort of put all the different variations on a single grid, and counted up how many times the final letter hit each square across the diagonal, where the Es are in that 5th blue grid. Next, we did the same thing with a four letter word - MORE. 


This time, he understood what he was supposed to do with the letters, and filled in the chart completely on his own. I helped with the chart where all the words are "stacked" into the same grid, and we counted them up. At first, he was thinking that there was 2 places where those center diagonal Es are used, so we added that up (the equations are at the bottom of the picture), and it was only six - but we'd clearly filled 8 charts, so that couldn't be the number of times they were used. He went back and found the missing numbers and got the correct equation.

We did the same thing for a 5-letter word, but we used Hero's real name, so no pictures of that on the blog. It was more challenging to keep track of - we had a couple of missed solutions and a couple of duplicates, so it took us some time to sort it out and get our equation to work out the way it was supposed to do. Tomorrow, I want to go back and look at that again. He didn't do them in any particular order, so they were easy to mix up. But when I did the next chart, for a 6-letter word, PUZZLE, I did them systematically, and kept things straight no problem. I didn't want to draw the whole grid anymore, so I printed some graph paper for this one. As I was counting things up to see how many times the final E fell in each square, I used some little squares in the middle to help me keep my place.


By now, I'm noticing a whole bunch of interesting patterns. For instance, the letters always fall in the same places. No matter how I follow the rules - turn right or go down - I never need to put two letters in the same block. That's true all the way through. And the equations that this makes are pretty interesting, too. I think that you could make some kind of equation or generalization for how they go:

1+1
1+2+1
1+3+3+1
1+4+6+4+1
1+5+10+10+5+1

I'm not sure how to generalize how that's going into an equation, but there's clearly a pattern, and you could figure out what it is for any iteration, if you could generalize it into an equation. Which would be cool. I'm tempted to do a 7-letter word, which would be 64 squares, just so that I can make a prediction about what the equation would be and then check to see if  I'm right. This is kind of a fun game.

Also, the numbers are squaring. We haven't done the squared numbers unit in Miquan just yet, but after doing this, I think we're going to in the next few days. This is a pretty cool introduction to squares. (Update: Yes, I eventually realized these are exponents, not squares. There's a follow-up post in the works.)

MEP's lesson plan suggested that this activity would take 9 minutes with a whole class of kids. I don't know who thought that was going to be possible; we took more like 20 to do the 3-, 4-, and 5-letter words, and then I spent a few more minutes doing the 6-letter word on my own. So their time estimate was way off. But I really like the way they are showing kids how to look for patterns and encouraging number play. This is a fantastic activity that we had a good time doing.


Part two is here.

25 January 2016

Book Review: From Saul to Paul

Paul has always been kind of mysterious to me. He's the author of a huge amount of New Testament material, but I've always hated reading those parts, because I really didn't understand large parts of them. So when I was out visiting my sister last summer, I saw From Saul to Paul: The Road to Apostleship by William Victor Blacoe, and I was super excited about reading it. It's taken me a long time to get through it. Part of that is that I just don't have a lot of reading time. Part of that is that I can't seem to limit myself to just one at a time. And part of that is that the book is somewhat dense: there's a lot in there, and there's a lot of things to think about. More than once, as I read I went and grabbed my Bible and made some notes in the margins.

This morning, I finally finished the book. Love it.  This first reading did something pretty amazing for me: it assembled the *story* of what Paul was doing in all those letters. I want to go back through the book again (though probably not immediately) and work through it side-by-side with my Bible, now that I have a better understanding of what the story is. I've always had a hard time assembling the story of what Paul is doing, after his vision on the road to Damascus. From that point, it's always been all mushy in my brain, and I didn't know anything about the various places that he's writing to. Now, I have a much more clear idea of what's going on. So understanding the story of his life (I knew that he was martyred, but I hadn't realized that he'd been decapitated), and some more about the culture of the time and place gives me a much better start the next time that I read Paul.

So that's what I did this first time that I read the book. What I'd like to do, next time, is sit with the book and my scriptures side-by-side, and go through Paul's writings very, very slowly. Probably also drawing his trips on a map as I go along. I think that would go a long way towards making things gel in my brain and helping me to be more comfortable with this section of the Bible. I'm looking forward to that project!

23 January 2016

Maybe Shakespeare?

I've noticed that, among the many amazing Mother-Educators in the Charlotte Mason tradition, there are a ton of very smart women who hold Shakespeare in very high regard, but I've never cared enough about Shakespeare enough even to dislike him. None of his works I've been exposed to was at all interesting; they have been uniformly dull.

Part of this comes from appallingly bad teaching. In eighth grade, when we "did" Shakespeare, the teacher had been a remedial teacher, but, he regretfully informed us, they had gradually taken his remedial classes away from him, and so he was teaching us. (I always felt so sorry for the struggling learners with no escape, and no inspiration to love learning from a man like that.) He waxed poetic about the value of watching the play, then showed us the same 5 minutes 5 days running, and no more. I think we might have read a few lines, too, but can't remember for sure. I was so painfully bored in that class that I often would watch the second hand go around the clock, noting the time each time it passed 12. For the whole hour. Because watching the second hand was more interesting than the class. So that's how we did Act I. Then he told us that nothing of importance happened in the middle, and we skipped to the end, which he butchered in precisely the same fashion he had used on Act I. 

