I re-branded the hundred grid as a dollar grid, so let's see...
This many!
It looks so cool that I considered having Sydney glue the pennies down to the grid so that we could keep it...
And then I thought, "Heck, no! I'm not wasting a whole dollar!"
The girls have recently wearied of all this talk of coins and commerce, so our math is moving on to geometry. Geomags, constructive triangles, spirograph, geoboard, patterns blocks and mirrors--that ought to hold us for a while!
Do not give me that sulky face, and don't you dare tell me that you clearly cannot homeschool your child because you obviously don't remember how to divide fractions.
Of course you don't remember some math stuff! You learned all that a zillion years ago! But you know what?
You are a grown-up adult. You can pick it back up. It's really not that big of a deal.
Also, remember that time that you tried to learn some math thing back in school and it was too hard and you got mad at yourself and said that you hated math and you're not good at it?
You were NOT a grown-up adult back then. You were a child.
How fun, then, not to pass that same negative mentality on to your own kids?
Elementary math can be so much fun for kids! Elementary math is fun manipulatives. It's fun games. It's jumping and screaming and singing. It's drawing and painting. It's measuring and pouring. It's reading books together, and doing puzzles, and figuring out interesting problems. It's some of my happiest memories with my kids.
ELEMENTARY MATH
Both my kiddos studied math informally until second grade, then began in Math Mammoth's Light Blue Series at either Level 2 or Level 4, depending on the kid. Math Mammoth took them both all the way through elementary and middle school math.
For part of elementary and middle school, we also used this text as a combined math/science/history study:
Here are some other textbook, reading, and viewing resources that we used:
Almost all of these came from the library, and most consist of fun picture books that I found for us to read together--even older elementary kids (and even high schoolers!) love great picture books!
And here are our most important manipulatives:
There are tons more manipulatives that I created myself or Googled, downloaded, and printed. I'm a BIG proponent of DIYing as much as possible!
Below, I've listed tons of the enrichment activities, extra reading/viewing resources, and fun stuff, that I did when my kiddos were elementary ages. They're not listed in any particular order, because they don't have to be done in any particular order! I liked to have the kids doing some kind of hands-on math activity every day, and if it wasn't inspired by them wanting to bake or build or draw or read together, then I invented a fun invitation or set up a game or suggested a project or offered up a puzzle.
I also set up enrichment and hands-on activities to support skills that the kids were struggling with, or to expand on skills that they were blazing through. Seriously, ask me how many hands-on activities I know for teaching rounding!
So scroll through my list of fun enrichment activities, and definitely set them up to support something specific, but also feel free to engage in them at random. I mean, most of what we did in elementary was totally random, and those were some of the best years of my life!
Building Big Numbers with Base Ten Blocks. This is the BEST math activity that my younger elementary kids ever did. It's endlessly repeatable when they're little, and builds that crucial number sense that they need to make everything else make sense!
Clock Cake. Clock reading is a skill taught in elementary math, but it's ever more abstract these days, as every device has a digital clock and analogue clocks are becoming more of a rarity. The solution? Bake and decorate your own clock!
Roll the Time. To get even more clock-reading practice, write minutes onto a blank die, combine it with a twelve-sided die, and have a kid roll the time. She can tell you the answer and draw it onto a blank clock face.
Pascal's Triangle. You can find the blanks for these online, and seconds later, you've got an in-depth addition review!
Roll to a Hundred. I'd completely forgotten how many of those printable hundred charts we used in the early elementary years! There are endless amounts of games you can make using them, all of which reinforce numeracy and computational skills.
Add Multi-Digit Numbers using an Abacus. Just as when the kids were learning to read I wanted them to see all kinds of letters in all kinds of fonts and all kinds of sizes and made of all kinds of textures, I liked the kids to practice counting and adding and subtracting in all kinds of ways, with all kinds of manipulatives. If you've never used an abacus, it's well worth learning how to work it properly!
Metric Conversions in Grams using Rice Models. If you have a balance scale and some rice, kids can make their own metric conversion models, using a LOT of problem-solving and practical life skills in the process. And even in high school, we STILL pull out those rice models whenever a kid needs a metric conversion refresher!
Hands-on Rounding. For some reason, Syd really struggled to master this concept, and so now I have a zillion concrete, physical, hands-on ways to teach rounding.
