I have found quite often that if I ask a child to explain the answer, I discover that that answer really does make sense from the child's point of view. This is especially true later, when they get to story problems. It's surprising how differently things can be interpreted -- language is not nearly as precise as we think, and children don't always know our presuppositions. (I'm a bit off topic, since Miquon doesn't have many story problems, but I'm sure we ran into the different-interpretation thing on some M pages, too. It's just so long ago that I don't remember which.)

100 Recommended Science Fiction and Fantasy Books for Junior High Students

It sounds to me as if you and dd are both discouraged, so that math has become as much about emotional baggage as about number concepts. When students become discouraged, their brains tend to clam up in self-defense -- they go into survival mode, only taking in enough to make it through today, and refusing to care about long-term understanding. Why care about the impossible? It would hurt too much. There is a math program designed especially for children who are in that self-defense mode about math. It won't cost you anything to try it, except the cost of some printer ink and about one month's worth of lesson time. It's a different approach to teaching, and to make it succeed will probably take a bit of mental revamping on your part as well as hers. But if it succeeds, it could make a world of difference for your daughter. Background to help you understand the program External Research that Supports JUMP Math's Approach The barriers that keep students from learning math, and how JUMP Math is designed to answer each problem. Teachers, students, parents, tutors and other educators describe their experiences using JUMP Math Videos about the program. The most helpful to me in understanding the program were the videos featuring John Mighton and . The latter includes encouraging comments from several students, too. Review of JUMP Math at the NY Times What you need to start the program You have to create a free account on the website to download the books. Everyone starts with the Introductory Unit on Fractions, then after your student finishes that unit (which should take about a month), you proceed to their grade-level book. You and your daughter would need the unit for 5&6th grades: Teacher's Manual for Getting Ready for JUMP Math: Introductory Unit Using Fractions (read and follow it carefully) Student workbook Answer key for practice test and final test

I don't know how CTS translates this, but in the logic statements I've seen before, the squiggle means "not" whatever comes after it. Since what comes after it is the parenthetical statement, the squiggle is basically claiming that "If C then D" is not true. FYI: You can make an arrow while typing with two dashes and a greater-than sign: "-->".

If you want to be able to download a single big file to cover a year's worth of material, you want the grade level workbooks. The links called "doc" will give you a Word file of student lessons and exercises. The links called "AK" will give you the corresponding teacher file with answers and additional comments. Not all grade levels have these all-in-one "doc" files. If you click on the words "For students in Xth grade", that will take you to a page that lists all the KISS exercises, some of which will be links (meaning there is an exercise for that lesson in that grade level). These are exercises covering the SAME topics that are in the big grade-level workbooks, but using sentences from DIFFERENT literature. If you want to blaze your own trail, you can follow those links and find literature that may match what your child is reading. These print perfectly from the webpages, but you have to print them one by one, and be sure to also print the "Instructional Material" and the "AK" (means "Answer Key"). The exercises will be the same as in the big all-in-one workbooks, but the sentences will be different. But if you want to keep it simple, just choose the all-in-one grade level workbook that is closest to your child's level and stick with that. WHATEVER grade level your child is in, he or she should start with KISS Level 1. Each KISS level is approximately one year's worth of work. The KISS levels build on each other, and they must be taken in order. If your child has done other grammar before, he or she may be able to skip several individual lessons, but you must do enough of each level to be sure that the topics (and the style of marking a sentence) are mastered.

Free resources: Guide to everything about fractions Understanding division of fractions Analyzing a story problem about fraction division

Excellent: Guide to Everything Fractions I did notice a typo, p.9 (and where there's one, there may be more), but this is a very thorough set of lessons to help you really understand fractions -- and you can't beat the price! Also extremely good: Division of Fractions Starts with a review of dividing whole numbers, and then applies this to understanding why fractions work the way they do. Test your understanding: The Frustrating Fractions Quiz If you can explain the answers to these questions, then you truly understand fraction math. (Answers are in the comments below the post.)

Ed has discussed diagramming: Diagramming Sentences within the KISS Approach No, thanks! I'll stick to marking up the text the KISS way. It makes sense to me, lets me understand the sentence, and doesn't take nearly so much space.

