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Says my math(y) son
Proud of my DS7 we are (mostly) done with math operations (addition, subtraction, multiplication and division) except review. Boxes are checked, tables learned, carrying, borrowing, long multiplication (including exponents), long division with remainders done and done.
We're working on fractions finishing up equivalent fractions now, and mastered using math operations (above on decimals)
Figured we'd work the rest of the way through fractions, decimals, percents and all of the various associated knowledge and tasks. I think we'll be through it by the end of the summer.
So, what comes next? A lot of smaller topics like averages, ratios, area, more word problems? He's set on some algebra in the next year or so not sure he's ready for the logic leap.
By the way, this is work we do at home (about 10 minutes each evening unless DS gets in "the zone" and insists on continuing) he's working on math operations at Montessori school, so there will be a lot of review of the above concepts. He doesn't seem to mind so far, and it makes me comfortable that the concepts are "solid."
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HandsOn Equations is a great way to introduce algebra without requiring the logic leap, but yet building the foundation for it. My dd did it at age 5 or 6, although it's recommended (I think) for ages 811. You'll probably find that your ds can finish it in a couple of weeks, but I think the approach and the conceptual awareness it sets up is so valuable that it's a good investment that will pay dividends for many years. I wish there was a cheaper version you could make and print up and make at home, but Borenson was such a genius for devising what he did that I suppose he deserves the $35.
What else is there? Well, I would do ratios almost in parallel with fractions, decimals and percents. They're just another way to represent the relationship between two (or more) amounts. Then there's all the geometry, area of triangles and circles, volume and surface area of prisms and cylinders, pythagorean theorem, unknown angles in figures comprised of triangles and parallel lines, probability, exponents and scientific notation, multistep word problems, cartesian coordinates, interesting sidebar topics like Eratosthenes' sieve, the Golden Ratio and Fibonacci's series. I'd be diverting him as much as possible into conceptual and problemsolving aspects of math with brain teasers, stories and projectoriented explorations.
I'm still not clear why you've chosen to institute a math program for him at home in addition to what he's getting at school. In your situation I would respond to his curiosity and questions around math, but not do any parentallyled 'work.' Instead I'd be trying to broaden his interests out, and not exacerbate the mismatch with his schoolbased learning, by trying to interest him in areas that fall outside the realm of traditional K7 academics: musical instrument study, robotics, computer programming, 2nd language, gymnastics, children's theatre, martial arts, astronomy. To each her own, though.
Miranda
Mountain mama to one great kid and three great grownups
Thanks Miranda this is helpful. I will look at these resources.
Regarding the lastDS is in a new school this semester where, if he shows the aptitude and the mastery, he won't be slogging through a year of multiplication and a year of division. The school will subject accelerate which is a good scenario for DS.
What you say is welltaken in his old school he had to work through the curriculum at the pace it was taught to everyone, and it nearly killed his early love of learning.


That's great that his new school will subjectaccelerate, but keep in mind that there may be an upper limit to what they're willing and able to do. Assuming this isn't a K12 school, he may end up somewhere with more constraints. In middle school they may be willing to offer Algebra II but not Geometry or PreCalculus. At the high school level he may have difficulty finding any courses if he's more than a couple of years ahead. I've heard of advanced kids having trouble accruing the required number of math credits as high schoolers because they finished two or more of the standard high school courses prior to actually being enrolled in a high school and therefore those courses didn't count as math credits when applying to colleges.
My dd11 is about to start a course at school that is more than 4 years ahead of her agegrade; that's pretty unprecedented and only worked for us due to some very unusual school circumstances, including the fact that she doesn't actually attend school except for math. We're happy to let her move ahead because (a) it's the only math she's doing, (b) we're in Canada where you can earn high school credits while not actually enrolled in high school and (c) being part of a homeschooling family she's not going to be constrained by what level of math a high school is able to support her in learning as she gets older.
Miranda
Mountain mama to one great kid and three great grownups
The logic leap between basic math operations and advanced algebra is steep he may not take it in as easily.
We have a special school district where he could get support if he turns out to be a math genius. However, his language arts talent is actually much higher than his math abilities, if we consider his test scores. He may eventually realize it and gravitate in a different direction.
My two cents is that there is a real value in having the experience as a child of doing at least some interesting and challenging academic work. Not at the expense of the art, music, sports, language, programming, but enough to build a sense of recognitionthis is what it feels like to master something hard and interesting.
