This past week was our first week of school. We started with only two subjects: math and circle time. As circle time is a new feature for us, I'll describe it first. After we have cleared the breakfast table, I gather everyone to read the Bible, some devotional books and missionary stories, work on a memory passage, read some poems, and sing a song. On Monday, I received serious push-back from E11. I believe he had expected we would do circle time outside or sitting on the futon, and when I refused to move it from the kitchen table because I wanted people to be able to draw during the readings, he threw a fit. However, he then proceeded to draw a tree during the reading, continuing to add details throughout the week, and he seems to be enjoying it now. Allowing the children to draw while they listen is a successful strategy, allowing even E3 to stay at the table and pay some attention much of the time. (He still needs frequent reminders to return to the kitchen). During our poetry reading, I have P13, E11, and B7 read some of the poems. They all need to work on reading slowly, loudly, and clearly, but already I see some improvement. Having all the children together to discuss the devotional book is helpful because, although it is technically part of B7's curriculum, H5 often chimes in with a question or comment, and P13 and E11 are able to summarize and explain in ways that are easier for B7 and H5 to grasp. A real advantage to doing circle time is that, when it has ended, everyone knows that school has started and I am less tempted to do "just one more" housekeeping task (which can turn into "just 5 more") before getting started.
Immediately after circle time on Monday, I gave P13 her first lesson from Core Plus Mathematics. We investigated the physics of bungee jumping by connecting rubber bands and attaching varying numbers of nickels (5-gram weights) to the end before dropping them from the top of a yardstick. It took a bit of trial and error to find a way to effectively attach the nickels to the end of the rubber band chain and to measure the maximum stretch, but P13 devised a cone out of paper towels which she tied on to the chain with another rubber band, and I moved my hand incrementally down the yardstick until I didn't feel the point of the cone touch it when dropped. Our plotted data showed an approximately linear relationship, with the length of the rubber band - nickel cone assembly growing by about 7/8" with each additional nickel. E11 found himself drawn into the investigation despite himself, and making mathematical observations. Later in the week, he was similarly drawn into our investigation of a game of chance in which a fundraiser pays out $4 if a die shows a 4, but receives $1 if the die shows any other number. Unfortunately, this investigation was much harder to conduct with only one student, because the randomness of the results after only a few trials far overcame the general expected linear trend if you were only to look at the fundraiser's profits after every 50 trials. Had we had another 5 students or so, everyone could have played the game 50 times, and we would probably have gotten better results without spending a prohibitively long time rolling dice. However, P13's mathematical insight allowed her to predict what should have happened if we had been able to conduct hundreds of trials: on average, every 6 rolls will lose the fundraiser $4 and gain it $5, for a net gain of $1 every 6 rolls. P13 seems to be enjoying this program and it certainly forces her to think and express herself clearly. And if it can draw in my reluctant 11-year-old, that says something for it!
Speaking of E11, I gave him a lesson from Life of Fred: Fractions on Monday after P13 was done with the bungee jump simulation. He is over halfway through the book and theoretically knows how to add, subtract, and multiply fractions and mixed numbers. We read the chapter (part of a continuing story) and he worked on the problems in the "Your Turn to Play" section. Unfortunately, he seemed to have forgotten absolutely everything over the week or two since he last did math. He was trying to find common denominators before multiplying, and to add the denominators when doing addition, among other painful errors. Worse, when I tried to ask questions to understand his reasoning, he stormed off, refusing to answer. When he was ready to try again, and I tried to explain the concept using a simpler problem, he shrieked that I was wasting his time. When I tried using 2 different methods to explain the concept using the problem that was actually causing him difficulty, he again moaned that I was not making sense (without taking time off from moaning to hear any of my words, or to tell me what part of my explanation confused him). Some days, he is REALLY hard to teach. Because he had such trouble with the first problem set, I decided to give him a similar problem set every day until he mastered it, instead of proceeding to the next chapter. He was furious, because the chapters contain quirky and amusing stories, and plain problem sets don't. On Tuesday, he got the egregious result that 1/3 - 1/12 = 3/0. (He remembered to find like denominators - and then subtracted them!) With much difficulty, I got him to listen to explanations (involving pizza, or squirrels) of what was going on in each problem. On Wednesday, he got all 5 problems (covering the same concepts as Tuesday) right on the first try, with a much better attitude. It's the same pattern as over the summer! On Thursday, we went on to the next chapter (more of the story! Yay!) and he retained what he had learned over the previous days - and the same thing happened on Friday. I really need to remember (over the screaming) that just because he seems to have completely forgotten a concept doesn't mean he'll have as hard a time re-learning and retaining it as he did the first time.
