Best challenge/supplement math for a young student?

[sunnyday]

My DS7 loves math. He LOVES it, and he has an uncanny grasp of mathematical concepts. He is great at puzzling over challenges, and believes this is how he grows his brain and becomes a smarter boy (though he prefers not to work *too* far "above his level"). For various reasons I would like to slow his progress through arithmetic, and in the process deepen his grasp of it and of other tangential topics. He's also very interested in math competitions -- we looked at a Math Kangaroo sample and I narrowly managed to talk myself out of trying to host a testing site. ;)

 

I've heard a lot about Zacarro Primary Challenge Math. But someone recently mentioned the Borac Competitive Mathematics series and I love the topics it covers and the level it's written at. And then Hard Math for Elementary has been mentioned as well.

 

So...can anyone compare these for me? For reference, DS is in the process of accelerating out of Singapore 1B, simultaneously working on wrapping up the practice pages for Beast Academy 3A and starting  the first unit of 3B, and is in public school where the teacher has him working on two-digit addition via IXL (which he finds tedious) and Thinking Blocks (which he enjoys).

 

I think I could swing getting two of the three (counting the whole Level I Borac as one "book") but not all of them at this time.

[Crimson Wife]

Is there a reason why you're having him do Singapore 1B with BA 3? If he can do BA 3, then he's way beyond Singapore 1B. BA 3 is more on par with SM 3 & 4 (depending on the specific topic).

[sunnyday]

Is there a reason why you're having him do Singapore 1B with BA 3? If he can do BA 3, then he's way beyond Singapore 1B. BA 3 is more on par with SM 3 & 4 (depending on the specific topic).

 

Yep. Basically I bought BA 3A for the Shapes chapter in order to enliven the first grade geometry unit he was doing at school. But he demanded to move forward in the book, and has been in heaven every step of the way. Unfortunately although he knows place value really well, and he knows regrouping really well, he's not as solid on higher values as I'd like. For example, he got 59 + 31 in IXL recently and just did not see it. He answered 18 or something silly and was so frustrated. He may just have been tired but I feel like that Singapore 1B chapter on numbers within 100 is something we still should do. And I don't feel like I should rush it since he's in public school and it's been a journey in itself just to get them to give him something besides "count the dots on the dominoes" addition problems.

 

In the meantime he's gleefully filling out times tables and hundreds charts from Beast, doing great at skip-counting and weight-balancing, perimeter problems, all that jazz. He *loves* BA. I think this weekend we'll aim to do at least a page or two each of balancing weights and perimeter & area.

 

There's a chance we'll skip right over Singapore 2, I've been pondering the scope and sequence, but we'll see. In the meantime, a little elementary number theory and counting sounds just about right. I finally found a sample of Zacarro, and it doesn't feel like it'll add much to Beast and Singapore. And Hard Math looks to be written to an older child (Simpsons references?!) So I went ahead and ordered the Borac books. Will report back!

[Crimson Wife]

Gotcha. With my DS, it seems often that "easy is hard, and hard is easy".

[kiana]

I have never heard of the Borac series, but it looks REALLY interesting. Looking forward to the report.

[Dmmetler]

Continental math league. It's too late to compete this year, but you can get the practice books. Math kangaroo-not too late for this year, and practice is available there, too (I like the Canada site better than the US one)

[sunnyday]

Gotcha. With my DS, it seems often that "easy is hard, and hard is easy".

Yeah, I feel grateful that he is so tolerant of a wide range of difficulty. :)

[MissKNG]

Penrose the Mathematical Cat books are a hit with my mathy big girl.

[Kerileanne99]

Penrose the Mathematical Cat books are a hit with my mathy big girl.

Mine too! She likes Penrose even more than Fred, and that is saying something:)

I do too...for the youngest of mathy kids it seems like the so-called harder concepts (more fun) are so quickly grasped. I think it is absolutely understandable to want to play with more advanced mathematical concepts in a non-standard, non-linear way of learning math whilst continuing with traditional practice.