Decanomial Square. You're going to see me refer to this a lot, as it's one of our most-used math manipulatives. It's well worth DIYing or buying one, because your kids will still be using it in high school!
Multiplication Touch. It's quite the project to build the roll-up hundred mat and the number tiles from scratch, but Multiplication Touch is well worth it! It's surprisingly fun to play, so works great not just for memorizing the facts, but also for reviewing them for years.
Model Long Division with Base Ten Blocks and Cuisenaire Rods. You can cover a LOT of mathematical ground with just those two types of math manipulatives! By the time a kid hits long division, she's already starting to get math instruction that's more focused on teaching her how to plug numbers into an algorithm than it is on understanding what she's doing, and that's not cool with me. When I teach long division, I like to drag out all the blocks and show a kid exactly--and I mean EXACTLY!--what is physically happening to the literal numbers that she's dividing.
Literally Walk through Long Division. The beauty of homeschooling is that nobody--not you, and definitely not the kids!--are trapped at a desk. Get the wiggles out and bring whole body learning into your math study by drawing a GIANT long-division problem on your driveway and then having your kids solve it. Who knew there was so much walking, crawling, and skipping in math?
Model Converting Mixed Fractions to Improper Fractions. You need circle fraction manipulatives for this activity, but the good news is that it makes converting between mixed fractions and improper fractions as clear as a bell and as easy as pie! Here are the circle fraction manipulatives that we own:
Level these fraction models up to middle school and high school by bringing them out whenever kids need a review. They WILL randomly forget how to convert between mixed and improper fractions, but going back to the manipulatives will quickly remind them, and every time they re-learn it, they'll cement it into their brains even better!
Montessori Pink Tower.Playing with the Pink Tower can be soooooo satisfying for the pattern-loving child, and it's great for their hand-eye coordination and number sense.
Montessori Pink Tower and Cuisenaire Rod Patterns. If you're loving the idea of open-ended exploration of math manipulatives for young learners, then you should really check out Montessori math! These kid-built, elaborate patterns are satisfying to create and look at, and since they're built on a Base Ten system at a centimeter scale, they're terrific for building a kid's number sense. Here's the Montessori Pink Tower:
Level pattern-building using the Montessori Pink Tower and Cuisenaire rods to middle school by having kids create their own diagrams or pattern cards from their creations. Perhaps they want to share them with a younger learner, or even publish them!
Blow Bubbles with Geometric Figures. What happens inside a prism when you dunk it into bubble solution? More fascinating geometrical models! Here are our Zometools:
Find the Area of Irregular Polygons using Graph Paper. Everything is more fun when it's on graph paper! For even more reinforcement, use centimeter graph paper and fill in the polygons with Base Ten hundreds, tens, and ones, and Cuisenaire rods.
Make Mandalas with a Compass and Protractor. Here's a fun art activity that happens to teach compass and protractor use while also offering a lot of scope for creativity and process-oriented art.
Level this activity up for middle and high school by encouraging even more elaborate, thoughtful creations.
Origami. This is one of the best geometry activities that your kids won't even recognize as math work! Start with SUPER simple builds so that they don't get frustrated with the fine motor requirements, but no matter what they make, they're building an intrinsic knowledge of angles and shapes and how they work together in two- and three-dimensional spaces.
Level this up to middle school and high school by working through ever-more-challenging how-to books.
Pentominoes. Allowing kids free exploration of mathematical models and manipulatives and interesting shape puzzles is one of the best things that you can do with them in elementary, whether or not you're officially homeschooling. Pentominoes are especially fun for older elementary kids who enjoy stretching themselves with challenging puzzles.
Level pentominoes up to middle school and high school by working through ever-more-challenging puzzles, and calculating the number of possible solutions to puzzles.
Symmetry and Similar Figures with Pattern Blocks. This is a more challenging activity for older elementary, but you get to drag out ALL the pattern blocks and it makes the kinda abstract concept of similar figures crystal clear!
Tangrams. This is another math manipulative that's endlessly entertaining, even onto middle school and high school. Heck, *I* still love to play with tangrams!
Zometool Stellations. To stellate a polygon is to extend its line segments. It always makes something beautiful, and it encourages kids to stretch their imaginations and become more mathematically creative thinkers.
