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When math is never a challenge?


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DS just turned 7 and is in 2nd grade.  I moved him up an entire level in math and skipped to the second half of the year and it is still way too easy for him.  It feels like math has always been a review.  I don't know how it is possible to have never "taught" something to a child and yet it seem like review.  DD even threw the concept of simple variables on him over the summer and he seemed to completely understand the concept and know how to use it (with simple problems) without practice.  He has always connected with numbers. Should I add in supplements?  If so, I would love suggestions.  Should I change math curriculum altogether?  I have always used Saxon and it has worked beautifully to lay a good foundation for my other kids so I am hesitant to change.  

 

thanks for the thoughts,

 

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some options:

 

- switch to Beast Academy when he's ready (might not be ready yet - starts at grade 3)

- switch to Singapore

- switch to MEP (?)

- supplement Saxon with the Intensive Practice or Challenging Word Problems books from Singapore

- supplement with something else, e.g. Cleo Borac problem solving books

Edited by wapiti
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what wapiti said...

 

Honestly, I would get Beast 3A right now and just see how he does with it.  You can always shelve it for 6 months or so if it is too hard.  You can still continue with Saxon in the meantime if you already have it on hand but supplement as Wapiti suggested.  At some point for this child you may need AoPS when he is older.  

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A lot of elementary math is just logical, so some can figure it out on their own. In addition, a lot of review is built in and a lot of "new" material is just incremental, so advanced learners don't need the next increment(s) spelled out. For example, math programs will introduce addition, then later introduce double-digit addition, then re-grouping in addition, then triple-digit addition, etc. Some kids can just see how one follows from the other, so when they get that lesson, it is easy/review. We started homeschooling when my oldest was in 2nd grade.  Her gifted kindergarten class had everyone doing first grade math, which was easy/review for her. We switched schools partly because the new school pre-tested and differentiated math, and she tested out of second grade math and did third math in first grade, then tested out of fourth grade math and started fifth grade math in second grade.

 

I haven't used Saxon, but I understand that it is hard to compact. We used Math Mammoth in elementary. I would give them the test for a chapter (as a pre-test), then only print and give them the pages for the concepts they didn't do well on (and circle only some of those for them to do, because they usually didn't need all those problems). In this way, I was able to avoid them being bored or missing concepts. 

 

ETA: Beast Academy would probably be a better choice now. It was too late/took too long to release new books for mine. We did move to AoPS after completing MM6, and it has been great for them.

Edited by MASHomeschooler
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Some kids do seem to become quickly fluent in mathematical thinking without much direct instruction, like the way children absorb much of their primary language without being explicitly taught.


At that age my dd enjoyed Zaccaro's Primary Grade Challenge Math, discussing interesting math topics and doing problems from Mathematics, a Human Endeavor, and going to math circle.

Eta: BA3 first came out when dd was 7, and she loved that too. She was so impatient for each new book to be released!

Edited by slackermom
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I have one (or possibly two...) for whom mathematical concepts just seemed natural, like what slackermom said above... 

 

We've always used Singapore Math (the intensive practice and challenging word problem books INSTEAD of the workbook to reduce unnecessary repetition -- I even pick through the challenging word problems books, too, never assigning the easy ones). When ds started high school he said the first 7 months of his geometry class were all review because *he'd learned it all already way back in Singapore Primary Math 6*. That blew my mind and I happily continued using Singapore Math with the younger kids.

 

10 year old really likes Beast Academy.  If it was up to him, he'd do that instead of Singapore Primary Math (but we do both).  Because we do both, we will often skip the "easy stuff"and a large portion of the repetition (in the textbook) in Singapore.  I usually assign ALL of the Intensive Practice.  Those problems make them think.

 

For my dd, who doesn't ooze mathematical thinking, but who almost never makes a computational error, we used Singapore Math.  If she saw a page of problems and groaned, I'd assign the hardest 2-4 and if she got them all correct, she could skip the easier ones.

 

 

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Seconding pretty much everything already posted.

 

Beast Academy was the first time DD was ever really challenged by math. I used to "teach" her one lesson in our previous program and then she would play with manipulatives and talk aloud; if I let her play for 30 minutes, she would simply discover for herself what the next several lessons would cover.

 

I didn't see Hands On Equations mentioned above, but DD is currently loving it as a supplement to Beast.

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My son likes Beast Academy as well. I'd say he is solidly at a second grade math level, third grade stuff is a little challenging, and he can work at fourth and fifth grade level in a few topics. I can't say that BA is challenging him though because he only does the problems he can do automatically and skips the rest. Anyway, all that to say that BA hasn't been completely inappropriate for a math-intuitive child at second grade level.

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I am biased, as a mathematician, but I agree with suggestions above.  It is probably not math that is unchallenging but saxon math.

 

One thing to watch for however as you crank up the level, is that a child who has never seen any real math may balk at first when the math gets hard, as it may challenge the child's confidence, so it is important to remind her/him that essentially everyone thinks (real) math is challenging, but that challenge is worth it.

 

Good luck, and good for you for noticing that something needs enhancing with this child.

 

Here is a little example of a simple sounding but apparently very hard math problem:  a positive integer ≥ 2 is "prime" if it has no integer factors greater than 1 and smaller than itself.  Then all such prime numbers greater than 2 are odd, so the sum of any two of them is an even number greater than 4.  (The first few primes are 2,3,5,7,11,13,17, 19, 23,29,31,37, 41, 43,47,...)

 

What about the reverse?  Is every even number greater than 4 the sum of two odd primes?  It sort of looks as if it is so, since 6 = 3+3, 8 = 5+3, 10 = 7+3 = 5+5, 12 = 7+5, 14 = 11+3 = 7+7, 16 = 11+5 = 13+3, 18 = 11+7 = 13+5, 20 = 13+7 (also 17+3).....

 

Even a bright grammar school child may appreciate this question, but no one alive knows if this is always true.

 

In general I think number puzzles offer a fun way to keep a clever child engaged with math.  E.g. the fact that if a number is divisible by 9 then so is the sum of its digits.  E.g.  81 and 8+1 are both divisible by 9; 135 and 1+3+5 are both divisible by 9,.....

 

In fact this works backwards too, so since 1+3+5 is divisible by 9 it follows that not only 135 but also 531 and 351 and 153 and 315 and 513 must all be divisible by 9 too!  The child may have fun checking this by dividing.

 

Or maybe the way to present it would be as a question.  Ask the child to take any number that is divisible by 9 and rearrange the digits and see if it still is divisible by 9.  Ask if that seems always true.  Try it with other numbers, are there other divisors where it still works?

Edited by mathwonk
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Some kids do seem to become quickly fluent in mathematical thinking without much direct instruction, like the way children absorb much of their primary language without being explicitly taught.

 

 

At that age my dd enjoyed Zaccaro's Primary Grade Challenge Math, discussing interesting math topics and doing problems from Mathematics, a Human Endeavor, and going to math circle.

 

Eta: BA3 first came out when dd was 7, and she loved that too. She was so impatient for each new book to be released!

 

This is what we did in a similar situation.  Primary Grade Challenge Math, Problemoids, math games, Beast Academy.  And we put him in a math enrichment program run by two math PhDs which presented very young kids with fun and challenging math and philosophical concepts.  One class I especially remember him enjoying was all about infinity and Zeno's paradox.  

 

One of the best things for young kids who excel at math is to be around other young kids who excel at math.  

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