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Exploring Algebra and beyond with Littles

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If you've taught, or are teaching Algebra--or above--to children under 10 and you have created lessons, games and activities for your children, then would you be willing to share how you taught/what you did?

I know that a couple of members have mentioned playful ways that they were able to engage their young children in higher level mathematics at an early age. They've either created or found engaging games and activities to help their children learn and understand mathematics while young @Mike in SA and @Gil have both mentioned creating games or designing activities with their young kids for sure, but I doubt that they're the only ones.

I could really use some fresh ideas from others who are successfully teaching or have successfully taught "higher" math to their younger children in a playful or creative manner. Is there any way that we could brain storm and compile such ideas for shared use? I have a couple of Algebra and geometry activities that I've made and that Jr enjoys, but they're not "very gamey" and I'm struggling to come up with more games.

 

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I used dragonbox learning’s app and it had a lot of Algebra concepts built in. Another resource is critical thinking company’s balance bender, Venn diagram books etc. it  was a while ago, so I don’t remember how many of their books I bought, but they all helped learn algebra concepts without actually teaching any algebra topics as such. Another resource was beast academy books (the late elementary ones).

Edited by mathnerd
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I create nothing, but I do use some good options that others have created. 

Dragonbox apps were a lot of fun. Dragonbox 5+ and 12+ cover simplifying equations in a way that doesn’t look anything like equations at first. Dragonbox Elements is an introduction to Geometry.

Hands on Equations isn’t exactly fun, IMO, but it does really get to the idea of an equation as two balanced sides. My kid liked the hands-on nature of it for a while.

We played some with number tricks, like these ones, took them apart to see why they worked, and then made our own.

Not really higher math, but we recently did a bunch of cryptarithm puzzles together. Those were fun; you can find some silly ones in a google search.

We’ve worked our way through about half of Patty Paper Geometry and just decided to get it back off the shelf. Not a game, but it’s been a much more fun introduction to Geometry than any regular curriculum would have been. The book is written so you can either use a more instructive approach or a more discovery-based approach.

have you already done the Penrose books? How about the Math and Magic in Wonderland/Camelot books? None of it is higher math, but it’s all interesting stuff that isn’t always covered at all in math curriculum.

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Not algebra, but we found "Exploring the Shape of Space" by Jeffrey R Weeks was a great, playful introduction to topology.  Lots of great activities and games like torus tic-tac-toe etc..

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We did a ton of "shapes" questions to prepare for algebra :-). We did them entirely by guess and check, although as we progressed through them, we could do much harder ones. I'm attaching a system of equations that we did last term, for example (she filled in the shapes.) If you're interested, I'll attach others. 

I also found that not doing any algorithms at all for a good long time and doing all calculations using a solid definition and logic helped my daughter really internalize properties of the operations. We've just started formal algebra now, and the idea of distributing something like (x+1)(x+2) is really trivial to her, since she's been doing that kind of distributing with numbers all her life. The idea of doing the same thing to both sides of an equation was also really easy, since we've always been very clear on what equals signs are. 

Fraction shapes.jpeg

Edited by square_25

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On 1/7/2020 at 12:10 AM, mathnerd said:

I used dragonbox learning’s app and it had a lot of Algebra concepts built in. Another resource is critical thinking company’s balance bender, Venn diagram books etc. it  was a while ago, so I don’t remember how many of their books I bought, but they all helped learn algebra concepts without actually teaching any algebra topics as such. Another resource was beast academy books (the late elementary ones).

Thank you for the suggestions. We are a No-Screens-for-Kids house hold so the kids don't play apps, watch videos, read eBooks or anything like that, so all apps or video game stuff is out.
I have looked at a lot of CTCs offerings, but I don't see anything along the lines of what I'm looking for, but it's been awhile, so maybe I'll look again.  We had originally thought that we'd wind up using Beast Academy but we've found the actual books to be "meh" and had decided against it.