To level this to middle school, have the kids measure the angles both inside and outside their polygons.
I don't blog about every single thing that I do with the kids, so here are some of the Pinboards where I collect even more elementary-level math resources. Some I've done, some I haven't, but I think they all look pretty cool!
I LOVED doing math with the kids in elementary. I loved exploring open-ended activities with them--activities that I, too, thought were fun! I loved reading math poems and picture book biographies of mathematicians together. I loved every single time a kid was happy while doing math, every single time she felt confident, every single time she took a risk, every single time she struggled and struggled and finally understood.
It's exactly what learning should be, and it was my privilege to give that to my kids.
We had a great week last week! Mind you, a day in our house is never what you'd call tantrum-free, but the majority of each day contained content children who worked hard on their responsibilities, played together, played outside, and didn't give me too much of a hard time.
This chalkboard helps, I think:
I've been compiling it on Sundays, as I'm finishing up the next week's lesson plans, and then during the week, I really only have to update the daily chore list and erase the special events as they pass and the memory work as it's successfully memorized.
For memory work, daily practice on Mango Languages is a constant, as daily guitar practice for Syd will be when I can sort out her lessons. Mango Languages can be a little frustrating, as it's designed for adults and therefore moves quickly, but I continue to explain to the children that I do not expect perfection, or speedy progress, just the consistency that will allow their brains to master the material. And they do seem to have settled into their daily practice:
I'm studying Hawaiian, too, as I've never learned an Austronesian language before. Will does some Hawaiian, but also likes to explore the other languages, but after trying Mandarin Chinese, Syd seems happy to stay with Hawaiian for now. Here's she is comparing her pronunciation to the native Hawaiian speaker's:
Written work also went well last week, and has tended to go much better since I made the commitment to myself that when the children were working at our school table, I would be working there, as well, generally on my computer, which allows me to answer the random ready-reference questions that always come my way, but also with a white board and dry-erase marker at hand, tools that are essential for easily demonstrating math calculations. By these ages the children ought to be able to do their written work independently, but if working in companionable silence with me helps them focus, then I'm not going to protest--especially as I always have plenty of my own work to do!
Having a chick at the table to assist is also essential, apparently:
Anyway, this week's memory work includes Mango Languages, Will's World War 1 poem (Syd has mastered hers, but Will's is more challenging), the countries involved in World War 2, spelling words, and Hawaii state symbols. Spelling words and the poem can be knocked off the list by proving to me that they've been mastered, and we'll move on from World War 2 countries to World War 2 leaders next week, whether or not the kids have the countries down--this won't be the last time that we study World War 2, so I really just want the children to be familiar with these facts, not necessarily have them memorized cold.
The children also have an assigned book to read each day, and this week's books include picture books of butterfly and frog metamorphosis, living books on Hawaii and World War 2, a biography of Marie Curie, and some titles for STEM enrichment or that are related to the kids' current Girl Scout badges in progress.
Here's our week!
MONDAY: We're starting the week with some hands-on math enrichment. Syd loves fractions, so on this day she'll be exploring a set of fraction blocks and activity cards that I checked out for her from our local university's education library. For Will, I put together this model for multiplying and dividing by powers of ten, and printed out a multiplication by powers of ten worksheet for her to complete using the model. I laminated the strips that you pull through the model, so with a dry-erase marker, she can write each problem down on the strip, physically manipulate it to show the process, then erase it and begin again with the new problem. I think this will make the process very clear very quickly, as Will is excellent with patterns.
We don't follow a formal spelling curriculum; I prefer to keep an ear out for any words that a child needs help spelling, then create a list that contains that word and words that are spelled following similar rules or that have similar sounds. This week, for instance, the spelling list contains "oo, ue, ueue, ew" words. Next week's list, I already know, will contain "wh, w" words. Some weeks I use the spelling word list as cursive copywork, but this week I've created a word search; when finished, the children will keep the page in their binders as a study sheet.
I wanted the children to be able to recognize a few specialized terms in our brief mosaics unit, mostly to help them remember that there is a science even to artworks. I won't have them memorize these terms, but I do want them to practice their infographic-making skills to create a reference sheet that we can display.