 

And the Penrose books introduce so many concepts, mathematicians, and math history that they would not see for quite some time in a traditional math path. LOVE them:)

[sunnyday]

We did the Amazon Look Inside for Penrose and read a chapter about non-decimal number systems. We got a good conversation about it, but he wasn't exactly dying to know what happened to Penrose like he used to love hearing more Fred antics. :) I kind of wanted him to love it, as Sir Roger Penrose is one of my heroes. ;) I wonder if it's a girl/boy thing, I hate to stereotype but girls sure do love things to have a story to them. Maybe I'll get the books next year for DD, she's more linguistically oriented but is better with numbers and math ideas than DS was at this age, so... :)

[Brad S]

I'd consider sticking with one series so you don't jump around, double covering some topics and miss others. Singapore Math Primary Math is pretty solid, and I'd consider it, as well as AoPS (Beast Academy). For Singapore, I don't think I'd skip a book. If it's mostly review, I'd still do the textbook and the Challenging Word Problems. I'd skip the Intensive Practice if it's mostly review. IXL would probably be tedious as your DS said...it seems to be drill and kill. I haven't looked at the Life of Fred books before "Fractions," but, based on what I've seen with the later books in the series, that would probably be another solid supplement.

[sunnyday]

I'd consider sticking with one series so you don't jump around, double covering some topics and miss others. Singapore Math Primary Math is pretty solid, and I'd consider it, as well as AoPS (Beast Academy). For Singapore, I don't think I'd skip a book. If it's mostly review, I'd still do the textbook and the Challenging Word Problems. I'd skip the Intensive Practice if it's mostly review. IXL would probably be tedious as your DS said...it seems to be drill and kill. I haven't looked at the Life of Fred books before "Fractions," but, based on what I've seen with the later books in the series, that would probably be another solid supplement.

 

Yes, I agree that there are foundational concepts of elementary mathematics that I don't want to miss, perhaps *especially* since my guy loves the subject. But I also have to keep it fun and engaging, and for him that means challenging. I'm convinced that it's possible to add challenge without straying beyond elementary school math. Currently my strategy is to march along with the Singapore spine but to dance around finding interesting problem-solving challenges that seem more relevant (whether that's figuring out areas with the Beasts or telling him about how I got to college and realized that counting was more difficult than I'd expected, LOL.)

 

We do love Fred, we're on Goldfish, but the math in the series seems to be in a bit of a holding pattern except for the Rows of Practice, so it's harder to motivate him to play with it right now.

 

So far the Borac books look like a perfect fit! Any of y'all who might be in the same boat, I highly recommend going to Amazon Look Inside and reading the Foreword to any of the books. It exemplifies perfectly the mindset I have going into elementary math. Love it!

[Halcyon]

My mathy 8 yo is doing Zaccaro right now which he adores. I like the look of Hard Math for Elementary. He is also about halfway through MM4 but dislikes the drill components. Unfortunately, he needs SOME drill and so we try and move through it fairly quickly, just doing the hard parts. 

 

He is a word problem lover, so I am sure we'll get back to our CWP series at some point, but at this point we have enough. Oh, and we will definitely be buying the next in the Zaccaro series. I am not 100% sure why he loves Zaccaro so much, but I think it has something to do with the "thinking" nature of the questions--there is very little rote drilling, of course, but many of the questions require a lot of abstract thinking which he really enjoys.

[MamaSprout]

We did the Amazon Look Inside for Penrose and read a chapter about non-decimal number systems. We got a good conversation about it, but he wasn't exactly dying to know what happened to Penrose like he used to love hearing more Fred antics. :) I kind of wanted him to love it, as Sir Roger Penrose is one of my heroes. ;) I wonder if it's a girl/boy thing, I hate to stereotype but girls sure do love things to have a story to them. Maybe I'll get the books next year for DD, she's more linguistically oriented but is better with numbers and math ideas than DS was at this age, so... :)

My dd has never warmed up to Fred or Penrose. She likes Beast, loves AoPS and Vi Hart videos, Critical Thinking company books and oddly Singapore and Dolciani books. She didn't always like Singapore though. Her other favorites are Number Devil, Khan Academy and Sir Cumference books. ETA Zaccaro too.

