Stretching Math

[KaceeM]

I have a 4yo (almost 5) who is working at a first grade level in everything (reading level is currently 1.6). In math I am worried that she is moving too fast for herself, she always wants to move on before adequate mastery of a concept is shown. I am wanting to slow her down some without holding her back. Would it be too much to spiral through MEP Year 1, Math Mammoth 1 and Miquon Orange/Red? Right now she can easily complete 2 MEP pages in less than 10 minutes and still wants to do Miquon every day. I am thinking of alternating 2 pages of MEP one day and a lesson from MM the next and letting her do Miquon as she wants. Using this schedule she'd take 1.5 years to do 1st grade math and start 2nd grade right about the time she turned 6. 

[Jackie]

"Too much" is incredibly subjective and child-dependent. That would have been far too much for my kid, who detests any form of repetition, but it's no more total math than we've done. I have found that my previous plans of "slowing down" were massive mistakes. As of now, my daughter has conceptual understanding of math through about mid-Algebra 1, but arithmetical abilities of a 3rd-4th grader, and that's ok.

 

An alternative, especially for a concept-driven kid, is living math books and hands-on projects and games. We have used piles, likely a couple hundred, living math books. MathStart by Stuart J Murphy, Time-Life I Love Math, Sir Cumference, Murderous Maths, and an amazing amount of library books (call number 510, I can walk straight to it), plus MathMania magazines. Legos, Zometool, Keva blocks for toys. Logic games - Pirate Hide and Seek, Balance Beans, Laser Maze Jr, Logic Links, Rush Hour Jr for single player; multi-player includes Gobblet, Forbidden Island, Qwirkle, CrabStack, Ticket to Ride, Othello, and Dr. Eureka. More directly Math-related games include Toss Up!, Rat a Tat Cat, Zeus on the Loose, Sleeping Queens, and Double Shutter.

 

Our math programs are diversified, but not duplicative. Right now, she uses Beast Academy 3 as a main program, and Hands on Equations and Developing Fraction Sense to pave the way towards the future using hands-on materials.

[EndOfOrdinary]

It isn't like the first grade concepts are going away. By the very nature of her doing second or third grade math she is going to repeat darn near all of those concepts. Elementary school math is generally one big old spiral until PreA, and even then the concepts just deepen. So even if she hasn't mastered them, if she moves on she will get them again no matter what.

 

For young gifted kids, just let them fly as far and as fast as they want. When they hit bumps, and they will, then be there to instruct and mentor. She is young enough there is very little that could go wrong with letting her consume huge amounts of material. Even better, if she learns young that she is going to hit road blocks and have to slow down and critically think through them, you will have gotten her through one kf the largest gifted hurdles out there.

[Dmmetler]

Honestly, I found that the thing that stretched math the best was getting past arithmetic. The concepts just keep getting repeated over and over again, and once DD knew them, she could extend and apply them. Once we got to Algebra and beyond (and found AoPS), it's been easier to slow down because there are so many parts of math that open up, all of which have new concepts.

[SarahW]

I have a 4yo (almost 5) who is working at a first grade level in everything (reading level is currently 1.6). In math I am worried that she is moving too fast for herself, she always wants to move on before adequate mastery of a concept is shown. I am wanting to slow her down some without holding her back. Would it be too much to spiral through MEP Year 1, Math Mammoth 1 and Miquon Orange/Red? Right now she can easily complete 2 MEP pages in less than 10 minutes and still wants to do Miquon every day. I am thinking of alternating 2 pages of MEP one day and a lesson from MM the next and letting her do Miquon as she wants. Using this schedule she'd take 1.5 years to do 1st grade math and start 2nd grade right about the time she turned 6. 

 

 

What do you mean by "adequate mastery"? Being able to do an addition worksheet and get 100%? Or.. ???