Here are a few that are good for dabbling, I think (stars for ones I think would be good for that age):
math history with exercises / worksheets / projects /short essays–good for dabbling
Algebra Activities from Many Cultures
Agnesi to Zeno: Over 100 Vignettes from the History of Math
AIMS Historical Connections in Math vols 13 biographies and discoverybased printables**
Multicultural Math: HandsOn Math Activities from Around the World
Famous Problems and Their Mathematicians
Can You Count in Greek: Exploring Ancient Number Systems**
Islamic Geometric Patterns
chapter / picture books with vignettes / photographs / drawings but few exercises
Mathematicians Are People, Too**
Why Pi? Go Figure!
Joy of Mathematics
The Math Book
Squares: Shapes in Math, Science, and Nature
collections of puzzles and logic problems
Math Without Words
The first part of the puzzle is figuring out what is being asked; the second part is solving the problem. Very engaging. Varied levels of difficulty.
Code Breakers, Venn Perplexors, etc.**
Logicbased activity books. Inexpensive.
24 Game (players are given 4 numbers to make into an expression that equals 24)
books of math games
Family Math**
put out by Lawrence Hall of Science. Games and activities to explore mathy ideas. More “how interesting” than “here’s how it works.”
Math Around the World
Thoughtfully sequenced look at the math behind games like mancala. Uses examples from around the world. Also LHS.
Just to add, my experience with an accelerated mathy kid has been that the leaps and lulls are both quite pronounced, and disconcerting.
Domesticidy11 My son also has leaps and lulls (we call the lulls hibernation in our house) when DS is ready to learn I try to get I there fast, because he can accomplish a lot in a short span. When he's in hibernation, I've learned to back off and let him find his own interests. It's cyclical. One exciting development is that DS is showing an interest in writing short stories I think it may grow into the next passion as his writing skills improve.
I noticed that with two of my kids, less so with one, and not at all with the youngest. I keep expecting her to hit a wall and it never comes: she just moves steadily forward. I was totally expecting her to hit a one to twoyear lull in progress at the beginning of high school math but she sailed through that. Now I'm waiting for it as the academic stream bifurcates into regular and honours: she'll hit that point in a few weeks. We'll see.
I am curious, though, why you think the sense that "this is what it is like to master something hard and interesting" can't come from something like building a 2D platform game using C++, achieving an exceptional state ranking in chess or gymnastics, or performing a piano concerto movement on an honours recital.
Miranda
Mountain mama to one great kid and three great grownups
We are trying chess next month, and I gotta admit, I'm excited. Chess would be great so many benefits. DS loves to read, and is now trying to write short stories it's an exciting development.
Most people don't understand that DS likes plain 'ol math computation. He thinks it's fun to write out math problems to solve. The more success he has with it, the more he wants to learn. I'm sure it looks like I'm pushing there have been times when he's asked to learn something then realized that he bit off more than he could chew. I've learned to back off in this scenario.
I think my kids' schools taught basic algebra concepts spiraled into the curriculum in 2nd grade. I know they did in 3rd (I can remember back that far — dd2 is in 4th this year). If he's into it I don't see any problem continuing along those lines. Have you gotten into geometry? Money? Chess sounds great, too.
Mama
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"All you fascists are bound to lose" — Woody Guthrie
I noticed that with two of my kids, less so with one, and not at all with the youngest. I keep expecting her to hit a wall and it never comes: she just moves steadily forward. I was totally expecting her to hit a one to twoyear lull in progress at the beginning of high school math but she sailed through that. Now I'm waiting for it as the academic stream bifurcates into regular and honours: she'll hit that point in a few weeks. We'll see.
I am curious, though, why you think the sense that "this is what it is like to master something hard and interesting" can't come from something like building a 2D platform game using C++, achieving an exceptional state ranking in chess or gymnastics, or performing a piano concerto movement on an honours recital.
Miranda
Interesting on the difference among children! I admit I just assumed my younger one would be the same. Will be curious now to see.
Oh, yes, absolutely, the feeling and recognition of deep learning can come from ballet or programming and so on. What I meant is that it's ideal if kids have at least intermittent experience with thoughtful academic work, too, if apart from the richness of going deeply in other pursuits there's a recognition of what real math looks like, for instance. That the kid is enriched by any kind of challenging work, but that perception and understanding of math is useful in itself.
heather
These are all great suggestions! Thanks again and always appreciate the thoughtful discussions.
I am soooo hoping DS enjoys chess enough to play on a team. We have after school and chess camps + a fantastic city chess club that caters to children learning the game.
