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I think my son picked up a lot of mathÂ from playing Monopoly and other games (rolling two dice, buying property, making change) as well as dayÂ to day life (spending money, figuring out how much he'll have left if he buys a certain item, baking, general curiousity).
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Are you just planning to do some math at home over the summer, or are you switching to home schooling? If you aren't going back to the school system in the fall, you probably don't need to worry so much about grade level expectations she may not learn things at the same pace or in the same order as she would inÂ a classroom where that order and pace is set out for her.
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Regardless of your approach,Â Â I think it is important to keep it fun and relevant, so that she enjoys math and feels competent. There are some funÂ games (rocket math on the ipad; Dreambox; Khan Academy) that my son has enjoyed too. He likes anything if it is on a computer ;)
Writing, reading, unschooling.Â
I'm a special education math teacher and I like to use the "war" games with regular old playing cards as described at this site.
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http://letsplaymath.net/2006/12/29/thegamethatisworth1000worksheets/
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There is also another variation, but you need 3 people. Two players and a judge. Each of the two player grabs a card and puts it on his forehead facing out WITHOUT looking at it. So each player can see each other's card, but not his own. Then the judge calls out the sum (or product, if doing multiplication) and the first person to guess his own card wins them both. This is good for teaching fact families, and is actually an algebraic thinking skill. Â
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Have you seen the Right Start Math Games? DS is learning math facts at a crazy rate just by playing the games (which he'll willingly do for well over an hour at a time). Right Start is similar to Singapore in the way it approaches math so it's a great compliment if that's what she's getting at school.
Mama to DS (6/07)Â ,Â DD (6/09)Â , and DD (07/12)Â ..
We like the Right Start Math Games Kit (which you can buy separately).Â I also have my kids do Xtramath.com every day.Â It just takes a few minutes to complete, but it's been a good way to practice their facts every day in a short amount of time.Â
Personally I would not focus on memorizing math facts as in: "What is 8 + 3?" Instead I would give her opportunities to use the facts in meaningful situations. The end result will be memorization, but that path to that end will likely be quicker, more efficient, and will have a mathematical context: a conceptual foundation on which she can build her future math learning. I really think that moving too soon to the symbolic form of numbers (i.e. written numerals) and using only those as the tools of arithmetical mastery is one of the main things that leads kids to get offtrack with their math learning. When mathematics is presented as the memorization of relationships between symbols, rather than as a tool to describe relationships between the characteristics of things, some kids will memorize instead of understanding. If understanding comes first, memorization almost always follows.Â
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Family Math is great. Monopoly is great. Snakes and Ladders (especially with two dice, first using dice with dots and then dice with numerals) is great. Arranging dollops of cookie dough on a cookie sheet is great, noticing speed limits, recording the daily outdoor temperature, counting eggs in the carton, building with Legos, playing with Boggle cubes or cuisenaire rods, counting her cousins, learning about Roman numerals, keeping track (in groups of ten) of how many times she has made her bed or brushed her teeth, playing Go, hopscotch, number guessinggames. all that sort of stuff. If you feel the need for a curriculum or set of structured resources I would encourage you to stay away from those that focus on drill and instead look at more conceptual and handson approaches like RightStart, Singapore Math (with lots of emphasis on the use of manipulatives), Miquon Math or MathUSee.Â
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If I were in your situation, between now and the end of the school year I would substitute math games for the drill you're doing. Make time each day to play War, Snakes & Ladders, Shut the Box, etc. or to play around with math manipulatives, like building towers or pyramids or patterns out of cuisenaires, or making patterns with a 10x10 abacus. Not only will that allow you to enhance your dd's math learning, but you'll accumulate a lot of interesting observations about how she currently processes quantitative problems. Once you begin homeschooling I would use those observations to then consider an appropriate conceptuallybased curriculum.Â
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Miranda
Mountain mama to two great kids and two great grownups
Our son was not able to learn the addition facts when they were "jumped around" too much.Â He needed to learn them in a methodical order.Â Begin with only what you can do with 0, 1 and 2.Â When that group of addition facts has been thoroughly practiced and completely memorized, introduce 3 and the facts you can make with that and all the other numbers that have been introduced already, practice those with all the other previously learned facts, then introduce 4, etc.Â Â Not learning these thoroughly will cause problems later, and some kids will never learn them by just playing games and other types of "random assortment" exposure.Â
and 3 , in our happy secular
Not trying to beat a dead horse here, but what exactly is there to memorize about n + 0 and n + 1 "addition facts?" If a child has to memorize these, he doesn't understand the meaning of numbers or the meaning of addition. To me this illustrates the danger of emphasizing memorization and drill: kids can cover up a lack of understanding with rote memorization giving everyone the pleasant illusion that they are progressing nicely.