B7 has been steadily working through the Art of Problem Solving Pre-Algebra book. This week, we were working on finding the least common multiple. B7 has epic mental math ability, but he writes like a 7-year-old, so if I ask him to write down his complete solutions, his brain gets to the correct result many minutes before his brain has time to tell his hand to write down the steps, which is frustrating for him. So I have a deal with him: he has to write down all the steps for the first problem we work, and then he only has to tell me verbally and I will write them for him on subsequent problems. At the rate we are going through the book, it will probably take 2 or 3 years to complete, but that's okay - we can wait until he's 10 before starting algebra! On days when I am too busy or overwhelmed to spend 30 minutes working on math with him, I can ask him to work on Alcumus, a math game on the Art of Problem Solving website (https://artofproblemsolving.com/alcumus), which allows him to review concepts he has learned in the past and forces him to write down his own answers.
H5 is a lot of fun to teach, because he is so enthusiastic about everything. I'm not using a single, formal curriculum with him, though I'm using Miquon as a general outline for where to go next. I have ideas of concepts he'll need pretty soon, and present them using games and manipulatives. We have been using the Right Start place value cards to practice counting to 100, and playing Coin War using cards with pictures of coins I made when P13 was in kindergarten. He also enjoys using Khan Academy's "Early Math" exercises.
I'm glad I decided to start school slowly, as it allows me to work out kinks in each subject and see ahead of time what might cause problems. In previous years, when we've started full steam with all subjects on the first day of school, I've felt more overwhelmed at the end of the first week, with fewer ideas of what specific things need to change. My plan for next week is to add in music practice and lessons, P13's Koine (New Testament Greek) lessons, and some kind of physical activity for everyone. The following week we'll add science and current events (for P13 and E11), the next week writing, and when we get back from our September trip to the mainland, be ready to go full steam with all our subjects. I plan to continue making weekly updates, so check back to see how we're doing.
Immediately after circle time on Monday, I gave P13 her first lesson from Core Plus Mathematics. We investigated the physics of bungee jumping by connecting rubber bands and attaching varying numbers of nickels (5-gram weights) to the end before dropping them from the top of a yardstick. It took a bit of trial and error to find a way to effectively attach the nickels to the end of the rubber band chain and to measure the maximum stretch, but P13 devised a cone out of paper towels which she tied on to the chain with another rubber band, and I moved my hand incrementally down the yardstick until I didn't feel the point of the cone touch it when dropped. Our plotted data showed an approximately linear relationship, with the length of the rubber band - nickel cone assembly growing by about 7/8" with each additional nickel. E11 found himself drawn into the investigation despite himself, and making mathematical observations. Later in the week, he was similarly drawn into our investigation of a game of chance in which a fundraiser pays out $4 if a die shows a 4, but receives $1 if the die shows any other number. Unfortunately, this investigation was much harder to conduct with only one student, because the randomness of the results after only a few trials far overcame the general expected linear trend if you were only to look at the fundraiser's profits after every 50 trials. Had we had another 5 students or so, everyone could have played the game 50 times, and we would probably have gotten better results without spending a prohibitively long time rolling dice. However, P13's mathematical insight allowed her to predict what should have happened if we had been able to conduct hundreds of trials: on average, every 6 rolls will lose the fundraiser $4 and gain it $5, for a net gain of $1 every 6 rolls. P13 seems to be enjoying this program and it certainly forces her to think and express herself clearly. And if it can draw in my reluctant 11-year-old, that says something for it!