 

My kid was always wanting to move forward before I felt ready. I did see his point sometimes - I think it was 2nd grade math that seemed to consist of just addition and subtraction, over and over, just with more place value. "Okay, and now thousands!" made him raise his eyebrows and say "and millions? and billions? and so on, right?" He was shaky on things like 6+7 for a long time ("is the answer 15?") but really, yeah, until you get past Pre-A you're doing the same thing over and over, just in different ways. He practiced his sums with decimals and long division, and I think he's got them all right now.

 

Accuracy with arithmetic is important, yes. But I don't think that's what being talented in math consists of. 

[kiana]

I didn't have my math facts down until after pre-algebra. My mother kept moving on conceptually until she hit problems where it really mattered that I needed to stop and think about multiplication facts and I learned them through repeated computation. 

 

As long as you don't allow a calculator and there are no learning disorders, that type of mastery will come, but imo it doesn't make sense to stop and wait on concepts until facts are learned. 

[HomeAgain]

More of the same is more of the same.

 

You can stretch by adding in additional concepts:

Sudoku or other logic games (Nrich.org was recommended on here and it is fantastic.)

Anno's math games

Tangrams

Chess

Number play (creating different sets or groupings using different criteria)

Mathematics story books

 

[KaceeM]

To me adequate mastery isn't a specific point, it's when I can see she truly understands something.

[Pegs]

I second Jackie's suggestion of living math. If you don't believe that your child is benefiting from worksheets, perhaps try something different, rather than just adding more worksheety programs.

 

Kitchen Table Math might be a good place to start if you feel you need some pedagogical guidance in this alternative approach.

[Guest]

To me adequate mastery isn't a specific point, it's when I can see she truly understands something.

Ime, if the light bulb doesnt come on, she needs more experience with pre-req skills most likely, or more time to digest them. Follow her cue and work on something else.

[Arcadia]

To me adequate mastery isn't a specific point, it's when I can see she truly understands something.

Sometimes kids need to chew on something while they pick up something else. My kid chewed on fractals while he picked up binary systems. Now he is still chewing on fractals. We did lots of living maths at that age. We skip curriculum for K and 1st so started at MEP2 and SM2 when oldest was 4.

[quark]

With young kids, don't ever worry about moving on before true understanding develops because you can't always predict when that will happen. Like others have said, go deep and wide with a variety of topics and resources. Sometimes, understanding will suddenly click, when you least expect it. For my kid that was usually late at night or in the car or the bathroom while we did something totally unrelated like listening to an audiobook or brushing teeth or making sandwiches.

 

Over repetition is the easiest way to kill love of a subject unless the child specifically asks for that repetition.

 

We have also never worried about going back a level if that was necessary for understanding but that was only done with the kiddo's total buy-in. Most of the time going ahead helped understanding of previous concepts to click faster because the level ahead usually applied the level before in ways he might not have previously considered.

[EKS]

Honestly, I found that the thing that stretched math the best was getting past arithmetic. 

 

This.

[Crimson Wife]

 

For young gifted kids, just let them fly as far and as fast as they want.

 

I'm going to have to respectfully disagree with this statement. Far better IMHO to go "deeper" in math than faster. It isn't a race to see who can get to algebra fastest coasting through an easy math program. The parent who chooses the "faster is better" is doing a disservice to his/her child compared to the parent whose primary goal is challenging the child.

 

If the OP wants to go "deeper" I would encourage adding in the Singapore Intensive Practice and Challenging Word Problems books rather than MM. Also Beast Academy once the student has reached 3rd grade level.

[EndOfOrdinary]

The very point that it is not a race is what I am saying. I meant was that before 8 or 9 the kid can race through anything they want, it is all coming back. There is no harm in letting a student that young read Calculus for Kindergarteners. It isn't that precludes them taking a formal PreA class. They will still have to take formal Trig. It doesn't do or mean anything other than allowing the child to freely explore numbers. So they want to geek out on permutations - great! Along the way they might pick up multiplication facts. So they want to get overly into tessalations or fractiles or logic - awesome! They might begin to glimpse visualizations of exponents. There is very little harm that can be done if a kid this young decides to pound astronimical amounts of math at a break neck speed. They flat out have to repeat the formal subjects. Just let them fly with it and then when Intro to Geometry comes around, they will have a much larger pool of information which might be pulled from. They will have to take Algebra 1 at some point no matter what is done at 4. So what if she wants to pull down the book and read about modal algebra? She might get nothing for it, but she is only 4. Nothing is lost even if nothing is gained, and what great things can be gained!

