Hey, what are some of your favorite explanations and examples for teaching "Averages" and the nuances for different averages (mean, median and mode)? Does your curriculum teach it in a memorable, concrete or relatable way at the elementary level? Did your teacher when you were in school, teach it in a way that made it understandable and memorable?

We don't use a published program, instead we do a lot of "read-draw-write" from regular bookss. Before we make an effort for the kids to learn history though, we teach Geography systematically first. We take the time to put a strong visual map in their minds. Start with the continents, oceans, mountains, deserts, rivers, etc. The physical geography and geographic regions. Then they learn the countries of the world geographically and once they've done the whole world, we go back and do each continent by region again. We mention "there used to be a country called, such and such here" and things like that. After a strong geography base, we do world history from this book and fold in lots of other library books. It seems' to be working very well.

I have the Teacher and Student books for NL Science 3-5. I love that it really develops the students knowledge base while guiding them in close-reading and directly coaches them in study skills. I wanted something systematic and knowledge-based. The NL program is packed full of information and my kids love the whole highlight-draw-color interaction with their texts. They retain the information after going through the booklets. We do a lot of "just-read" so actually having workbooks or booklets is novel to them and they enjoyed it immensely. They've been able to apply the same type of annotate-the-text logic to their regular books and suddenly their retention in history is shooting up too and the interactive reading from science is also spilling over to novels and chapters books for Jr. too. In my opinion, the informational coverage is really really good for elementary science. I love that the students are expected to still know the information much later and the booklets make it easy and realistic that they go back and re-view any information that may have been covered earlier. It's pricey, but it covers Science well, and includes Reading Comprehension and Study Skills, so it's kind of 2.5 courses in one. We do science every day, so a level doesn't last us a full year, but I'd rather a solid and foundation in study skills and the boost in reading comprehension be laid early and reinforced often before we get out of Elementary years. If you get the full kit, then you have a lot of digestible information and the manipulatives and doo-dads that make it all "pop" for a pretty good price. We did the books for Levels 3-5. We have access to a ton of Science manipulatives and so we pull those together if it's something that's needed vs a "nice to have". We didn't really add anything, other than we included NL in what we were already doing. "Just reading" quality nonfiction books. For my kids there's definitely been a difference in both their science knowledge and scholarly reading skills since we went from "Just Reading" to "Just Reading, NL and applying the techniques of NL to whatever it is that we're 'Just Reading'". What made me keep at it is that it's engaging, the kids loved it, the program was very do-able, straightforward and was making a positive difference in my childrens education and literacy skills.

Well I'm more finnicky with the way things are verbalized, but I was just responding to the OP about "what does it mean to show work for a problem of this caliber" for young kids. By the time my students are in a position to write out the work to problems of this caliber algebraically, they've already learned to think through the problem and discuss the solutions. I gradually teach an explicit understanding of equality and the equal symbols so there is a background of understanding before the kids get there. You've clearly lead a long and full life without a particularly clear understanding of whatever it is that you missed in Arithmetic and/or Algebra, so you know how little it will impact you in the long-run if you do or don't get this concept while in school.

10-A = 9 would be solved and written out so that the equal signs are lined up, one equation per line, and with shorthand because I teach my kids to verbally, explain the answer so they'd tell me "add A on both sides", then "-9 from both sides" and "so you can see A is 1" so mathematically the working would look like this: 10 - A = 9 | +A on b/s 10 = 9 + A | -9 from b/s 1 = A They don't do write out the middle steps, but the note what that step is.

There is a story that involves 2(or 3 generations) of a family. The basic premise is that the Children of the latest generation are being baby sat by an estranged Uncle that they don't really know much about. Their Dad (the brother of the estranged Uncle) doesn't like his siblings and the kids don't know why. Estranged Uncle tells stories about the childhood of himself, and his brother -- I think that there's a couple more siblings from The Estranged uncle's Generation. In the Estranged Uncle's flashbacks, I think he talkes about "Uncle Sam who came for 1 week and stayed 16 years" or something along those lines. So, those would be the 3 generations that I'm remembering. My kids want to read this book again and for the life of me, I can't recall the title.

Keys to Algebra is a series of 10 workbooks that I think goes over Algebra 1 No Nonsense Algebra is a workbook that goes through much of Algebra 1

Are there any local middle or highschools around that might appreciate the donation?

It sounds like the school has a particular system worked out for how they use Abeka materials. You should really speak with the school. IF they've placed her in the 6th grade level of certain subjects, talk with them and find out what is their stated plan for next year and the rationale for that plan. Abeka publishes materials for up to the 12th grade for many subjects so it is possible that a student could just be advanced a year in some of the subjects outside of the 3Rs. Definitely talk to the school.