 

HTH

[Kathleen.]

Yes, I agree that there are foundational concepts of elementary mathematics that I don't want to miss, perhaps *especially* since my guy loves the subject. But I also have to keep it fun and engaging, and for him that means challenging. I'm convinced that it's possible to add challenge without straying beyond elementary school math. Currently my strategy is to march along with the Singapore spine but to dance around finding interesting problem-solving challenges that seem more relevant (whether that's figuring out areas with the Beasts or telling him about how I got to college and realized that counting was more difficult than I'd expected, LOL.)

 

We do love Fred, we're on Goldfish, but the math in the series seems to be in a bit of a holding pattern except for the Rows of Practice, so it's harder to motivate him to play with it right now.

 

So far the Borac books look like a perfect fit! Any of y'all who might be in the same boat, I highly recommend going to Amazon Look Inside and reading the Foreword to any of the books. It exemplifies perfectly the mindset I have going into elementary math. Love it!

 

Can you elaborate on the Borac books?  I'm thinking of getting this for my 2nd grader.

[sunnyday]

Can you elaborate on the Borac books?  I'm thinking of getting this for my 2nd grader.

 

Yes! I got all four level I books, and we've played with the first few sections of each. In "Observation and Logic," for example, there are word problems that require that instead of just picking out the numerals and deciding what operation to do on them, you actually have to READ the problem and determine what it MEANS. In "Operations" there is a lot of work on associativity and commutativity, including the concept that thrills my son: subtraction is commutative IF you treat it as addition of a negative, and move the sign along with the number! It practices order of operations, and also discusses how much of our mathematical syntax is just a convention -- and there are other conventions out there (like Polish notation). "Arithmetic" does a lot of work with building numbers out of digits based on the properties of the digits. It does some strategies for those cool puzzles that replace digits with letters; it does a strategy for complicated word problems with a bar model type approach. "Counting" is about discrete patterns and extrapolating from them. Patterns like the toothpick problems and triangle-counting problems in Beast Academy 3A, but perhaps even more devilish in some cases? In many problem sets it gives you a simpler pattern (a 5x5 checkerboard) as a scaffold to a more difficult pattern (a 42x42 checkerboard).

 

I completely adore it. Nothing requires *computation* above a first-second grade level. It's all whole numbers, light multiplication and division, a little addition and subtraction of no more than 3 digit numbers. But everything requires a deeper *thought* process, and a strategic approach.

 

A note though, these are *practice* books. There are a few notes on strategies, some directed at the teacher and some at the student. There are some "experiments" to lead the student to discover new principles. But it's not primarily a teaching textbook, so a little inventiveness on the part of the teacher might be needed.

 

I cannot recommend enough that students of accelerated elementary students, especially those who might be feeling a little overwhelmed by the choice to go faster vs. deeper, should read the introduction to these books, whether they go on to buy them or not.

[SeaConquest]

I looked briefly at the Borac books. Do you recommend waiting until after 2nd grade math is completed before starting them, or could they work earlier as a supplement?

[Kathleen.]

The samples look really intereesting. How much time do you spend on it? Do you do this after school or wait for weekends?

[sunnyday]

I looked briefly at the Borac books. Do you recommend waiting until after 2nd grade math is completed before starting them, or could they work earlier as a supplement?

 

DS has just this week finished Singapore 1B, and was enjoying the problems before that. Like I said, they mostly only require addition and subtraction as far as actual computational skill. But they also require that the student have the motivation to try more than one strategy and possibly be wrong.

 

The samples look really intereesting. How much time do you spend on it? Do you do this after school or wait for weekends?

 

It's one of many supplements we use at home. We mostly only have the energy to do any afterschooling on weekends or breaks. But we just had a long break, so for example one day this weekend we spent maybe 15-20 minutes in the Operations book, and then he spent time over his lunch flipping through Arithmetic I think. But the next day we did Beast Academy and Singapore. It's all a bit random, but I have the Borac out today and will see how he's doing when he gets home, judge if we have 20 minutes or so that we can engage his interest to play with it this afternoon.