On 1/7/2020 at 12:30 AM, Jackie said:

I create nothing, but I do use some good options that others have created. 

Dragonbox apps were a lot of fun. Dragonbox 5+ and 12+ cover simplifying equations in a way that doesn’t look anything like equations at first. Dragonbox Elements is an introduction to Geometry.

Hands on Equations isn’t exactly fun, IMO, but it does really get to the idea of an equation as two balanced sides. My kid liked the hands-on nature of it for a while.

We played some with number tricks, like these ones, took them apart to see why they worked, and then made our own.

Not really higher math, but we recently did a bunch of cryptarithm puzzles together. Those were fun; you can find some silly ones in a google search.

We’ve worked our way through about half of Patty Paper Geometry and just decided to get it back off the shelf. Not a game, but it’s been a much more fun introduction to Geometry than any regular curriculum would have been. The book is written so you can either use a more instructive approach or a more discovery-based approach.

have you already done the Penrose books? How about the Math and Magic in Wonderland/Camelot books? None of it is higher math, but it’s all interesting stuff that isn’t always covered at all in math curriculum.

He didnt like cryptarithm puzzles when we tried them a good ways back, but I may offer them again and see if he likes them better now. We do not have the Penrose of Wonderland/Camelot books so I"ll look into them.

21 hours ago, wathe said:

Not algebra, but we found "Exploring the Shape of Space" by Jeffrey R Weeks was a great, playful introduction to topology.  Lots of great activities and games like torus tic-tac-toe etc..

Oooh, even better than algebra is topology!!! We played with some topology a while back and it was a big hit. Thanks. I"m definitely going to be checking into this.

1 hour ago, square_25 said:

We did a ton of "shapes" questions to prepare for algebra :-). We did them entirely by guess and check, although as we progressed through them, we could do much harder ones. I'm attaching a system of equations that we did last term, for example (she filled in the shapes.) If you're interested, I'll attach others. 

I also found that not doing any algorithms at all for a good long time and doing all calculations using a solid definition and logic helped my daughter really internalize properties of the operations. We've just started formal algebra now, and the idea of distributing something like (x+1)(x+2) is really trivial to her, since she's been doing that kind of distributing with numbers all her life. The idea of doing the same thing to both sides of an equation was also really easy, since we've always been very clear on what equals signs are. 

Fraction shapes.jpeg

So far his algebra skills are coming along really well; we've transitioned from playing algebra with socks and baskets to drawn shapes and blanks to traditional variables.  He can work some rather sophisticated looking equations and systems of equations very easily now. We try and do a variety of mathematical topics for the kids and I'd like to add a greater variety of playful activities to my lesson plans because the content isn't a problem, but the format is for me. I feel like all our "games" follow the same pattern and don't want him to get bored because of that.

I feel like we're right in that tricky spot where it;s more challenging to  hook his interest and I'm struggling with keeping the presentation imaginative and fun enough to be sustainable.

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1 minute ago, mathmarm said:

Thank you for the suggestions. We are a No-Screens-for-Kids house hold so the kids don't play apps, watch videos, read eBooks or anything like that, so all apps or video game stuff is out.
I have looked at a lot of CTCs offerings, but I don't see anything along the lines of what I'm looking for, but it's been awhile, so maybe I'll look again.  We had originally thought that we'd wind up using Beast Academy but we've found the actual books to be "meh" and had decided against it.

He didnt like cryptarithm puzzles when we tried them a good ways back, but I may offer them again and see if he likes them better now. We do not have the Penrose of Wonderland/Camelot books so I"ll look into them.

Oooh, even better than algebra is topology!!! We played with some topology a while back and it was a big hit. Thanks. I"m definitely going to be checking into this.