 

Her child will never run out of math. Neither will playing around at six (regardless of mastery) allow her to skip ahead. There is a reason most all of the precoscious math kiddos here go through PreA or Algebra1 somewhere between 7-9. Most of those kids have done all sorts of background work. Ds is having his Algebra class for his p currently take 3 months for the whole year's credit. He took Algebra forever ago, but granting formal, outsourced credit wasn't reasonable until 12 (frankly, his handwriting is STILL attrocious enough he has to redo pages more often than not). But he has to take it. It has to show up somewhere. Quark's son still has to take the Calc classes. He either has to test out of them or has to take them. He is doing it early, but all his previous work didn't make it disappear.

 

So let the kid race through whatever, even if she doesn't get it. At 8 or 9 when formal curriculum really gets going, or when her kid decides that Beast is the greatest and just wants to fully invest, or when it actually has any kind of weight (personal or otherwise), then set a path. But not at 4. At 4 let the kid just eat as many and as much number information that she wants to cram in her head for the sheer joy of doing it.

[SarahW]

To me adequate mastery isn't a specific point, it's when I can see she truly understands something.

 

Okay, I'm still not sure what exactly that means. She's doing two pages of MEP 1 (are you doing the teacher portion with her?) and then wants more math with Miquon every day? It would seem that MEP isn't too difficult for her, and she likes Miquon, so I'm not sure where the problem is that you feel needs fixed.

 

Like others have said, understanding can come slowly, or in fits and starts, or in sudden flashes. As long as she enjoys doing what she's doing with MEP and Miquon consistently and is able to get the lesson done with some accuracy, then on some level she must be understanding it. At least, understanding on the level the curriculum expects.

 

It just sounds like in your OP that you want to add in MM just to slow her down. First, this tends to make kids frustrated. Second, they defy every scheduling plan. Sure, I like to sit down with a math book and look at the number of pages, and the number of chapters, and roughly calculate how many pages to do every day to be done in so many months. It has never worked out that way, though.

 

And MM has its good points, but I'm not sure what it would add on to MEP and Miquon. All we're saying (I think) is that another linear program probably isn't necessary, and could be harmful, and probably won't work. If you want to back off a bit to let a concept "stew" then you can do something like turn Friday into "fun math" day where you read a Sir Circumference book and play a related game or something.

 

If you think she's flying through MEP but doesn't really understand what she's doing, that's a different issue.

[CadenceSophia]

I think I have some concept of this problem. My daughter is the same way(i think, from your post). She can do 60 pages in a workbook in one day when she understands the concepts. When you do all 60 pages that, for example, deal with addition and subtraction within 20, it doesn't mean you will necessarily be ready for addition and subtraction within 100 by next week. The child may be ready to fly through the within 20 work but still not have a full concept of place value or be able to count to 100 at all.

 

I don't know if it is the right strategy, but for my daughter we have chosen just to let her go with what she loves at any time, across subjects so she doesn't hit wall. She did all the worksheets MUS primer over the course of a single week (she loves worksheets) when she was either 3 or 4 years old (mom brain..) but really wasn't ready to move up in math concepts so we just attracted her attention or another subject she was ready to tackle and stalled with living math, rather than more problems, until her conceptual development began to pick up. Then I set her free on the worksheets again to her hearts content. We are content-bingers over here though. My kids all have long attention spans and would never tolerate only 10-15 minutes of something per day, every day.

 

I think you will have to look really closely and see what she wants more of. More of the same? More difficult? More puzzles? Wanting more doesn't always mean wanting harder or really ready for harder.