We have our weekly volunteer gig at our local food pantry today; while I stock the pantry and assist customers, the kids can be found weeding and harvesting in the garden, repackaging bulk food, rinsing storage bins, snacking, helping themselves to seed packages to plant in our home gardens, or reading or playing quietly. They keep themselves entertained!
TUESDAY: Math is back to Math Mammoth today; Syd has a lesson on estimation, and then some review, and Will has word problems. She will be SO excited to move away from decimals next week!
Time spent outside on lovely summer days has allowed the children to become interested, again, in insects, so I have a few activities that we can build on if they seem to enjoy them. One is this BumbleBee Citizen Scientist Program, which will involve the children hunting down a bumblebee to photograph, and will give them the opportunity to research an identification for it, and to have that identification confirmed by an expert in the field. We'll see how it goes.
For our World War 2 study this week, the children will be labeling a world map with the countries that participated in World War 2, using these World War 2 notebooking pages. This lesson won't have a lecture component, but will simply be a useful reference for the rest of the unit.
Syd has a playdate planned for this day, and you might remember that I count even playdates as part of our scheduled day, since playdates aren't exactly the same thing as free time, and preserving the children's free time is very important to me.
WEDNESDAY: Syd has Math Mammoth again on this day, but for Will I created worksheets to teach her how to use this model to multiply decimals. Her worksheets simply consist of decimal multiplication problems, each followed by enough clip art hundred flats (you can also use a blank hundred grid) to model the problem, and space below to write the answer.
Syd is currently working on her Girl Scout Detective badge, so she and I will be making invisible ink using lemon juice, and playing with invisible ink pens that require a black light to reveal their writing--lots of good science there! Will is working on the Comic Artist badge, so she'll be studying comic strips and creating her own, for lots of good visual arts and creative writing practice. See why I love the Girl Scouts so much?
I've been sitting on this book that I need to review, and since Mango Languages has recently gotten the children interested in the variety of world languages that exist, I thought we'd give reading a chapter out loud a go. We'll read it together, looking up the pronunciation of the French words that we encounter using an online dictionary. We'll continue that next week if the kids seem to enjoy it, and if they don't seem to, I'll just pass it to them to finish reading on their own. Regardless, it's a nice little intro to the French language.
Will has often expressed interest in creating a butterfly collection, and I finally feel confident that I've done enough research to choose the most humane way to go about it. I've found some Youtube videos that provide a good overview of the process of collecting, euthanizing, preparing, and displaying insects, and I've purchased all the relevant supplies, so I'll have the kids watch these videos on this day, and if they're still enthusiastic about it, we can begin!
THURSDAY: Syd has her Math Mammoth, but Will has a review of multiplying and dividing by powers of ten and multiplying by decimals. If she doesn't have the process down cold by this day, then we're just going to move on anyway and revisit it in several months.
Our geography assignment for this week is simply a coloring page of Hawaii state symbols and facts, which the children can color while listening to traditional Hawaiian music streaming on Spotify. These facts will then be added to their memory work to review until they've mastered them.
Our homeschool group's playgroup is on this day, and that tends to take up most of the afternoon. Will has her horseback riding lesson following it (we've switched stables recently, and I think it was a good decision), and while she's in her lesson, Syd and I do a project together. Last week, we started a blog for her, and this week, I think we're going to work on some decorations for her bedroom.
FRIDAY: I purposefully stock Friday with work that the children can do independently; throughout the week I encourage them to work ahead on Friday's work so that they can have that day off, and even if they don't do it, assigning work that doesn't require my input still gives me a bit of a break on this day. Their grammar comes from library copies of Exploring Grammar (Syd) and Mastering Grammar (Will), with laminating pages over the workbook pages so that the children can complete them using dry-erase markers.
Froguts is a frog dissection ipad app that's realistic and humane--yay!
We now have a decent approximation of many of the basic fossil cleaning tools used in a paleontology lab--x-acto knife, dental pick, test tube brush, paintbrush--although I still need to buy some super glue, and as I recently also bought several specimen boxes, we've been able to get some good work done on cleaning and preparing our fossil finds from our 2014 dinosaur dig. Fossil prep is a LOT of work, however, and I anticipate that it'll be a long time before our specimen boxes are complete. In addition to this work, Will is studying a college-level intro to paleontology textbook, and then discussing each chapter with me.