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Miranda
Mountain mama to two great kids and two great grownups
Yes, and it is also possible for a kid to have a great grasp of the concepts  they do understand numbers and the meaning of addition  but cannot efficiently move further into their math materialsÂ because they have not developed fluency with the facts.Â Both are important.Â Â My son is one who struggled with fluency even with the 0 and 1 facts, just as he struggled with fluency with even the easiest phonics words and sight words.Â He has visual processing challenges.Â He has sequential memory challenges.Â Both come into play with math facts, even the ones that seem ridiculously simple to the rest of the world.Â Some kids struggle with this.Â Not that they can't figure it out, but that the energy they will spend figuring it out each and every stinking time they encounter it is wasted brain power.Â Doing the work to commit them to memory is worthwhile.Â For some, this is such a minimal amount of work that they don't even notice it as work and call it ridiculous.Â And for some, it actually takes a lot ofÂ effort to build fluency to the point of being able to quickly retrieve 3+1=4 and make use of the fact in an efficient way.
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Not trying to beat a dead horse here, but what exactly is there to memorize about n + 0 and n + 1 "addition facts?" If a child has to memorize these, he doesn't understand the meaning of numbers or the meaning of addition. To me this illustrates the danger of emphasizing memorization and drill: kids can cover up a lack of understanding with rote memorization giving everyone the pleasant illusion that they are progressing nicely.
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Miranda
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and 3 , in our happy secular
thank you so much for the responses! My baby's been teething so I haven't had much time to reply. DD does know how to add, but does it slowly, on her fingers. Even plusones. I've been trying to work with dice to recognize groups of numbers by sight, but even after a few weeks, she still has to count. (doesn't recognize two rows of three as six, for example) I downloaded rocket math on my iPad and it is a HUGE hit! We'll be doing more of the games suggested, as well. I will also focus on trying not to project my own anxiety!
Some people have trouble processing the visual information in those dice patterns.Â They don't recognize the pattern and then remember the number of dots that goes with the pattern, so they count the dots over and over. Â If you want to use the dice patterns, it might help to study larger version of the dice faces drawn on index cards, and use a colored marker to connect the dots to make a continuous figure  kind of like explaining constellations by filling in lines to complete the picture.Â Â For 2 and 3, just connect them with lines.Â For 4, make a square.Â For 5, make an X.Â For six, make a rectangle.Â This can help her to recognize the dot pattern more quickly and retrieve the correct number.Â Â Or she might do better with hash marks, or just the numbers themselves.
and 3 , in our happy secular
Yes, and it is also possible for a kid to have a great grasp of the concepts  they do understand numbers and the meaning of addition  but cannot efficiently move further into their math materialsÂ because they have not developed fluency with the facts.Â Both are important.Â Â My son is one who struggled with fluency even with the 0 and 1 facts, just as he struggled with fluency with even the easiest phonics words and sight words.Â He has visual processing challenges.Â He has sequential memory challenges.Â Both come into play with math facts, even the ones that seem ridiculously simple to the rest of the world.Â Some kids struggle with this.Â Not that they can't figure it out, but that the energy they will spend figuring it out each and every stinking time they encounter it is wasted brain power.Â Doing the work to commit them to memory is worthwhile.Â For some, this is such a minimal amount of work that they don't even notice it as work and call it ridiculous.Â And for some, it actually takes a lot ofÂ effort to build fluency to the point of being able to quickly retrieve 3+1=4 and make use of the fact in an efficient way.