No, but @UHP has used a few levels of SRA Connecting Math Concepts-- I think she has experience with levels D, E and F. I've seen the student book for SRA Level C and was impressed with it.

I purchase them used for steep discount--it takes a while but if you keep your eyes open they appear. For each level, you need the Presentation Book and the student materials. For Level C that's a workbook and textbook. For Level D and above it's just a textbook. You don't absolutely need the Teachers Guide or Answer Key--you'll know the correct answers from delivering the lesson to the student, and the Teachers Guide is a nice pacing schedule/over view but isn't used on the day-to-day at all.

I love the instructions and techniques in 100 Easy Lessons, but I remember noticing that the phonics covered were incomplete though it's been years now so I couldn't say exactly what it's "missing", but I don't think it teaches all of the sounds that a child will need to know. I would teach through the Ultimate Phonics Word Lists for a few months to hit the remaining phonics patterns and sound combinations, as well as work on Multisyllable words. It includes sentences for fluency building. Doing this and continuing your plan of reading a book a day and asking questions each day should be sufficient to get her through all of phonics and build her reading stamina and comprehension.

Is the assumption/given that I have access to sufficient reading material? If so I will put my energy into teaching reading and writing. Since I now feel able to teach basic spelling from a phonics book, and handwriting with just a pen(cil), highlighter and paper, I would make my 4 items: 1) Open Court Foundation Program ( Blue Book + Gold Book ) which makes a powerful 1 year reading program for beginning students and can be used to teach spelling as well. 2) WISE OWL Polysyllables for extending the phonics skills to longer words in context and vocabulary development. 3) SRA Reasoning and Writing C 4) SRA Reasoning and Writing D

I will disagree with you on the bolded. This is a matter of teaching sequence and the amount of "microconcepts" and "microskills" taught and mastered before hand. A student that has mastered the appropriate Place-value "microskills" of combining mathfacts and regrouping skills will not need to learn to add/subtract 2-digit, then 3-digit, then 4-digit, etc problems. Instead, they can apply their understanding of "microconcepts" and "microskills" to calculating any amount of digits on the same day that they learn the vertical addition/subtraction format type.

I only browsed the article, but I'm glad that more mainstream educators are thinking about and discussing the need to correcting the Pendulum Swing in Education away from Knowledge to Thinking. Or at least talking about how there needs to be a thoughtful balancing of the two. Obviously, a person can't think critically when they have no knowledge to think with or think about. It's a little hard to understand how this is even "news" to anyone who's been in education for a couple of days is a little unsettling. Talking about teaching "critical thinking" ignores the fact that a human being is naturally always thinking and will naturally think about whatever knowledge, experiences, skills and materials that they have access to and will look for connections between what the know when faced with a normal everyday problem. Just watching a toddler solve the problem of getting something that's out of reach--they'll use whatever tools that they have access to to either knock it down to the their level or get up to the prizes level. Trying to lay a foundation with "critical thinking" instead of "knowledge and skills"has always been a "cart before the horse" type of thing.

Ours is a family that definitely tries and front-load as much as possible while the kids are young, so I guess the Gift of Time is earned back in school years when you've got time and options to go in different directions. We're always trying to monitor the Effort:Easy ratio for our kids. So far, none of our children have presented serious learning challenges, which has allowed us to keep on the continuum at an accelerated pace. It's interesting because we know that by the end of Elementary we want the kids to have 1) Good concentration skills (1 hour) 2) General Knowledge Base (facts and connections in science, history, geography, technology, art, music, math and literature) 3) Solid drawing skills--able to accurately draw things that they've seen as well as able to draw things from their imaginations, and draw mental maps for knowledge as well. 4) College-ready skills in mathematics and reading. For the 3Rs' our biggest priority is that the kids end up with fluency, automaticity and rock-solid mastery so we try to make the accumulation of these skills as gradual and straight forward and rewarding as possible. We are always on the hunt for the best explanations, the best structured exercises and lots of well designed drills. Instead, we encourage problem solving and productive struggle in athletics, music, and real life during the elementary years. We do try and teach perseverance and effort. However, we've found that keeping things at their level also keeps the effort level reasonably high. I wish that I had a better grasp on where the best place to push was, but I don't feel that I do. I do not that there have been seasons where it feels like even simple things are difficult and so scaffolding or backing up is appropriately challenging. Then there are seasons where everything is effortless and we sail ahead. I think that it requires active monitoring and constant reassessment on the part of the parent/teacher. What's a gentle push at one point might be a mighty-shove at another and you just have to keep checking on the child to see where they are and how they're doing.

