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  1. Dreambox has a monthly fee, but it's terrific for developing good number sense and mental math skills. (And fun, too.)
  2. Oh my goodness, it sounds like you have a child who REALLY thinks ahead! Thanks so much for taking the time to post this--it totally made my day. That's wonderful that she enjoyed it so much. In the works, but it will still be a while... Yes, the $200(!) price on Amazon is my self-published version that is now out-of-print. Well-Trained Mind is publishing a new edition, with a lovely professional layout and way more adorable cover than I was able to put together on my home laptop. (The Amazon page is here. Amazon is projecting it to be available January 3rd, and you can watch the forums to see when WTM has it in stock on their website.) Subtraction Facts will also be coming out in January, with Amazon expecting to have it available January 31.
  3. I'm not personally familiar with one, but try asking over on the High School board. I bet the parents there would have a lot of good suggestions.
  4. It can be so challenging to tease out what exactly is responsible for learning (or lack of it!) So many factors impact how we learn that it can be hard to separate out only one. But, it's certainly true that brain maturity is an important one of those factors. Sometimes, kids just aren't quite ready to "get" a concept, and they just need a little more time to grow up before the concept becomes understandable. My most dramatic experience of this was last year with my daughter, who was in kindergarten. Her little five-year-old self just could not deal with the written minus sign. She would happily answer questions about taking away stuffed animals and counters, but she got completely frustrated any time I tried to put a simple written subtraction problem in front of her. After banging my head against this wall for a week or so, I realized that it was simply a matter of maturity--and that it wasn't worth worrying about for a kindergartner! I kept on working on subtraction with her, but only with manipulatives. Six months later, the subtraction sign doesn't pose any problem to her any more and she's now moved on to translating word problems into subtraction equations. I didn't do anything magical to make the change happen, but her brain just matured.
  5. I highly recommend going in order. For the most part, the chapters build on each other very elegantly: skip-counting from chapter 2 is used to find areas in chapter 3, which is then formalized as multiplication in chapter 4, which is used to go in-depth with perfect squares in chapter 5, and on and on. However, like Bolt said, chapter 1 is a big exception to this! It's crazy hard, and fine to save for when you need a break from all the multiplication sometime in chapters 2-5.
  6. For the Independent Learning Module, it's really up to you. I'll be using the main textbook (Elementary Mathematics for Teachers) as a spine for the course and referring to it in the lectures. However, you should be able to understand the lectures just fine without having read the textbook. If you'd like to do the problem sets that accompany the lectures, the textbook is a must. It frequently refers to the Primary Mathematics books and asks you to analyze teaching sequences in those books. It most frequently refers to 3A, sometimes refers to 4A, and only occasionally to 5A. So, if you'd rather not buy 4A and 5A, you'd still be able to do most of the problems, but not all.
  7. This discussion board is for all students enrolled in Math That Makes Sense: How to Teach Elementary Arithmetic (live, delayed, or independent learning module). Here, you can discuss the topics we’ve studied in class, pose questions, and generally think “out loud†(or at least, in writing) about how your learning is impacting your math teaching. Just as our kids learn best when they have a chance to think through new ideas and try new things in a supportive environment, my hope is that this board will be a place where you feel encouraged and stimulated as you develop deeper expertise in teaching elementary math. I’ll be checking the board weekly until January 2017. My focus will be on our in-class discussions, but I’m excited to see how you use this board to collaborate, share stories and resources, and follow any rabbit trails that the class inspires. Happy math! Kate
  8. For equivalent fractions, try using simple hand drawn squares. Use vertical lines to subdivide the square to match the denominator of the simplest-form fraction, and shade the rectangles you make to match the numerator. Then, use horizontal lines to divide the square to match the denominator of the other fraction. The beauty of cutting squares like this is that it helps show why we multiply both the numerator and denominator by the same number to find equivalent fractions: the shaded rectangles (which represent the numerator) and the total number of rectangles (which represent the denominator) are being cut by the same lines, so they increase by the same factor. Here's a quick sketch I did to illustrate. Hope it makes sense!
  9. How about bedtimemath.org? They provide a math-y story of the day and then three levels of questions (for kids of different ages). The Evan Moor 2nd grade daily word problem book would fit the bill, too. They're stories about animals, with a wide variety of problems as well as some charts and graphs.