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Mine is the same way. She has absolutely grasped the meaning of numbers, and absolutely grasped the meaning of addition. However, she counts from 1 no matter what. So, 6 + 1, she will solve by counting to herself, 1234567.
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She does have n + 0 fine, though I understand that not all children grasp that concept  but she did.
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n + 1, though, yes, we have to drill. What else would we do? She knows how to add but she needs to memorize it so she doesn't exhaust herself figuring such simple sums.
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Her father (my DH) doesn't have his math facts solid even now, and it's given him quite a bit of anxiety about math. He just shuts down. So, of course I am working with DD to help her memorize these so she can move on. I met DH in college, and I tutored him in statistics, and it was strange because the stuff that was hard for everyone else came easily for him (the concepts) but the mechanics sent him into a tizzy. He is absolutely thrilled that DD asks to do math and frequently states she loves it.
Homeschooling mama to 6 year old DD.
I think it was my Kitchen Table Math book that pointed out the idea of counting with kids starting at different numbers.Â Doing that helps them with this sort of thing.Â So when adding 2 onto 6 comes up in daily living, for example, I've taken to putting out my closed fist for 6 and saying "six" then sticking up one finger "seven" and another finger "eight".Â It seems to work well in getting them off starting at 1 every time.Â Now my oldest will do that herself.Â
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Tjej
Yeah, that makes sense to me but DD just hasn't caught on to it. I've worked with her on it and... I dunno.
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That's why I just decided to move right along into memorization. I think the rest will come with time  though I don't know for sure. I do know for sure that she thinks differently than I do, so I'm in unfamiliar waters.
Homeschooling mama to 6 year old DD.
Mine is the same way. She has absolutely grasped the meaning of numbers, and absolutely grasped the meaning of addition. However, she counts from 1 no matter what. So, 6 + 1, she will solve by counting to herself, 1234567.
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She does have n + 0 fine, though I understand that not all children grasp that concept  but she did.
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n + 1, though, yes, we have to drill. What else would we do? She knows how to add but she needs to memorize it so she doesn't exhaust herself figuring such simple sums.
If she is not able to do the n + 1 facts without memorization and drill, then I would suggest that she doesn't understand the prerequisite concepts fully enough. If I ask you what 429 + 2 is, are you able to work it out intuitively as 431? Or do you deconstruct the 429 into 420 and 9, and then use the memorized math fact 9 + 2 = 11 and regroup the 11 with the 420 to make 431? Â If you're like the vast majority of people you intuitively recognize that you just need to "count up two" from 429 to get to 431. If your dd is not doing this with the n + 1 math facts, she either doesn't have a deep enough understanding of addition, or she doesn't have a strong enough number sense to know that, for instance, 8 is the number that's next in sequence after 7.Â
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The exercise Tjej suggested will help. If she doesn't understand why this works, or how to use it try using counters so that she discovers the inefficiency of counting over from 1. Give her 8 pennies in one pile, and 1 penny in the other pile (or any n + 1 problem). Explain that this is a type of addition exercise. She's to count the pennies in one pile, then the other, than work out the sum, writing it down like this: 8 + 1 = 9. The first few times she does problems like this, she may count the 8 pennies, and then she may count them all over again to include the ninth penny. Do a bunch of similar problems. At some point she will realize (or you can point out) as she begins the second count that she's duplicating her counting. "Wait a second, you already know there are 8 in this pile. You just finished counting these. I heard you say 'five, six, seven, eight.' [pointing as you go] So what's this one over here? Seven, eight, ____? Right! It's penny nine!"Â
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If she's not getting it, she may need lots more practice at ordering sets and objects, in playing with dice and markers, etc..