So far his algebra skills are coming along really well; we've transitioned from playing algebra with socks and baskets to drawn shapes and blanks to traditional variables.  He can work some rather sophisticated looking equations and systems of equations very easily now. We try and do a variety of mathematical topics for the kids and I'd like to add a greater variety of playful activities to my lesson plans because the content isn't a problem, but the format is for me. I feel like all our "games" follow the same pattern and don't want him to get bored because of that.

I feel like we're right in that tricky spot where it;s more challenging to  hook his interest and I'm struggling with keeping the presentation imaginative and fun enough to be sustainable.

 

Hmmm, why not just use algebra for something more fun? I think of algebra as basically "awesome algorithms that let you solve things you might want to." But it's not fun by itself, I don't think, unless you're wired like my kid and prefer "abstract structure" to problems, anyway. 

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4 minutes ago, square_25 said:

Hmmm, why not just use algebra for something more fun? I think of algebra as basically "awesome algorithms that let you solve things you might want to." But it's not fun by itself, I don't think, unless you're wired like my kid and prefer "abstract structure" to problems, anyway. 

Well, as I kinda-mentioned in the OP, I"m really looking more for inspiration and ideas on fun ways to present topics from higher level mathematics than a specific resource.

Jr loves algebra (though he doesn't know what 'algebra' is vs 'arithmetic', to him it's just "math").  I have a hard time making up games and activities for algebra/probabilty/trigonometry/topology/geometry etc.

It can be done, I just am not super duper imaginative and short on time so I like to plan and prepare ahead.

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1 minute ago, mathmarm said:

Well, as I kinda-mentioned in the OP, I"m really looking more for inspiration and ideas on fun ways to present topics from higher level mathematics than a specific resource.

Jr loves algebra (though he doesn't know what 'algebra' is vs 'arithmetic', to him it's just "math").  I have a hard time making up games and activities for algebra/probabilty/trigonometry/topology/geometry etc.

It can be done, I just am not super duper imaginative and short on time so I like to plan and prepare ahead.

 

Well, "fun" really depends on what your kiddo likes :-). What inspires him? As I said, my kid is inspired by structure and not by games, so I'd need a bit more data about what he likes. 

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I'm sorry to be so unhelpful! I happen to have a kiddo who is much more inspired by abstract structures than she is by games or puzzles. I've designed lots of activities for her, but I'm not sure if it's worth going through them, because they mightn't be what you're looking for. 

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Well to start with he's 6 so what "inspires" him depends on his mood, lol.

He enjoys math--whether it's solving equations "just cause" or working through story problems. He has really enjoyed the the geometry concepts that we've covered so far. He's not the kind of kid who I can give a worksheet to and turn away. He is an eager learner, but he needs heavy-interaction during school time. If we're doing a page-based lesson then we usually wind up sharing the page during a math session or working at the whiteboard together.

 

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Gotcha! So, as I said, my kiddo is mostly inspired by abstract structures, so we've mostly done enrichment in that direction. We played with different bases, combinatorics and primes, specifically. (She also liked negative numbers, but I assume you've covered that?) Have you covered those? 

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4 minutes ago, square_25 said:

Gotcha! So, as I said, my kiddo is mostly inspired by abstract structures, so we've mostly done enrichment in that direction. We played with different bases, combinatorics and primes, specifically. (She also liked negative numbers, but I assume you've covered that?) Have you covered those? 

We've done a lot of math and it'd be hard to list it all without going back through my notes and documents. He is fluent in arithmetic with integers and rational numbers.

  • a lot of play with prime and composite numbers. He occasionally likes to find the prime factorization of 3 and 4 digit numbers for a fun challenge.
  • numbers, and addition/subtraction in base-2, base-5 and base-8
  • transformations of graphs
  • area, perimeter and even "tricky" area and perimeter problems
  • a lot of number lines, coordinate grid work
  • word problems (tons of them. We just use workbooks that I bought at this point)
  • some lite percentage work
  • algebraic equations
  • gentle graph theory
  • functions
  • gentle, lite topology
  • fractions and decimals

We do a lot of math play and a good mix of math lessons as well. But I feel like our games are stale--I only have a few tricks up my sleeves and I would love to keep my presentations and activies "fresh" so that a boring format doesn't taint the math as we continue down this road.