Speaking of E11, I gave him a lesson from Life of Fred: Fractions on Monday after P13 was done with the bungee jump simulation. He is over halfway through the book and theoretically knows how to add, subtract, and multiply fractions and mixed numbers. We read the chapter (part of a continuing story) and he worked on the problems in the "Your Turn to Play" section. Unfortunately, he seemed to have forgotten absolutely everything over the week or two since he last did math. He was trying to find common denominators before multiplying, and to add the denominators when doing addition, among other painful errors. Worse, when I tried to ask questions to understand his reasoning, he stormed off, refusing to answer. When he was ready to try again, and I tried to explain the concept using a simpler problem, he shrieked that I was wasting his time. When I tried using 2 different methods to explain the concept using the problem that was actually causing him difficulty, he again moaned that I was not making sense (without taking time off from moaning to hear any of my words, or to tell me what part of my explanation confused him). Some days, he is REALLY hard to teach. Because he had such trouble with the first problem set, I decided to give him a similar problem set every day until he mastered it, instead of proceeding to the next chapter. He was furious, because the chapters contain quirky and amusing stories, and plain problem sets don't. On Tuesday, he got the egregious result that 1/3 - 1/12 = 3/0. (He remembered to find like denominators - and then subtracted them!) With much difficulty, I got him to listen to explanations (involving pizza, or squirrels) of what was going on in each problem. On Wednesday, he got all 5 problems (covering the same concepts as Tuesday) right on the first try, with a much better attitude. It's the same pattern as over the summer! On Thursday, we went on to the next chapter (more of the story! Yay!) and he retained what he had learned over the previous days - and the same thing happened on Friday. I really need to remember (over the screaming) that just because he seems to have completely forgotten a concept doesn't mean he'll have as hard a time re-learning and retaining it as he did the first time.
B7 has been steadily working through the Art of Problem Solving Pre-Algebra book. This week, we were working on finding the least common multiple. B7 has epic mental math ability, but he writes like a 7-year-old, so if I ask him to write down his complete solutions, his brain gets to the correct result many minutes before his brain has time to tell his hand to write down the steps, which is frustrating for him. So I have a deal with him: he has to write down all the steps for the first problem we work, and then he only has to tell me verbally and I will write them for him on subsequent problems. At the rate we are going through the book, it will probably take 2 or 3 years to complete, but that's okay - we can wait until he's 10 before starting algebra! On days when I am too busy or overwhelmed to spend 30 minutes working on math with him, I can ask him to work on Alcumus, a math game on the Art of Problem Solving website (https://artofproblemsolving.com/alcumus), which allows him to review concepts he has learned in the past and forces him to write down his own answers.
H5 is a lot of fun to teach, because he is so enthusiastic about everything. I'm not using a single, formal curriculum with him, though I'm using Miquon as a general outline for where to go next. I have ideas of concepts he'll need pretty soon, and present them using games and manipulatives. We have been using the Right Start place value cards to practice counting to 100, and playing Coin War using cards with pictures of coins I made when P13 was in kindergarten. He also enjoys using Khan Academy's "Early Math" exercises.
I'm glad I decided to start school slowly, as it allows me to work out kinks in each subject and see ahead of time what might cause problems. In previous years, when we've started full steam with all subjects on the first day of school, I've felt more overwhelmed at the end of the first week, with fewer ideas of what specific things need to change. My plan for next week is to add in music practice and lessons, P13's Koine (New Testament Greek) lessons, and some kind of physical activity for everyone. The following week we'll add science and current events (for P13 and E11), the next week writing, and when we get back from our September trip to the mainland, be ready to go full steam with all our subjects. I plan to continue making weekly updates, so check back to see how we're doing.
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