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Also very productive for my kids have been number guessing games like "I'm thinking of a number that's bigger than 6 but smaller than 12. Guess and I'll tell you whether you're correct, to big, or too small." We've played these sometimes for hours in the car. Back and forth between cluegiver and guesser, increasing the complexity, or adding in twists, for fun and for challenge.Â
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Miranda
Mountain mama to two great kids and two great grownups
<shrug> One of the reasons I homeschool is so that people who don't know my daughter or aren't familiar with rightbrained learning or who assume everyone thinks the same won't waste everyone's time assuming she's remedial when she just thinks differently.
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She is extremely strong on the concept of numbers and order. She also definitely knows intuitively not only what is a bigger or smaller number, but can even look at two separate unsolved sums (say, 5+6 and 4+9) and tell me which sum will be bigger (without solving). Spending more time on that will just bore her stiff. Yes, I do work with her on getting her to count from the larger number, but I certainly don't need to go back further than that, thanks.
Homeschooling mama to 6 year old DD.
Okay, I was just trying to be helpful. I would not have thought of memorization as a particularly productive strategy in a rightbrained kid. That's certainly not how my rightbrained kid learned math. But I'm sure there are many different ways of being rightbrained.
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Miranda
Mountain mama to two great kids and two great grownups
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Single mom to Rain (1/93) , grad student, and world traveler
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I agree that this is how MY brain works with the n + 1 stuff. But I see with my DH (who is, obviously, grownup, intelligent, etc.) that his brain is wired differently, and DD is clearly similar. DH finds it difficult to look up things in the yellow pages, for example.
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Believe me, I'm no "sit and drill with flashcards all day long" kind of person. In fact, I originally assumed we wouldn't do it at all until we got to the multiplication tables.
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However, I see the flashcards helping the CONCEPT click, not just the memorization skills. We did do n + 0 (and I have to add here, that if it's standard that no child should ever need n + 0 or n + 1 flashcards, then why do they come in my prepurchased standard flashcard pack?) and she very quickly got it. Before, she got it but then would sometimes forget the concept. One round with flashcards and it's solid, weeks later. I don't bother with n + 0 anymore.
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n + 1, she will be shaky on the first few when we start. (We've only done them twice at this point, with a week between them). She will answer them correctly but have to figure it. And then it'll "click" and she gets it and start answering the questions easily.
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Right brained kids do VERY well with memorization as they are visual creatures. So flash cards and other visual aids (also guidance to picture things in their heads) are major tools for the right brained child.
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But the tools of memorization are doing a lot more than helping her memorize  in fact, I daresay she hasn't memorized a thing yet, really, It's showing her the concept. When I explain to her about the "next" number it doesn't sink. When we do worksheets with different facts, it doesn't sink. When we sit there and do flashcards for n + 1, bam, bam, bam, it clicks. She sees the pattern. I will find out soon if it's sunk in permanently yet or if we need a few more rounds. I have at least noticed that even if it's not permanent yet, it takes a lot less time for it to click now; it clicked a few times and it's easier to remember it. Obviously we have to get her to the point where it doesn't have to click anymore, it's just there, but the flashcards are literally the only thing that produced the click at all.
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Since rightbrained people are highly spatial but not so verbal, I think it's harder for my DH and DD to access the "next" number or the "next" letter (looking up stuff in the dictionary). It's easy for me to find H after G, or 5 after 4. But while they see relationships between things (and probably better than I do), it seems "directionality" is not as strong for them. DD mirror writes and sees things written backwards just as easily as forward because it doesn't matter to her. To my leftbrained way of seeing things, it matters a heck of a lot.
Homeschooling mama to 6 year old DD.