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Ah, that is a nice list! Just off the top of my head, I can think of some other topics that might be fun to explore. 

For combinatorics, I had a fun hook with my daughter: she had a book of "Make Your Own Monster," where you could pick the head of the monster, the neck of the monster, the middle of the monster, and the bottom of the monster (I think.) I believe each one was chosen out of 5 or 6 different possibilities. So our goal was to figure out how many total monsters we could make, and we worked on a variety of related problems first. That also easily leads into choose notation and binomial coefficients, and then into probability. It could also tie into graph theory. 

Square roots and irrational numbers might be really fun to explore, too: for example, you could challenge him to see if he can find a fraction equal to the square root of 2. 

Oh, and complex numbers are a lot of fun! I think manipulating a number that isn't "real" can seem like a game to kids. 

A friend of ours recently suggested an exploration of area that would lead to Pick's theorem: http://jwilson.coe.uga.edu/EMAT6680Fa05/Schultz/6690/Pick/Pick_Main.htm

It could also be fun to veer into linear algebra, since it's very visual and actually requires a lot less math background than the standard math sequence. Something like group theory is also probably very explorable. 

Personally, at his age, what I enjoyed most were math contest problems. Have you looked at math contests at all? For his age, there's the Math Kangaroo, and he might be ready for things like AMCs relatively soon, if he's not ready already. 

Please let me know if any of this is helpful, or if you're looking for something totally different!! 

Edited by square_25

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3 hours ago, mathmarm said:

I have looked at a lot of CTCs offerings, but I don't see anything along the lines of what I'm looking for, but it's been awhile, so maybe I'll look again.  We had originally thought that we'd wind up using Beast Academy but we've found the actual books to be "meh" and had decided against it.

https://www.criticalthinking.com/balance-math-teaches-algebra.html

https://www.criticalthinking.com/balance-benders-level-1.html

https://www.criticalthinking.com/pattern-explorer-level-1.html

https://www.criticalthinking.com/building-thinking-skills-level-2.html

Take a look at the sample pages of some of the above books to get ideas to use.

I also started the AOPS prealgebra curriculum with my son when he was almost 7. I taught it to him at a slow pace using a white board and we worked on the problems together. It would never have worked any other way because my son wanted math books with fun animal stories at that age! You could see if your DS is ready to learn from the aops books.

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Disclaimer: I just use pre-made resources, and the fun-math-games bar is set pretty low around here since my math-loving kid thinks AoPS textbooks are great fun. That said, when he was 5-6yo he LOVED our Algebra Lab Gear blocks. I'd suspect that a creative person could probably come up with some pretty interesting activities to do with them.

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We used LOF algebra when our son was younger. It's story book form and he was a book worm so he loved it.

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On 1/9/2020 at 12:48 AM, Cake and Pi said:

Disclaimer: I just use pre-made resources, and the fun-math-games bar is set pretty low around here since my math-loving kid thinks AoPS textbooks are great fun. That said, when he was 5-6yo he LOVED our Algebra Lab Gear blocks. I'd suspect that a creative person could probably come up with some pretty interesting activities to do with them.

 

Yeah, that would have been me. I wanted to bang my head against hard puzzles; I didn't need games to make math fun for me. My daughter's different: she's somehow mostly motivated by finding cool new abstract structures. I've seen this orientation in professional mathematicians, but not previously in a little kid, so it's been interesting for me to think about how to inspire her. However, for a kid who likes puzzles and games, I'd probably lean heavily on AoPS materials and contest problems. 

Edited by square_25

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This will be his first year eligible for math contests. He's taking the math kangaroo in a couple of months, and we've signed him up for a local contest. But we don't want to over emphasize prizes and contests too soon. We have the practice of having a couple of tough problems each day so we're not doing any special preparation for the tests--just going to keep doing math as a group subject and trying to keep him engaged.