[KaceeM]

I second Jackie's suggestion of living math. If you don't believe that your child is benefiting from worksheets, perhaps try something different, rather than just adding more worksheety programs.

 

Kitchen Table Math might be a good place to start if you feel you need some pedagogical guidance in this alternative approach.

 

I actually started this year planning on not using worksheets, but she i a worksheet kid. I came fully prepared with cuisinaire rods, a base 10 set, multi link cubes, fraction cards/circles, and pattern blocks and trays thinking it would last the year. She quickly got bored and wanted "real math" so we started Miquon. I have Kitchen Table Math but she finds most of the things boring or too easy. 

[KaceeM]

I think I have some concept of this problem. My daughter is the same way(i think, from your post). She can do 60 pages in a workbook in one day when she understands the concepts. When you do all 60 pages that, for example, deal with addition and subtraction within 20, it doesn't mean you will necessarily be ready for addition and subtraction within 100 by next week. The child may be ready to fly through the within 20 work but still not have a full concept of place value or be able to count to 100 at all.

 

I don't know if it is the right strategy, but for my daughter we have chosen just to let her go with what she loves at any time, across subjects so she doesn't hit wall. She did all the worksheets MUS primer over the course of a single week (she loves worksheets) when she was either 3 or 4 years old (mom brain..) but really wasn't ready to move up in math concepts so we just attracted her attention or another subject she was ready to tackle and stalled with living math, rather than more problems, until her conceptual development began to pick up. Then I set her free on the worksheets again to her hearts content. We are content-bingers over here though. My kids all have long attention spans and would never tolerate only 10-15 minutes of something per day, every day.

 

I think you will have to look really closely and see what she wants more of. More of the same? More difficult? More puzzles? Wanting more doesn't always mean wanting harder or really ready for harder.

 

THIS. She has the mechanics of it but not the conceptual understanding yet.

[CadenceSophia]

Math Mammoth is really boring. I would not add that, but maybe Singapore's Challenging Word Problems. The nice thing about Singapore is that the mastery aspect can let you see exactly where she is concept wise and you can easily speed up or hang out in one area. (We do our CWP on the white board every morning and I just mark down which child and the date for each problem they complete) depending on HOW shaky she is conceptually, you could give her Singapore Essential Math as play-worksheets after math time. They are K level, nice big layout, lots of coloring in boxes and filling numbers in order. They might serve as "math processing space" without actually going forward. Maybe just the B level.

 

But feel free to ignore me if that doesn't sound right. I only have experience with my daughter and she's only 6 so I don't know if what I am doing is right. :) Also, I don't think you can go wrong with any of Jackie's suggestions above.

[Crimson Wife]

I never really wrapped my head around MEP 1 to be honest. I had started MEP Reception with my DS when Right Start A was a bad "fit" and he wasn't ready yet for RS B. He did well with MEP Reception and 1A but while I felt he was doing a lot of cool problems, the progression was so different from RS that I had trouble trusting the design of it. RS B has kids adding 4 digit numbers by the end of it while MEP 1 only adds within 20. So I ended up switching back to RS after MEP 1A.

 

If MEP 1 seems too easy, then it might very well be for your child.

[CadenceSophia]

I never really wrapped my head around MEP 1 to be honest. I had started MEP Reception with my DS when Right Start A was a bad "fit" and he wasn't ready yet for RS B. He did well with MEP Reception and 1A but while I felt he was doing a lot of cool problems, the progression was so different from RS that I had trouble trusting the design of it. RS B has kids adding 4 digit numbers by the end of it while MEP 1 only adds within 20. So I ended up switching back to RS after MEP 1A.

 

If MEP 1 seems too easy, then it might very well be for your child.

MEP Reception is for kids who would enter the school year at 4 years old. MEP 1 is for kindergarteners (entering at 5 years) so that is why it only covers within 20 work. Actually I think it looks party advanced for K.