Â I was considering various curricula, but I think I have enough materials for facts for a while, plus other things (workbooks, the book "Family Math" and a set of first Grade Brain Quest) to take up at least the entire summer. I just want to get her up to grade level (as opposed to where she and her class are at her school).
Have you ever read Anno's Math Games and it's sequels? Â They read almost like story books. Â The n+1 that is being discussed here is represented in a section by a magic machine. Â 3 birds fly in one side and 4 come out the other. Â Then 4 dragonflies go in and 5 come out. Â First you are asked, what does this machine do, anyway? Â Once you've figured out what this fantastic machine does you are asked, what would happen if the 4 birds flew back through again? And again? Â And again? Â Then what would happen if the flew in the opposite direction? Â What do you suppose would happen then?
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I just love this series, because there are no places to write an answer, you can just read it like a book. Â Sometimes the scenarios are pretty fantastical, like magic glue and the magic machine mentioned above. Â The three books altogether cover a lot of math concepts. Â What I love most, besides the art and storybook style, is that the concepts are taught in a way that is anything but memorization. Â I was always good at memorization in school, and it has served me quite well in a basic way, but purely visual, mental concepts are extremely slippery in my brain, and that is what these books focus on. Â Wonderful books for firstgraders like my oldest daughter. Â
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"Let me see you stripped down to the bone. Let me hear you speaking just for me."
Ack!, Learning is so complicated! Â (and I have a master's in Education!) Â
Luckily homeschooling does not need to follow a prescribed order. Â My daughter figured out the concept of multiplication shortly after she learned to add and loooooong before she thought about subtraction. Â
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Sometimes I think that folks with education degrees have a harder time *embarking* on homeschooling than those of us without. Â I have nothing to back that statement up, it's just something I notice and wonder about sometimes. Â If something my daughters do is entirely different from what they are "supposed" to be learning at whatever age it's easy for me to accept and rewrite what I understand about how kids learn. Â Perhaps because I'm just learning how *my* kids learn and haven't bothered much about how kids learn in general. Â Am I making sense? Â I mostly just take things as they come, with a bit of a view of what's on the horizon and my overall goals. Â
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When starting out I think that less can be more. Â Especially, less thinking, more observing.
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"Let me see you stripped down to the bone. Let me hear you speaking just for me."
It is very individual.Â With math, some people can get a concept first and then have no trouble learning facts in a haphazard way and assembling them all to be organized in their heads.Â Others can get the concept fine, but find it impossible to accumulate the facts without a methodical, gradually building approach.Â And some people really do better to memorize first because that is easier for them, and then with lots of practice, the picture of how the numbers relate to each other comes together in their head and that is how they finally get the concept.Â I think I am the last kind and when I learned math, the approach that was used was the opposite of what I needed, and I was a kid who was labeled with a "learning disability" in math, staying years behind and having to repeat classes...and it really didn't come together for me until college.Â I don't want our kids to have the same struggles, so I experiment to see what is the best way for each of them to both learn the facts and get the concepts.Â DS2 is completely different than DS1.Â He gets the concept of addition, and he is catching facts like bugs in a net and retaining them without any need to learn them in order.Â He could probably learn them really well through games that offer random factsalad.Â But DS1 just can't get them that way.Â I tried it that way for 2.5 years and he just could not learn like that.Â This is his 3rd grade year and I have had to stop all math and take him back through the beginning with a program that does it in a more methodical way.Â He is finally learning them.Â I wish I had realized earlier that this was the approach he needed.Â Not many math programs do it this way anymore, because it's very boring, oldfashioned etc.Â But this is what he needed all along.Â
and 3 , in our happy secular
Look at Timez Attack.Â They have a free beta (I think) of the addition and subtraction modules.Â
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We have done memorization for multiplication and division with Timez Attack.Â If we get much further and anyone needs fingers for 9 + 6 or 12  4 then we'll have to break it back out.
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