First, wind what stage he's orally fluent at, then start there. Building oral fluency is easier if you use text much lower than his independent reading level. Get a ton of easy readers and early chapter books--many of them are meant to be read with expression to bring the stories to life. We look for fluency at the word level, couplet level, phrase level and sentence level. There are different levels of sentences too, so simple sentences are hardly more challenging than phrases, but a complex sentence would need to be parsed. Once he's starting at the sentence level, teach him question words and to alter his tone at question words until he gets to the question mark. (Be on the look out because 'did', 'has'/'have' and 'are' can be question words--not just the 5Ws and H.) You can also take a page of text and type it up, but sentence by sentence needs to be set out like a paragraph. Enlarge the punctuation marks to be super-duper obvious. Then practice reading from punctuation to punctuation so that he can get used to reading with flow. After each punctuation mark, he reads from the beginning of the sentence to the end of the sentence. "George Washington, who became the first president of the US, was a Virginian--meaning that he came from Virginia." would be broken down as George Washington, George Washington, who became the first president of the US, George Washington, who became the first president of the US, was a Virginian George Washington, who became the first president of the US, was a Virginian--meaning that he came from Virginia. Once he's been through a parsed out passage--re-reads are helpful and reading more from that text that hasn't been parsed gives him a chance to apply what he's learning to the same content without the extra "trainer-wheels". This type of practice with parsed text has been very helfpul and in building up oral fluency, though it might take 3-6 months of support like this, so far the effects are long-lasting.

Yikes! Some way the rest of my post got eaten. OP, We've been wrestling with the idea of grade placement for JR. who may enter BM school next year. Currently, academically, he's much closer to the 8th-10th grade range in his 3Rs. Socially he does well within 2 years of his age. Physically he's on the larger side of average for his age. Chronologically he should go into 4th, but we are exploring the possibility of a single or double grade skip for him to find a good fit emotionally, academically and socially. Also, we have to think about his extra curriculars. If we officially put him up a grade or two, that affects some of the ECs that he does or plans to do.

I like to think that we did a lot of Organic Reading Compression with the kids, (discussing the 5Ws and H) but something that really helped push their reading comprehension up to the next level was learning to compose sentences according to various patterns. The first year of learning to write, we point out Sentence Patterns that they are encountering in their reading a lot. After that, they're able to pretty reliably able to make the connection for themselves between whatever they're reading and what the author is Saying.

We don't have a formal grade skip, instead we start offering literacy and numeracy experiences and skills early and continue much further down the continuum than most published programs. Once the child is school aged, they work at ability level. In our homeschool a student is never limited to "grade level" and we allow them progress at their rate.

OP, I was like you. I was not into "good classic literature" as a child. I wasn't a great reader. Reading to my children was an intentional choice and very effortful for me, personally. I wanted my kids to read better than I did at their ages, and to feel capable of reading big books, even if they didn't love reading big books. We tried very hard to intentionally read to the kids daily when they were younger and that part went well. The desire to not have to read to them was especially strong once they could reliably read to themselves, but we push on because we've made books an enjoyable part of our family dynamic and the kids (usually) enjoy that part. For longer books, I don't read to my kids as much as we read with them these days. We try and keep a family read going, where everyone has a copy of the same book and we read in turns--kind of like a radio cast. Depending on the book, some people might read certain characters or certain pages. We do this with novels, chapters book and even picture books. Sometimes we read books that are easy for the kids to get into, other times we read books that are too hard for the kids to enjoy on their own.

@alpinegrace, you can preview the entire Saxon Math 5/4 (and Math 6/5) book online if you google it. A lot of schools have made the PDF of the books available online.

If I were going to assign a book to a 12yo for self-instruction and independent use, I'd start with The Draw Squad which is a more step-by-step version of The Drawing Textbook, which we use and love. There is also a book You Can Draw in 30 Days by the same author, that teaches the same skills, but was published more recently and contains less cartoony finishes.

I recommend FAN Math Process Skills in Problem Solving. This series actually teaches how to set up Bar Models and goes section by section. I recommend using Process Skills in Problem Solving first, because Challenging Word Problems just expects that you know how to set up the bar-model. I'm content to let my kids blow through material up through Arithmetic of whole numbers and fractions.

Two thoughts--this is the sort of thing we want to prevent. The kids should know how to play at least a dozen games that can be played with a standard deck of cards and that hundreds more are possible. And yay! The kids do know and play Crazy 8s. We'll have to teach them Rummy.