[La Texican]

Oh crap! That associative thing sounds like what my kid's working out. He asked me a few times if 3x5 is the same as 5x3 and such questions like that. He just learned about negative numbers on the computer and wants so badly to use it for something. He knows borrowing, knows his math book work means he has to borrow, but keeps hoping one of the answers will come out to a negative number, trying to make the ones or tens be a negative number, then seeing it doesn't work that way. I've told him and told him second grade subtraction is not going to be using a negative number, he has to borrow. He knows this, he just wants it to turn out to be something different.

Thanks to another thread I'm already going to have to buy the IP, one book at a time. I'm not sure if I should buy 2A IP, because he's on page 50 out of 112, or buy 2B because he's halfway done with this book already. Now it looks like Borac Operations is a stinkin' "must have".

I'm being whinny about the cost, but I'm secretly thankful you guys.

[bakpak]

Oh crap! That associative thing sounds like what my kid's working out. He asked me a few times if 3x5 is the same as 5x3 and such questions like that. He just learned about negative numbers on the computer and wants so badly to use it for something. He knows borrowing, knows his math book work means he has to borrow, but keeps hoping one of the answers will come out to a negative number, trying to make the ones or tens be a negative number, then seeing it doesn't work that way. I've told him and told him second grade subtraction is not going to be using a negative number, he has to borrow. He knows this, he just wants it to turn out to be something different.

Thanks to another thread I'm already going to have to buy the IP, one book at a time. I'm not sure if I should buy 2A IP, because he's on page 50 out of 112, or buy 2B because he's halfway done with this book already. Now it looks like Borac Operations is a stinkin' "must have".

I'm being whinny about the cost, but I'm secretly thankful you guys.

 

Why don't you have him make a number line that includes negative numbers then do some simple addition/subtraction? Knowing what it really IS will help him know what it isn't, if that makes sense. My 4-yr-old loves thinking about simple addition/subtraction with negative numbers, although she's not ready to do it in her head.

[sunnyday]

Oh crap! That associative thing sounds like what my kid's working out. He asked me a few times if 3x5 is the same as 5x3 and such questions like that. He just learned about negative numbers on the computer and wants so badly to use it for something. He knows borrowing, knows his math book work means he has to borrow, but keeps hoping one of the answers will come out to a negative number, trying to make the ones or tens be a negative number, then seeing it doesn't work that way. I've told him and told him second grade subtraction is not going to be using a negative number, he has to borrow. He knows this, he just wants it to turn out to be something different.

Thanks to another thread I'm already going to have to buy the IP, one book at a time. I'm not sure if I should buy 2A IP, because he's on page 50 out of 112, or buy 2B because he's halfway done with this book already. Now it looks like Borac Operations is a stinkin' "must have".

I'm being whinny about the cost, but I'm secretly thankful you guys.

 

You've got to make the choice for your kid; with mine I have opted to skip the IP and try to compact the whole 2 level because he's chomping at the bit to get to third grade stuff. But he loves the "More Challenge Problems" so much...we'll see, I might yet pick up one or the other IP for funsies.

 

I agree with bakpak that you may want to show him a number line and get the idea of negatives first. The commutativity ideas practiced are sort of discovery-ish, "Look, 1+2+3-2 is the same as 1+2-2+3! Look how much easier to compute! But subtraction isn't commutative, what gives?!"

 

Two digit "second grade" subtraction requires REGROUPING or DECOMPOSING A HIGHER VALUE UNIT, not borrowing. If you have completed the 1 level of Singapore math, this should already be part of your DS's skill set. Do you have the HIG? Also, sometimes DS solves word problems with some judicious use of negatives. It's all legit mathematics. We're separately working on the idea that the number sentence to express this outcome should be written as a subtraction.

 

We worked on Observation and Logic yesterday and it was really fun to play with how to determine the ways to distribute m objects into n<m boxes. He started over twice before coming up with a sufficiently organized way to keep track of the combinations.

[kiana]

But you *can* do subtraction with negative numbers if he wants to try it that way because he thinks it's fun/weird/different. 

 

e.g. 72-19. 70-10 = 60. 2-9 = -7. So your answer will be 60 + (-7) = 53, which is the same answer you'd get with the traditional algorithm.