We've got some other fun plans this week, of course--the Perseid meteor shower, an afternoon at the splash park, perhaps weekend swimming at the YMCA, and definitely the drive-in movie--but that encompasses our work week!
Last week was a great school week, with a combination of wild-and-woolly hyper-elaborate projects, field trips, and just enough seat work to calm things down every now and then. Frankly, this week looks like much of the same!
Will is gearing up for another spelling bee season, so for memory work this week, Wordly Wise is on hiatus in favor of the Scripps 2015-2016 spelling list. Other memory work includes Mandarin vocabulary for Will, ballet practice for Syd, and cursive. Books of the Day include more books on World War 2, including a couple of living books, a couple of Magic Tree House fact finders, and one more book on volcanoes. I'll be refocusing on having Syd read aloud to me each day from her book, as last week's work on her History Fair project has made it clear to me that she needs my one-on-one attention to encourage correct pronunciation and complete comprehension.
And here's the rest of our week!
MONDAY: Math Mammoth is still fractions for Will and multi-digit multiplication for Syd--restful chapters, since they both feel pretty confident about the material. Our only other assignment for this day is having the kids rehearse their History Fair presentations several times, as today has both our regular volunteer gig and our homeschool History Fair! I'm really looking forward not only to my own children's presentations, but also to seeing the presentations of all the other children in our group. The kids always enjoy this, too, and it's amazing how much history content is covered, and how much children can learn when they're learning from other children.
TUESDAY: One of my favorite things about Girl Scouts is the ownership that the children have of their own fundraising money. Back in the summer, we held a Girl Scout meeting to let the children make proposals about ways to spend their Girl Scout cookie earnings; the children prepared presentations on their proposals, the other children asked thoughtful, supportive questions about each one, and then they all voted on what we should do. One of the winners was this day's field trip to a nearby children's museum, complete with the rock wall experience, and lunch spent at an indoor playground across the street from the museum. It'll be a fabulous time for all of the children, as well as sneaky STEM, creative, and gross motor enrichment. It's great to be a Girl Scout!
WEDNESDAY: The kids have a bunch of extracurriculars on this day--Magic Tree House Club, ballet class, AND LEGO Club!--so although we only have room in our school day for one additional assignment, I've made that assignment more elaborate than usual. Inspired by this hundred grid fraction art lesson, I designed my own for the children. It will incorporate symmetry and equivalent fractions, and, for Will, decimals, percentages, and simplifying fractions. It will also require close reading of the instructions, which is another thing that I want Syd to work on, and creative expression, which Will always needs more outlets for.
THURSDAY: We are in the end-game of our World War 2 unit! By this day, we'll have completed my main goals for the unit--interviewing a World War 2 veteran, visiting Pearl Harbor, and completing History Fair projects--so on this day, we'll review the entire war using Story of the World, and then all that really remains is the atom bomb, the aftermath, and a comprehensive review of the geography of the war.
There's no real academic reason for having the kids do more how-to-draw books on this day, other, of course, than what they clearly provide in terms of fine-motor skills and creative expression. The truth, though, is simply that although the children adore working from these books, they also never seem to choose any from our library shelves to do on their own. Assigning the books, then, is a sure-fire path to a happy morning.
FRIDAY: An organized rock collection is something that neither child has ever come to on her own, but it's something that I think they would both enjoy. Organizing and categorizing the rocks and coral that they collected on our Hawaii vacation, then, will be both useful and a good way for me to gauge their enthusiasm about perhaps continuing that work with the rest of their giant box of rocks. It could be the basis of an entire geology unit!
Although we've already had one Girl Scout activity this week, it also happens that both children have recently finished the badges they've been working on--Detective for Syd, and Comic Artist for Will. This means that it's time to get to work on a new badge! I do have a few more activities that I want the kids to do relating to each badge, but those are beyond the scope of the badges, themselves.
Syd is living and breathing the Nutcracker these days, of course, and has yet another practice on this day, but a few weeks ago I signed Will up for a series of girls-only podcasting workshops, and I'm thrilled at how she's taken to them. From what I can tell, the children involved in the workshop really have ownership of their work, and Will has displayed excellent teamwork, has composed original work to record for the podcast, has read the work of others ("I had to record one poem FOUR times," she told me, "because I had to work on my breathing and enunciation"), and has been learning how to use all the other audio equipment involved in this production.