Right Start A is for kindergarten or 1st and B is for first or second. That is why you saw such a difference. MEP's numbering system is a year "behind" US school grades.

[Pegs]

I actually started this year planning on not using worksheets, but she i a worksheet kid. I came fully prepared with cuisinaire rods, a base 10 set, multi link cubes, fraction cards/circles, and pattern blocks and trays thinking it would last the year. She quickly got bored and wanted "real math" so we started Miquon. I have Kitchen Table Math but she finds most of the things boring or too easy.

If you think worksheets are the way to go for this kid, perhaps you can cobble some together but include some problems which will really stretch her and make her think. If understanding isn't occurring through repeated computation, why not try gaining fluency through the practice which is inherent in approaching tough problems?

 

Or! There have been a few curricula suggested already with a problem-solving focus. :)

[Crimson Wife]

MEP Reception is for kids who would enter the school year at 4 years old. MEP 1 is for kindergarteners (entering at 5 years) so that is why it only covers within 20 work. Actually I think it looks party advanced for K.

Right Start A is for kindergarten or 1st and B is for first or second. That is why you saw such a difference. MEP's numbering system is a year "behind" US school grades.

 

RS A is for K and RS B is for 1st. You can certainly use them in 1st and 2nd but that is using them a year behind what Dr. Cotter intended.

[Dmmetler]

For a worksheety young kid (especially if they like "cute"), check out https://www.themailbox.com/. You can get a good idea of what is there without getting a "Gold" subscription, but if you do, you pick a grade level, but also get unlimited printing and tools for the stuff for other grades, except for gold content. I keep a subscription to 1st grade for my math club kids who are too young for CML yet, but also sometimes pull from there for older kids just for extra, fun worksheets, folder games and the like. 

 

We also used Teacherfilebox quite a bit when DD was at the stage where she liked worksheets and the feeling of completeness, and needed to be at a range of grade levels, but the Mailbox is both cuter and cheaper, so if it would work, I'd try it first.

 

 

[SarahW]

If she's a worksheety kid, and she needs work on concepts, switching to MM as the main program might be a good idea.

 

I don't really understand how she can be consistently going through MEP quickly and not getting it. When I did it with my kid we found it a bit opaque, but we were trying to jump into the middle of it. MEP is supposed to build good conceptual understanding. But if it isn't working then it isn't working. That's fine. If she does still like it, you can pull out some of the puzzles and odd topics in it and do those as an "extra" sometimes.

 

My kid thought MM had too many questions. He thinks BA has too many questions, too. MM didn't fly with him, lol. Even with lots of modification. But your kid might be his complete opposite. If you poke around the MM website she gives links to additional worksheets, a worksheet generator, and there's also some videos and games. And there's also the suggested extension activities links she recommends for each chapter. You can spend LOTS of time with what she suggests to help things "click."

[KaceeM]

For a worksheety young kid (especially if they like "cute"), check out https://www.themailbox.com/. You can get a good idea of what is there without getting a "Gold" subscription, but if you do, you pick a grade level, but also get unlimited printing and tools for the stuff for other grades, except for gold content. I keep a subscription to 1st grade for my math club kids who are too young for CML yet, but also sometimes pull from there for older kids just for extra, fun worksheets, folder games and the like. 

 

We also used Teacherfilebox quite a bit when DD was at the stage where she liked worksheets and the feeling of completeness, and needed to be at a range of grade levels, but the Mailbox is both cuter and cheaper, so if it would work, I'd try it first.

 

What is CML?

[Sarah0000]

We did 1-3 grade arithmetic pretty much at the same time. For that I used primarily Singapore textbooks as my guide, DS did some Miquon on his own when he felt like it, and I gave him a few Mep sheets every now and then to test understanding. I don't require mastery. My goal right now at five years old is to keep his mind sharp and his interest high. Nowadays we mostly do living math books together and he does his own thing in workbooks. I figure in a few years when he's ready we'll go through some basic arithmetic practice of all concepts then hopefully really do as intended a good pre algebra program.