This did nothing to endear the Bard to me, and if we did any other plays in school, I don't remember it.

But the Ambleside ladies insist that he's worth reading, repeatedly, and they are, particularly collectively, very, very smart, so we're giving him a shot. The Ambleside Online schedule has Taming of the Shrew on their list for this year, so that's what we started with.

First, the boys and I read the Lamb's Shakespeare for Children version. And we liked it.

Then, the consensus being that Shakespeare is meant to be watched, not read, we watched the movie. The boys loved it. I was not so sure, and went back to the Ambleside ladies and grumbled a bit, and asked for more encouragement, which they very kindly gave.

So we printed out a copy of the frame story's script, and we looked up some of the hard words, and read through it, using stuffed animals on a blanket "stage" to help us follow the action. That was kind of fun. Hero and I did all the reading, but Dragon and Peanut both participated too - I helped them to say a few lines each. (Don't you love the Jedi suit? It was his Halloween costume, but he wears it all the time.)


Then, we watched the play again. This time, I liked it lots more than the time before. I'd understood the words the first time -- but not the puns and plays on words. And, with the additional context from the frame story (which the movie version skipped), the whole thing was just funny. Hero's favorite part is the part where Patrucio kisses away Katherine's refusal to marry, and my favorite is where Luccencio's dad shows up, and he's almost the only person not pretending to be someone else, but nobody believes him!

The ladies on Ambleside say that Much Ado About nothing is a good play for beginners, so I think that's going to be the next one that we do. Because maybe Shakespeare is worth a little effort!


22 January 2016

Nature in the Winter

So, I've had this book, Handbook of Nature Study, for years. Bought it probably five or more years ago... and never used it. It's jam-packed full of interesting stuff, but I just couldn't figure out how to get the information from the book to our Nature Study outings. So it's been gathering dust.

Until this week.

Three days ago, Kristyn of Beraca Valley Academy posted about how she was using this book. And when I read it, something finally clicked. She described her process: she reads a bit from the book, then she heads outside, later, with her kids. Oh. That's so simple! Why did that take so long for me to get it?

So, it's winter. I'm clueless about figuring out trees without their leaves, though I know that it can be done. There's no flowers. So as I was browsing through the table of contents, I decided that we'd work on climate and weather for a while. That section starts out with a pretty cool history of a Tower of the Winds in Athens, which made for some good conversation while we were out. The kids were (as usual) pretty excited to be at the park, and quick to zip off to their favorite hidey-holes in the brush, so we'll talk about it some more. Maybe see if we can find some pictures of the friezes to look at. And I'm thinking that the observation tower at the park might just become our own "Tower of the Winds".

All that is not too shabby for figuring out this book about 30 minutes before we were supposed to walk out the door yesterday - particularly since a good chunk of that time had to go to dressing for the cold. Cuz it's chilly around here. We had warmed up some - I think it was around 20-25F. Much nicer than the negative temps we had all last week.




So we played in the snow. Checked out some animal tracks. There were tons of bunny tracks around. Some deer tracks. And this, which I'm not sure what it's from.


The big kids were on the other side of a hill, so I didn't get any pictures of them, but the little kids had a great time in the quarry area. I think that Dragon(5) was a bit frustrated that the snow had covered over all the rocks that he loves so much, but he found things to do, digging around. Peanut(3) was right in there with him. My friend and I just tried to stay out of the way, so the kids can learn and enjoy.


It was snowing a little, so we stopped and checked out the flakes that caught on our gloves and coats. They were pretty amazing; it was a good day for that. They were actually big enough to (kind of) see.


When we went to find out what the big kids were up to, we saw tons of tracks. And had a lovely conversation about all the scat. The bunnies had been busy. Very busy. This picture really doesn't do it justice; the whole area was dotted. Next time we go, I want to look at the bushes they cluster around and see if we can see where the bunnies have been chewing on the branches.



Turns out the big kids were having a really good time. Who needs sleds, when you have snow pants and a slick coat?


About this time we decided that the littlest ones had had enough, and we started to wander back toward the car. I'm so glad we didn't take the short, easy way, because we found deer beds! There was three, though we only took a picture of two of them. We also had a nice conversation about how different deer scat is from rabbit scat, even though we didn't know for sure that it was deer that had made it until we got home and looked it up in a book. You can figure a lot out, just by looking and thinking a bit, which is pretty cool.


When we got home, we read our Snowflake Bentley book, as well as reading the sections of Tracks, Scat, and Signs. Today, using the photos I took, we made an entry in our nature journals. Nothing fancy - bushes and rocks and snowflakes aren't the easiest things to draw. But already, even though we do them somewhat irregularly, the nature journals are cool to look back through.

19 January 2016

Working With Patterns

Dragon has been working with patterns for several days, now. The first day, we did a worksheet, and it was tough. Especially the ones where he was supposed to leave a blank spot. He needed a lot of help to figure out what was supposed to be happening. So we've been practicing. 


So we've spent several days doing patterns of various sorts. Yesterday, we made rod shapes, which looked cool, but I forgot to take a picture. Today, he was already playing with the Duplos, so we used those to practice patterns.


It's still challenging, but with practice, he's making good progress.

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