I think that for "hard problems" Jr likes being right and feeling smart, more than struggling against a problem. He will work through a challenging problem on a topic that he's really confident in--he's not ready to do algebraic word problems that require he write quadratic expressions or anything like that.

But this year he's getting really confident and strong in word problems and has started figuring out ways of modeling a wider variety of problems. I prefer to collect techniques to textbooks so I'm not really looking for more products, until we reach a certain milestone for math there is nothing that we need to buy. We have books of premade problems and I have a few binders of notes, puzzles and exercises that I've written for him over the years.

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I didn’t even mean participation in contests, per say — just doing those sorts of problems :-). I’ve found Math Kangaroos a good source of “fun” problems.

My daughter also prefers a sense of mastery and being good at things to being stuck. For us, that meant we cover lots of abstract topics to achieve a sense of mastery in lots of things.

Are any of the topics I listed helpful? Or do you want specifically games? If you want specifically games, mind giving me an example of the games he’s really liked so far?

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I've used a balance scale with weights to explore algebra with younger kids. You can use plastic Easter eggs to hide your unknown quantities in--same color egg for the same variable, different colors for more than one variable.

If the unknown is going to stay on one side of the balance you can just calibrate to adjust for the weight of the egg. If you want the option of moving your variables from side to side they have to be offset by empty eggs on the other side (use a different color for these) so if you move one of your variables you also move an empty egg. Clear eggs would probably be ideal for this so it is obvious there isn't actually a quantity being moved, you are just accounting for the weight of the egg itself that isn't part of your equation. 

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On 1/8/2020 at 8:51 PM, mathmarm said:

Well, as I kinda-mentioned in the OP, I"m really looking more for inspiration and ideas on fun ways to present topics from higher level mathematics than a specific resource.

Jr loves algebra (though he doesn't know what 'algebra' is vs 'arithmetic', to him it's just "math").  I have a hard time making up games and activities for algebra/probabilty/trigonometry/topology/geometry etc.

It can be done, I just am not super duper imaginative and short on time so I like to plan and prepare ahead.

 

probability is fun with resource-using games.  What are the odds that the card/tile I want is still available?   We were playing Mille Bornes when we got into the discussion then went to gin rummy  but you  can do it with other limited resource games, double six dominoes, crazy eights, whatever works with the number of things he can hold in his mind. 

Edited by HeighHo
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Dragonwood and Qwixx are two more games where the probability is not explicit, but pretty easy to work with.

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On 1/8/2020 at 9:47 PM, square_25 said:

Ah, that is a nice list! Just off the top of my head, I can think of some other topics that might be fun to explore. 

For combinatorics, I had a fun hook with my daughter: she had a book of "Make Your Own Monster," where you could pick the head of the monster, the neck of the monster, the middle of the monster, and the bottom of the monster (I think.) I believe each one was chosen out of 5 or 6 different possibilities. So our goal was to figure out how many total monsters we could make, and we worked on a variety of related problems first. That also easily leads into choose notation and binomial coefficients, and then into probability. It could also tie into graph theory. 

Square roots and irrational numbers might be really fun to explore, too: for example, you could challenge him to see if he can find a fraction equal to the square root of 2. 

Oh, and complex numbers are a lot of fun! I think manipulating a number that isn't "real" can seem like a game to kids. 

A friend of ours recently suggested an exploration of area that would lead to Pick's theorem: http://jwilson.coe.uga.edu/EMAT6680Fa05/Schultz/6690/Pick/Pick_Main.htm

It could also be fun to veer into linear algebra, since it's very visual and actually requires a lot less math background than the standard math sequence. Something like group theory is also probably very explorable. 

Personally, at his age, what I enjoyed most were math contest problems. Have you looked at math contests at all? For his age, there's the Math Kangaroo, and he might be ready for things like AMCs relatively soon, if he's not ready already. 