 

Now, I wouldn't let him ignore the traditional algorithm. But if he wants to work the problems both ways and delightedly observe that he's getting the same answer, I think that'd be great.

[La Texican]

He "discovered" commutativity already , and he saw the negative numbers on a number line online, that's why he wants to figure out what they're for. I'm going to buy the IP and the borac, because that's the best I can figure to buy based on where he's at, and for the enrichment advice I'm reading. I was just giving you a hard time for showing me these Borac books that I've convinced myself that I "have to have" now. But, seriously, I'm glad you guys show me these things.

[sunnyday]

I feel ya, I sometimes feel silly for the quantity of math books I have thanks to these boards -- my kids go to public school, I really should probably leave the math to them! -- but it's fun and interesting to have lots of tools in the tool box.

[MamaSprout]

These are free options:

http://mathcounts.org/resources/problem-of-the-week

 

Grade 3-5 level:
http://mathlearnnc.sharpschool.com/cms/One.aspx?portalId=4507283&pageId=5051238
Grade 6-8 level:
http://mathlearnnc.sharpschool.com/cms/One.aspx?portalId=4507283&pageId=5149151
Answer keys are provided for each week's worth.

 

HTH

Bean

[Halcyon]

Those Borac books look great. What level would you recommend for an 8yo boy who is almost finished with MM4 and LOF Fractions and really likes word problems and abstract thinking?

[sunnyday]

Those Borac books look great. What level would you recommend for an 8yo boy who is almost finished with MM4 and LOF Fractions and really likes word problems and abstract thinking?

 

Your guess is probably as good as mine, since I only own the first level, and since my oldest student is only 7 and working mostly on 2nd-3rd grade material. :) Because the books are aimed at gifted students, they're labeled by age range; Level I is intended for ages 7-9. It also says grade 1-2, but I think the age range feels more accurate. There are some real stumpers in all four books, I've had to look at the solutions a lot while working through them. I would probably try the Level I if I were you. Try the Look Inside on Amazon to see some samples.

 

Level II states that you may need to review some concepts from Level I before attempting it, and that it's designed to help students prep for Math Kangaroo 3-4 and MOEMS-E, with additional concepts from AMC-8,  if you've ever looked at any of those sample problems.

[shawthorne44]

Since you are worried about arithmetic, have you looked at the Math Games book that is part of Right Start?  That may be the way to cement the low-level math.  

Part of the problem with 59 +31 was that his brain shut down in boredom.  I remember once in school being forced to do a math worksheet that was grades below my level.  (I think it was a confused sub)  I made mistakes.  Embarrassing mistakes.  

[sunnyday]

 

Since you are worried about arithmetic, have you looked at the Math Games book that is part of Right Start?  That may be the way to cement the low-level math.  

 

Part of the problem with 59 +31 was that his brain shut down in boredom.  I remember once in school being forced to do a math worksheet that was grades below my level.  (I think it was a confused sub)  I made mistakes.  Embarrassing mistakes.  

 

 

Thanks!

 

Oh, it's definitely boredom in most cases. It's becoming more and more clear that he is one of those kids who needs fewer repetitions and then to move on with fairly good retention. And that IXL is a terrible fit, since he gets bored/frustrated/makes a small mistake/has do do a DOZEN more problems JUST the same (because the adaptive algorithm resets). Worksheets aren't great for him either. But what else to suggest to the teacher that he does during math time? DS wants me to send Beast Academy problem sets and Borac pages.

 

But he did need work on place value (we had a couple of great talks and he's really internalized the relative values of units), and subtraction with regrouping needed some instruction and practice. But that's done now and I'm calling him done with 1B (we'll keep popping back to the IP and maybe do the time/money chapters some time) so now we're compacting 2A, did the first chapter in one sitting. Multi-digit addition is extremely solid and subtraction usually goes quite well, and multiplication and division are ramping up. Plus he's interested in math again to the point he wants to do it after school, which is great!

[Guest PIGGYWOLF]

IXL is a horrible learning site, it always frustrates me. They lied when they said "A FUN way to learn".