SATURDAY/SUNDAY: Saturday has shaped up to be a day of ridiculousness this autumn. Don't tell the children, but it's 100% another school day! Syd has both her regular ballet class AND a Nutcracker rehearsal, and Will has classes in ice skating and Mandarin. Sunday, then, is our only day fully at home this week, and hopefully we'll get to spend it fully AT home. If nothing else, I need to work on some autumn landscaping, and Matt and the kids need to winterize the chicken coop!
As for me, if I want to buy the children Christmas gifts this year (and I do!), I really, really, REALLY need to spend this week adding seasonal items to my etsy shop, futzing with the SEO tags on a few of my listings, and otherwise getting my shop in shape for holiday shopping. I also, of course, have writing assignments to complete, some mending to do, and there is an absolutely massive bunch of overripe bananas on the kitchen counter that must become banana bread today, if not sooner.
I may have Willow start doing all her math in her head.
For a few weeks now, Willow and I have been working on adding one- and two-digit numbers using carrying. We visualized the process by setting up the equations with Base 10 blocks--
--then trading up and physically carrying the ten bars over to the next place before adding everything together, and finally moving into the conventional method of carrying while working arithmetic problems on paper.
There was a lot of grumping, a lot of Base 10 block pattern building--
--and a lot more grumping, and the concept just didn't catch on. I'm pretty sure that the concept didn't catch on not because the kid didn't understand the concept, but rather because she was too busy grumping and pattern building to put the concept into her brain, but nevertheless, that's a lot of grumping and a lot of repetition just to learn (or NOT learn) carrying.
So we're just not going to learn that--not exactly, at least--right now.
In related news, last week my local indie teaching supplies store, which is normally too expensive for me to shop in, had their mid-summer sale, bringing their prices down to slightly more typical levels, and so I came home with the following:
I avoid math curriculums because I have no problem teaching elementary math, but I do like the idea of having a logical order to work with, and I do like some of the mathematical concepts that Singapore math, in particular, teaches, so the reasoning behind purchasing just the practice books is that I can pretty easily figure out the concept that's being practiced, teach it on my own, and reinforce it with the books.
Singapore 2B has a lot of review in it for Willow, but I'm not opposed to drill and repetition, and there are a few key concepts in it that she hasn't explored yet, so that's why we settled there for her. Singapore 1B looks like a good fit for Sydney overall, so yay there for her.
My point with this digression is that, right there in the Singapore 2B practice book, front and center just before a money review and some new exploration of fractions, is a series of mental math practice problems that involve a different method of solving one- and two-digit addition problems, mentally, WITHOUT carrying. Here's what it looks like:
First, she's rounding the one-digit number to the nearest ten, and finding the difference, which is an easy subtraction problem. She's going to hold that number in her head. Second, she's adding the ten to the two-digit number, using skip-counting. Third, she's subtracting the difference from that new number, and it's another easy subtraction problem to the answer!
Now, do not even get me started on whether or not this method takes more steps than simply carrying the ten (it does), because for the little miss, that's not the point. The point for the little miss is, apparently, the fact that the steps are broken down into simple problems that she can do in her head. While the connection to the concept of what you're physically doing with the numbers isn't as clear, to me, as it is with carrying on paper, especially as visualized using Base 10 blocks, it IS still connected to the concept, just in a different way that seems to appeal more to the miss.
So this method, combined with simple "counting on" when the units to be added will add up to less than ten, gives Willow all the tools that she needs to mentally add one- and two-digit numbers to each other, abilities that we've been practicing with a homemade deck of laminated number cards:
And thus we can put aside that dreadful carrying altogether, to be brought back up at some point in the near future, preferably after the little miss has forgotten her grumps about it!
, constructive triangles, spirograph, geoboard, patterns blocks and mirrors--that ought to hold us for a while!
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, and since Mango Languages has recently gotten the children interested in the variety of world languages that exist, I thought we'd give reading a chapter out loud a go. We'll read it together, looking up the pronunciation of the French words that we encounter using an 
(Syd) and 
(Will), with laminating pages over the workbook pages so that the children can complete them using dry-erase markers.
, and then discussing each chapter with me..jpg)
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