I apologize if I seem defensive about the math DS does love it, and although I do lead the curriculum, I try very hard not to push. I also worry about school mismatches, but have made peace with the "cross that bridge when we come to it" mentality. If it gets to a point that DS is unhappy and we can't find a "school" solution, I have the flexibility to homeschool.
I had the personal experience of elementary school coming (too) easily for me, and when I did reach a point of challenge (somewhere around high school algebra), I didn't handle it well. I tended to be the kind of adolescent and young adult who "quit" what was hard because I had no appreciation for the struggle it takes to master difficult subjects. I just thought I wasn't good and assumed that my harder working peers were more capable.
DS also shows signs of perfectionism and anxiety I am trying to keep him at a challenging level so that he can work through these feelings gradually, at a younger age, in a lower risk situation. We do things outside of academics to instill tenacity and work ethic taekwondo and swimming have been positive.
I totally agree, math is useful and fascinating and I can see that if gifted kids are just getting a diet of addition and subtraction math facts at age 7, that understanding that math is awesome may not arise. Although my kids, as unschoolers, have not been constrained by the school system's scope and sequence, I've still tended to put less emphasis on formal math than on creative and active outdoor pursuits in an effort to balance out my kids' highly cerebral natural affinities. But where I have taken steps to actively facilitate their math learning, my energy has mostly gone into exploring mathematical concepts rather than teaching arithmetic. I'm the mom who tried to trip her 5yearold up in a game of "Guess My Number" by picking things like pi or negative 8 as her secret number, rather than teaching her multidigit addition and subtraction.
Miranda
Mountain mama to one great kid and three great grownups
I want to be subscribed to this thread, because I also have a mathy kid who enjoys computation and who experiences leaps and lulls. I don't have much to add to the discussion, though. My son took a while to learn to read, so a lot of the math enrichment I did for him was reading Alice in Wonderland and The Number Devil to him. He also enjoyed the Blue Balliett trilogy that began with Chasing Vermeer, because it featured math puzzles. We also read a book about topology, which was kind of out there and maybe not recommended. I mean, the math was great for him, but it wasn't a kid's book and I was lost a lot of the time. But that's not really math enrichment as much as me finding overlap in our spheres of interest? Nice and fun, though.
But I do hear what you're saying about accelerating arithmetic. I used to do what I called "Mommy math" with him, which was giving him problems like how to figure a tip or how to multiply out a recipe, or figuring out how much something cost in the farmer's market. Mostly I've felt weird about the whole problem of math in school. I don't want him to do what you describe, coast until he finally gets to upper math courses and then crash. He's in fifth grade now and I have no idea what to offer him to keep him engaged. We watch math videos on Youtube together, some of which I have to make him explain to me.
Divorced mom of one awesome boy born 232003.
I don't want to hijack this thread, but which of the ideas to explore mathematical concepts might work for an interested 5yo? Because it makes me a little uncomfortable to see my very little kid plowing ahead on arithmetic (in the Miquon books), since I wonder if he might get ahead of his own understanding in some problematic way? He's much more interested in puzzles he can do than in stories or board games (possibly because little sis makes board games hard), can't read, and is turned off by anything with lots of words. He loves angles and symmetry and numbers and logic, though. (he brought me something with a label on it the other day, unable to read the label, but super excited to show me how the blocky font it was written in meant that the entire word was made of 90 degree angles, with no acute or obtuse ones).
DS at five (and now) enjoyed math games Yahtzee was big at 56 years and we still play the occasional tournament. Interesting shapes (nonagons, decagons, 3d shapes) we would try to draw them. Math apps were and are fun. I toss out word problems on car rides at five it was something like "if you have 20 jelly beans to split evenly between 4 friends how many will each friend get?"
There are some interesting math ideas out there  we looked at perfect numbers and DS broke down the factors for 496 on his own, we looked at the Knight's Tour and DS tried to draw his own (got 8 moves, not bad at age six), golden ratio is coming since we are learning a bit about ratios now. These ideas came from a library book about quirky math concepts. These are for age seven, but there were many more for older children. I wish I could remember the book title, but there are probably a lot of similar books.
Is it really a problem if the child learns math out of order? Does it make a difference if they understand arithmetic too easily? I don't this math is like ballet, where it can damage the foot if the child goes on pointe too early. Is it? We don't believe that their brains have a finite capacity for math, I don't think. Right? So far it's been my experience that my son can learn things in school even if he's mastered the concepts already.
For me, the big challenge is that I'm not good at math at all. I think of math enrichment as an opportunity to enjoy his thinking. Like what McKittre said about her son enjoying the right angles on the font of something he wasn't reading. I continue to get a kick out of how much fun he has with numbers, shapes, relationships.