Please let me know if any of this is helpful, or if you're looking for something totally different!! 

I thought sure I responded to this.  Thank you for offering so many suggestions.

He and Hubby have been semi-discussing permutations these last couple of weeks when discussing different sandwiches that they can make from the ingredients available. I wasn't planning to make a unit on it, but now that I think about it more that might be fun. Jr. used to really like a couple of childrens book we had with flipping half pages where the pictures changed and such. I'd love to know more about how you taught Combinatorics to your little one; any details, samples and progression or Scope/Sequences problems you used would be so greatly appreciated.

We celebrate Pi day every year, with math activities (not eating pie) so he has a developing awareness of irrational numbers. Plus he knows rational numbers are and but still developing an appreciation/awareness of irrational numbers. He has done a some work with irrational numbers from when we were working on exponents and such, but we'll need to revisit/expand on it more at some point.

We have been talking up to and around complex numbers off and on for a while now. He's not quite there yet but he's made a couple of comments as we've been playing with doing graphs in Cartesian space with the XYZ axis that demonstrate some curiosity about them, I've tried to drop a few hints to feed his intuition, but it's been lite. We've been graphing a lot together in preparation of playing with more linear algebra and complex numbers, but we'll need some more time. I'd love any suggestions for concepts from linear algebra that you'd recommend. I don't think that he's ready at all for all the book keeping that comes with matrices. But I've been doing XYZ graphs with him, and I was planning/hoping to do more linear algebra in the coming months, but I need to flesh out some lesson plans for teaching complex numbers too.

Picks Theorem! Of course! I'll have to put together a geoboard. I think that he'd really enjoy doing Picks because he liked Area/Perimeter.

I'm not super creative by default, so I would love any help with "porting" group theory concepts down to his level for exploration in a friendly way. Whether hands on or at the chalk/whiteboard.

On 1/14/2020 at 8:33 AM, square_25 said:

Are any of the topics I listed helpful? Or do you want specifically games? If you want specifically games, mind giving me an example of the games he’s really liked so far?

It's not so much that we need games. I'm just struggling to come up with good ways to approach and practice a lot of math concepts easily enough for him.

I don't like to introduce/explain things until I'm ready, that way I minimize the chances of confusing and frustrating him bygoing too fast, or skipping something or being unclear.

Edited by mathmarm

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What about books like Murderous Maths series? My son loved reading these and they dive into some interesting and tricky topics.

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On 1/14/2020 at 7:21 PM, mathmarm said:

I thought sure I responded to this.  Thank you for offering so many suggestions.

He and Hubby have been semi-discussing permutations these last couple of weeks when discussing different sandwiches that they can make from the ingredients available. I wasn't planning to make a unit on it, but now that I think about it more that might be fun. Jr. used to really like a couple of childrens book we had with flipping half pages where the pictures changed and such. I'd love to know more about how you taught Combinatorics to your little one; any details, samples and progression or Scope/Sequences problems you used would be so greatly appreciated.

We celebrate Pi day every year, with math activities (not eating pie) so he has a developing awareness of irrational numbers. Plus he knows rational numbers are and but still developing an appreciation/awareness of irrational numbers. He has done a some work with irrational numbers from when we were working on exponents and such, but we'll need to revisit/expand on it more at some point.

We have been talking up to and around complex numbers off and on for a while now. He's not quite there yet but he's made a couple of comments as we've been playing with doing graphs in Cartesian space with the XYZ axis that demonstrate some curiosity about them, I've tried to drop a few hints to feed his intuition, but it's been lite. We've been graphing a lot together in preparation of playing with more linear algebra and complex numbers, but we'll need some more time. I'd love any suggestions for concepts from linear algebra that you'd recommend. I don't think that he's ready at all for all the book keeping that comes with matrices. But I've been doing XYZ graphs with him, and I was planning/hoping to do more linear algebra in the coming months, but I need to flesh out some lesson plans for teaching complex numbers too.