I would take it even farther than that. Trade off with her, doing every other problem yourself. Whenever we have a difficult task to do, it helps to have a buddy share the load -- and right now, math is a very difficult task for her. She has spent several years excelling in a world that called for a follow-the-recipe understanding, and now you've thrown her into a new world that demands conceptual understanding. HUGE transition to make! For further reference: Buddy Math (how my daughter and I got through MM4) Relational and Instrumental Understanding (explains the difference between the school's goals in teaching math, and yours)

You've gotten some good answers so far. Let me see if I can think of anything to add... Important Background Information The key to understanding the KISS Grammar system, IMO, is A Psycholinguistic Model of How the Human Brain Processes Language. In this article, Dr. Vavra explains how we can understand sentences longer than seven words, even though we only have (on average) seven slots in our short-term memory. They "chunking" process he describes is what KISS Grammar teaches your student to analyze. If you're going to use KISS Grammar, you definitely want to join the KISS Grammar Yahoo Group, where you can ask questions as you work through the lessons. You WILL have questions! Choosing a Grade Level The easiest way to use KISS Grammar is to pick one of the grade level workbooks, and you should normally pick one at or below your student's grade level. My daughter used the 2nd grade book in 2nd-4th grade (we stretched the lessons out and took several long breaks), and then used portions of the 3rd and 4th grade books for 5th and 6th grade. Just this fall, as we were headed into 7th grade, I noticed that Ed had a 6th grade book out. At the rate we're going, it will probably last us into high school. Getting Started To start with, download the level 1 doc file (student book) and AK file ("Answer Key" - teacher book) for whichever grade you choose. Read through the book and try some of the exercises for yourself. Decide which ones you want your students to do and print those out. (It really helps if you print the answer keys in color.) If you have done other grammars, you may find that much of level 1 is review, and you can probably skip several of the lessons. The most important lesson in level 1 is identifying the types of complements, emphasizing the analytical process, so make sure your student masters that! Points to Remember My daughter and I use the buddy method to work through our KISS Grammar lessons: I do a sentence, then she does one, then me, her, me, her, all the way down the page. This year, using the 6th grade book, the sentences are much more complicated, and we will often do only two (one for each of us) or four of them. It may take us several days to finish one workbook lesson. Do not feel that you need to hurry through the workbook. We are learning together, and even one sentence a day is a good workout, when that sentence is near the edge of the student's ability to analyze. Also, keep in mind that mistakes are expected. Some phrases are complex, and we don't want to confuse students with all the nuances at first. So, for instance, until they have studied verbals (introduced in level 2, but not fully mastered until level 4), students will probably mark infinitive phrases as part of the verb. That's fine! And remember that alternate explanations are often equally valid. Sometimes Ed mentions alternative ways to mark a sentence in the answer key, but he couldn't possibly think of every alternative for every sentence. If the student's explanation makes sense to you, it is probably fine. Whenever you are unsure, feel free to post the sentence and analysis on the Yahoo group. Continue Through the Levels Take as long as you need on level 1. When you and your students are completely comfortable with that material, then go back to the printable books page and download the level 2 doc file (student book) and AK file ("Answer Key" - teacher book) for whichever grade you choose. Again, read through the file and decide how much you are going to do, then print out what you need. Work through the level 2 lessons at whatever pace is comfortable for your student -- even if it's only one sentence per day, or three sentences per week. The important thing is to master the material, not to get through it in a certain amount of time. When you are completely comfortable with the material in level 2, move on to level 3.1, and so forth.

The throat spray that numbs everything is great if you get "Sonlight Throat" from all the read-alouds.

Or here are some free resources online: An Economics Fairy Tale I, Pencil That Which is Seen, and That Which is Not Seen Economics in One Lesson Lessons for the Young Economist

Henry Hazlitt Economics in One Lesson. Thomas Sowell Basic Economics. The Myth of the Robber Barons by Burton W. Folsom and Forrest McDonald. The Invisible Heart: An Economic Romance by Russell D. Roberts. I also like the Great Courses set Thinking Like an Economist, even more than their regular Economics course. (To save money: Wait for it to go on sale and get the audio download.)

I don't know anything about their online program, but the card game 24 is great!

I have a journal of favorite quotes from math books I've read, which is the only journal I've ever kept up long-term. I also at times have kept a journal for problem-solving, but it tends to get lost, and then I end up using scratch paper, and then losing that! One year my son had a journal for learning bar diagrams, where he did one problem per day (which I copied out for him from the CWP books). One of my daughters kept a journal of vocabulary and other important notes to remember. My youngest is a writer, but not a journal-er (she's like me), so we tend to work things out on scratch paper or a white board. But a couple weeks back, she got stumped by a new concept and let it stew around in her mind, and then she wrote out a long explanation that would have been perfect journal fodder. She turned it into a blog post -- I guess her blog is her journal -- but I don't think she's hit the "publish" button yet. A friend of hers has written several math explanations on his blog: http://climbinggecko.wordpress.com/ More about math journals, from my math blog: Writing to Learn Math Writing to Learn Math II

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Explore Don Cohen's Map to Calculus -- just click, browse, enjoy! Lots of interesting ideas to play with. The items are numbered in the order they show up in the book, I think. At any rate, the book starts with Infinite Series (which is #1 on the map), and a lot of the later activities refer back to that.