We did try to read Flatland, which was kind of fun, but what went even better was Flatterland by Ian Stewart, which I read to him when he was 8. I used to go to the library and just poked around in the math section to see whether anything looked good to him or was interesting. Don't be horrified!
Divorced mom of one awesome boy born 232003.
I don't know why other parents in other countries are not bashful about enriching their childrens math skills. There is plenty of support to show that US schools often don't do enough for kids in the early years when it comes to math and many of our children are lagging behind international standards by the fourth grade.
The issue that Miranda has articulated is a good one kids may become unmotivated or unhappy if they already know the skills being taught in school. That was our experience we had to move schools to a more self paced, self directed environment. Now it's much better. Many parents don't have our flexibility. My bias would be to fight with the school rather than hold my child back but the results still won't be ideal.
I'm with you I'm not great at math which Is why I started this thread. My linear direction may not be creative I figured master basic math operations, complete shorter segments on fractions and other elementary math skills, then move to algebra. I wanted to check out other ideas which I received, but the conversation morphed (I think positively) into a more interesting one.
My rule of thumb is that if my child is a) interested in learning a particular topic and b) ready to learn the topic (skills and maturity). I'm happy to teach it if a and b are present.
While I'm sure that's the case with some parents and some places, I think there is a lot of pressure  social or scholastic  against parental enrichment and acceleration of academics in other countries. That's particularly true in Europe  Scandinavia especially, but also throughout the region. For example it's very much frowned upon to teach your child to read outside of school, with parents of spontaneous early readers often been berated by teachers for messing with the way things are "supposed to" proceed. My brother in England recently got a concerned and disapproving call from his 12yearold son's maths teacher because he'd explained logarithms to him.
Miranda
Mountain mama to one great kid and three great grownups
But in much of Asia tutors are standard and the tutors are multimillionaires! http://www.bbc.com/news/business20085558
Mama
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"All you fascists are bound to lose" — Woody Guthrie
Not sure, but I know my particular mathloving 5yo can more easily answer "I'm thinking of an odd number, less than ten, that's divisible by three" than he can answer "How can we divide 9 cookies evenly between me, you, and your sister?" And then he'll tell me to stop doing the cookies thing. In that sort of context, he seems to prefer the pure numbers, and I wonder if the difficulty of that translation means he's missing something important (though he certainly has plenty of time to get it later).
Mckittre my son was like that at five too. I think some kids intuitively understand how numbers work and can "abstract" after one short explanation. I remember when DS was barely four writing out our first equation, explaining the symbols, and that was it. DS moved from "cookies" (in our case, jellybeans) to equations.
One thing to watch out for when your son goes to elementary (unless you're homeschooling) is whether the school has a well rounded math curriculum we looked for one that taught both analysis and mechanics (e.g. math facts). My DS is a "learn by doing" kid so often by working through a problem, he would have a "eureka" moment, that he wouldn't have just by explanation.
You may need to look at acceleration options in your school, and/or gifted programs. Your son sounds like his skills are far beyond the typical K or 1st grade program. We made the mistake of choosing a school that said they support acceleration, but didn't support it well at all. Acceleration was "here's a math book, if you require teacher instruction, you don't need acceleration." We moved schools, and life is good.
Miranda agreed. It's probably not productive to generalize how other industrialized countries view math. I'm sure it varies.
I don't know about India, but in Japan and Korea acceleration is almost unheard of. The robust tutoring systems in those countries are all about improving test scores on standardized agegradelevelled examinations, not about moving ahead. Acceleration is culturally frowned upon, with the needs of the individual given less priority than the good of the group.
miranda
Mountain mama to one great kid and three great grownups
Not sure, but I know my particular mathloving 5yo can more easily answer "I'm thinking of an odd number, less than ten, that's divisible by three" than he can answer "How can we divide 9 cookies evenly between me, you, and your sister?" And then he'll tell me to stop doing the cookies thing. In that sort of context, he seems to prefer the pure numbers, and I wonder if the difficulty of that translation means he's missing something important (though he certainly has plenty of time to get it later).
My son also preferred the allnumber questions at that age. It was sort of a problem at school, but on the plus side, it gave him something to do that was challenging. You know, translating what he knew about numbers and their relationships to the actual counting of things. He has been able to do it, though.
A couple of days ago he told me that he thinks people add numbers to activities to make them more enjoyable.
Divorced mom of one awesome boy born 232003.
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