Picks Theorem! Of course! I'll have to put together a geoboard. I think that he'd really enjoy doing Picks because he liked Area/Perimeter.

I'm not super creative by default, so I would love any help with "porting" group theory concepts down to his level for exploration in a friendly way. Whether hands on or at the chalk/whiteboard.

It's not so much that we need games. I'm just struggling to come up with good ways to approach and practice a lot of math concepts easily enough for him.

I don't like to introduce/explain things until I'm ready, that way I minimize the chances of confusing and frustrating him bygoing too fast, or skipping something or being unclear.

 

I'm so sorry to be so slow to respond! I figured I should write something long and thoughtful, and that was intimidating me, so I kept not replying. So perhaps I'll get down all of my thoughts in an imperfect form instead of hoping to impart some real wisdom ;-).  

Here's my thread from earlier on about our combinatorics explorations: 

https://forums.welltrainedmind.com/topic/683856-cute-math-topic/

We moved on from Bertie the Bear to picking balls out of bins (we both did problems with one bin and with many bins.) She continued to color the balls in and in general, to think of combinatorics as ways to organize information. We also talked about picking balls out of bins when order matters and order doesn't matter. This got us into fairly large division, so that's where we quit exploring. I'd say that this was one of the units that we've covered that was NOT fully absorbed, but it was excellent for practicing multiplication, and she really enjoyed it. I think we'll probably revisit it sometime in the near future so it can actually get fully absorbed. 

This is a very brief description: I can provide more details of what we did if you're interested :-). I keep all of our math notebooks, so it'd be easy for me to remind myself what order we went in (and I could also send pictures.) 

I think complex numbers are easier if he can already fluently expand expressions like (a+b)(c+d), since you need to be able to do that to play around with numbers in the form a + bi. That's fun to play with, but maybe not a complete topic unless there's a LOT of comfort with operations in the abstract. For instance, I'm sure my daughter could expand out the product above, but I she hasn't internalized fraction rules well enough to be able to deal with something like (a+bi)/(c+di) without me teaching her procedural tricks I'm not planning to. 

Hmmm, I can think of a few ways to play around with groups (and rings, I guess)! I'm not entirely sure what your background is, so let me know if you need more details, but the ones I can think of off the top of my head are modular arithmetic and symmetry groups. Those are both fun and pretty different from kids usually see. For instance, if you work modulo a composite number, you wind up with no "division" operations except for certain elements! And if you're working with symmetry groups, then you can multiply elements and take inverses, but there's no addition! 

Is any of this at all helpful? This is not in a super organized format, but I thought it'd be better to finally get my thoughts down! I'm happy to provide details for anything that actually sparks your interest :-). 

 

Edited by square_25

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Have you seen this thread? (The post linked here has the total list of all the resources discussed in the thread, but the thread itself is one of the two that I revisit most on this forum.)

Other than that link, I'm probably not able to be of much help, since DS7 doesn't want to "do" math (work out problems, solve equations, etc), rather he wants to "think and talk" about math. He picks up random books from the library or his father's/DS10's bookshelves, reads them until he's found something interesting, and proceeds to ask a million questions and discuss the topic at hand until he's satisfied/bored/whatever, and then he starts the cycle over again. He read half of A Cartoon Guide to Calculus and then wanted to talk about limits, functions, and transcendental numbers for days. He read a Murderous Maths book and then explained to me how to add fractions with different denominators; once he showed me that he could do it, he was bored and moved on to something else. He picked up an intro to logic book and then proceeded to explain to me Wittgenstein's truth tables over breakfast. BUT, he hates to sit down and "do math". *insert rolling eyes emoji here*  Patty Paper Geometry is on my shortlist for his birthday this spring, along with some Zaccaro books that he's enjoyed from the library.

 

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