Another thing you can do with Buddy Math is to let the student choose which problems to do in what order. Sometimes my daughter liked to take a zig-zag path down the worksheet, just for something different -- and if there was a problem she felt would be too hard, she could avoid it (that is, make sure it came up on my turn). We have also taken time away from formal math to just play around and read library books. There is really no rush to get through arithmetic, and there are so many interesting things to do. Try taking a look at MoebiusNoodles.com for activity ideas that will stretch your daughter's understanding of mathematics.

I don't know of any US program that does as good a job teaching ratios and proportions as Singapore Math, and those topics are super important. I'd say stick with the course. It's easy to add in the few things that are usually included in prealgebra but that Singapore leaves till later. For example: Negative Numbers for Young Students Graph Mole and Line Gem

Most of the principles are the same, but the implementation will be specific to Blogger. So, for instance, you will still want the same things in your sidebar, to help your readers, but you will have to do them Blogger's way.

Student blogging can be a load of fun. I taught a blogging class for a few years at our homeschool co-op, until we changed buildings and lost our wi-fi. Most of my lessons are online, though, if your kids would like to work through them. The best of my students' blogs, for inspiration: Kitten's Purrings Intellectual Ramblings College & the Years After Nate's Nook Chicken Scratchings Moonlight Press And from my "correspondence course" students: King's Daughter Photography With Binoculars in Hand Musings of a King's Daughter Ponderings from the Son of Encouragement Mental Weight Also, be sure to check out the Homeschool Kids Blog Carnival!

Two ideas that I don't think have been mentioned: Books by Brian Bolt might be just at his level. My library carries several of these. Discovering Trigonometry with Sticks and Shadows (online lessons)

Definitely ease off on the errand-running days! Usually, I let independent reading count as "enough school" on days like that. You've gotten a lot of good advice here, and I don't have much to add. But here's a tip from my years with Singapore Math: A review (do they still call them "revision", or has that been Americanized?) is a chance to re-see the topics -- that is, to see them again, remember, draw them back to mind, and deepen the student's understanding. DO NOT use these as an "end of term" test!!! Your student should not be expected to go through these independently, as if she was a mini-computer with instant recall of everything she's ever learned. Humans don't work that way. Instead, go through the reviews together, with a "Let's see how much we can remember" attitude. If she remembers how to do the problem, let her "teach" it to you. If she doesn't remember, offer a hint -- often a few words will be enough to pull the concept out of the dust bunnies of her mind. And if she still doesn't remember, start the problem yourself, explaining as you work through it (slooooowly!), and let her jump in whenever she thinks she can finish it off. Okay, I do have two more ideas to add, which are applicable to any math program: 10 minutes per grade level: That's about the limit of how long you can expect the student to pay attention. Mental work is just as hard as physical labor. From grade 4 on, it's good to split the time into two chunks with a break in between. Buddy math : Having a partner makes any task more bearable, especially something difficult like math. I enjoy math, but it can be difficult, and facing a whole page of problems all alone can make it overwhelming. This will also help you curb her habit of working too fast and sloppy.

This sounds like a variation of Cassino, an old, Italian card game that shows up in Jane Austen's Sense and Sensibility. In Cassino only addition is used, and you can't combine cards in your hand but only on the table. The combining is done in one turn (making a "build"), and then you capture that stack in your next turn. This introduces a bit of suspense, since you have to hope no one else attacks your build in the meantime. Also, in Cassino, you can capture multiple victims, as long as they all add up to the number of the card you're using to capture them. Cassino is fairly easy to adapt for multiplication, division, and negative numbers (and even exponents and roots), as well as addition and subtraction. If you don't want to make up rules for yourself, there is a card game already prepared: Mathino website

It's a back-and-forth thing. You see one type of molecule that is out of balance, so you fix it. Then you check to see if that fix threw anything else out of balance. And remember that you can never have half a molecule -- for instance, you can't just increase the Oxygen in H2O without also increasing the Hydrogen. So you just go from one side to the other, checking and balancing, until everything matches (same number of each type of atom on each side). And then, when you have it all matching, then you look one more time: Are all the numbers of molecules even? Or all multiples of three? If so, you need to divide all the way through to put the equation into "lowest terms" or simplest form.