  10. Five is definitely too early to worry. It can be crazy-making when you feel like you've gone over the same thing over and over and over, but it's very developmentally appropriate for kids to struggle with reversals for quite a while. Their spatial sense just isn't quite developed enough to always get them straight. My son took until he was 8 to consistently get all of his letters and numbers correct, and my almost-six-year-old is still working on it. Here's a blog post I wrote on it with a few tips (Help! My Kid's Numbers are Backwards), but my main advice is to make sure your child has an alphabet and number strip always visible at her table so that she can look at it whenever she needs it. It will help imprint the correct "picture" of the letters and numbers in her brain--and keep you from always having to be the reversal cop.
  11. I've been mulling over some of the same considerations as I try to figure out what to do with my 4th grader for Latin next year. He tends to happier with whole-to-parts curricula--but he often underestimates how important all of those "parts" are. So, I've been trying to figure out a Latin path that will keep him reasonably engaged and interested but still give him a thorough knowledge of the grammar. I'm sold on the idea that it's important to master the grammar--but I know it needs to be fun and interesting enough to keep us going through the whole grammar. We did Getting Started with Latin this year, and it was a perfect intro since it never overwhelmed him with too much memorization at once. The daily exercises gave plenty of context to see the point of the declension or conjugation that he was learning, and the constant review allowed him to truly master the 1st and 2nd declension and 1st conjugation. Now, I've decided to go with Memoria Press' 3-year Henle I program as our main program, along with reading Lingua Latina once a week. What I like about Henle is that it focuses on grammar mastery and introduces only a limited vocabulary (like FFL) but provides passages and sentences for translating right off the bat. We'll still focus on the same grammar as if we were doing FFL1 (noun declensions and adjectives), but the exercises feel like a better balance between drill and translation.We'll read Lingua Latina once a week (or rather, listen to the author read it to us) and discuss the questions in the Pensum to keep Latin interesting and work on the direct reading skills. I expect this will be very informal, and that we won't get through too much of it, but it should be a nice counterbalance to Henle. Wish I had some btdt advice for you, but this is what I've got! :) I'll be curious to hear what you decide to go with.
  12. Binary's apparently very useful for understanding programming (according to my techie husband--I don't know much about programming myself). But it's certainly not an essential 4th grade math topic, so don't sweat it if it's stressing out you and your ds . :) If you want to give it one more go, I think the most helpful tip is to start on the "left" of the binary number when you're converting base-ten to binary. But, start on the "right" of the binary number when you're converting binary to base-ten. So, looking at p. 94, to convert 101 to binary, you start on the right side of the number (the lower place-value): "Okay, I have 1 one, no 2s, and 1 4. So, that's 5." This is a lot like adding up the expanded form of a number (such as thinking of 364 as 300+60+4), but each digit stands for one of the powers of 2 rather than our usual multiples of a power of 10. But, when you convert base-ten to binary, you start on the left side of the number (with the higher place-value). So, on page 95, to convert 50 to binary: "No 64s fit into 50. I'll put a 0 in the 64s spot. One 32 fits, so I'll put a 1 in the 32s spot. Now I have 18 left to account for. So, I can fit one more 16 in, and one 2 to use up the rest of the number." So, the answer is 110010 (since we drop the initial 0 for the 64s place). It's kind of like the repeated subtraction we do in the long-division algorithm, but you're always subtracting powers of 2. Clear as mud? ;) Truly, not a big deal if you skip this one.
  13. Another vote for a GSWL Level 2 here! I'm in the same boat as the OP: rising fourth-grader, finished GSWL, love the short lessons, and enjoy learning along with my son. I've hemmed and hawed for the past month and finally decided to do Henle with the Memoria Press First Year Henle guide. It feels a little crazy to be doing such a dry, academic program with a fourth grader, but I'm hoping to use it in the same style as GSWL: short, ten-minute, conversational lessons each day, learning each declension piece by piece and gradually adding words to his Latin vocabulary. I love Lingua Latina (and used it for self-study a couple of years ago), but I think it wouldn't be sequential enough for my son. He's really thrived on learning the grammar bit by bit in GSWL, so LL didn't feel like the right fit for our main curriculum. I'm planning to use it as a reading supplement every few weeks, when we need a little variety or my son needs some time for the grammar to sink in.
  14. Oops, I was just working with my daughter and realized that Book 4 is the one with the syllabification rules! Sorry for the mistake!
  15. I agree, AAR would be overkill. The one thing to watch out for is how well he's doing with decoding unfamiliar big words. A lot of kids hit a wall with multi-syllable words right around the 4th-grade level and still need some explicit phonics instruction to make sure they get past it. Explode the Code workbooks are a thorough, inexpensive phonics curriculum you could use to make sure your son masters these skills. (If you went with them, you'd probably want to start him in Book 5 for practice with syllabification rules.)
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