Tutorial: Roll-up Felt Hundred Mat

We have a laminated cardstock hundred grid that works with our number tiles, and I've recently realized that I can make some sturdy yet disposable hundred grids pretty easily from cardboard record album covers, but I was also wanting a hundred grid that would look nicer longer, and be easier to toss in my backpack for trips to the library or park to do schoolwork.

So I made one!

You make this hundred mat around the number tiles that you already own, so first you've got to make them. We have a set of clear one-inch number tiles that were great for matching to a printed hundred grid when the kids were littler, but now that they're older (AND have lost a couple of those tiles, sigh), I've made them a couple of sets of upcycled cardboard number tiles that are the same size, so they can be interchangeable. I've long wanted to make a set of number tiles out of Scrabble tiles, but I think their inevitable loss might break my heart, so...

Measure out the grid AROUND the tiles, so that when your kiddo puts a number tile on the grid, they'll still be able to see the border around the tile. A little extra space is always good for those fumbly kid fingers, anyway. For me, this meant measuring at one inch + 1 centimeter, and I still did a lot of double-checking:

Notice that I measured and drew this grid in chalk. I didn't end up making a mistake in my measuring, but if I did--chalk equals second chances!

When you've got the grid drawn out, get out a tiny paintbrush and some fabric paint, and carefully paint over your grid:

And that's it! You can roll up your mat, you can wash it, and you can play with it on the carpet:

I remember when Syd was first learning how to find numbers on the hundred grid, and now we're using it for multiplication and division. Ah, time...

Homeschool Math: Our DIY Roll to a Hundred Game

I have a strict Montessori-style policy that I do not discourage my children from doing academic work that is "too easy" for them. If Willow wants to play the Jump Start Kindergarten CD-Rom that I checked out from the public library for Sydney, then that's okay. If Sydney wants to spend the afternoon working color-by-number pages, then that is totally fine by me. If Willow suddenly develops a passion for those old First Chapter Books that she first read two years ago, and reads them all again, then good for her!

It's an important part of my homeschool philosophy that repetition reinforces skills, internalizes concepts, and builds the feelings of mastery that reward children for learning, and the confidence to take on more learning challenges.

Therefore, although our DIY Roll to a Hundred Game highlights skills that both my girls have already learned, we LOVE this game! It's excellent reinforcement for number recognition, sequencing, counting, and addition concepts. The unpredictable nature of the roll of the die prepares the girls for future lessons on statistics, graphing, and averages. The coloring requires fine motor skills, and is also graphing, and pattern-building.

Oh, and the game is based on a die, so the little one can win as often as the big one does, hallelujah.

To play Roll to a Hundred, you will need:

• a copy of a Hundred Grid for each person. You can use either a labeled hundred grid, or a blank hundred grid that the child labels for herself--this turns the potentially tedious activity of labeling a hundred grid into a useful activity that a child might choose to do for herself, by the way!
• one die
• crayons

1. Decide who goes first. The first player has the advantage, so it's important to remember to take turns.

2. During her turn, a player rolls the die--

--and then colors the same number of squares as pips on the die:

3. Change crayons each time so that you can see each individual roll on your hundred grid, and the first person to reach one hundred--

Wins!!!

We play such that you have to roll to reach 100 exactly--waiting for that perfect roll gives everyone time to catch up and makes the game a little more exciting.

Ways to modify the game:

• Use two dice, or a 20-sided die, etc.
• Play on a 200 number grid. 
• Play on a number line.
• Play Roll to Zero, where the game is subtraction!
• Multiply each roll by two.
• Assign a different mathematical operation to each number: One must be subtracted, Two gets doubled, Three gets added to the previous roll, Four gets divided by two, etc.
• Have everyone graph their rolls to see how many times each person rolled each number.

It's certainly not a bad way to spend a rainy afternoon!

Skip Counting with Coins on the Hundred Grid

Our family is going to be participating in Lemonade Day in our town this Spring, and to that end I've reintroduced the money math unit that we first began some months ago when Willow got interested in coin collecting for a while.

My goal is (taking extra care with pricing, of course) for Willow to be able to do all the math and make all her own change at the girls' lemonade stand--whether or not this goal is realistic, I have no idea!

First step: skip counting by each of the coin denominations, followed immediately by keying the counting to the denomination. In other words, I want both girls to be able to easily skip count by fives, tens, and 25s at least up to 100, to count by hundreds up to at least 1,000, and to recognize that skip counting by fives, say, is the same as counting nickels.

The girls have been creating their own skip counting reference sheets using, of COURSE, our ubiquitous hundred grid. For nickels, for example, one day's schoolwork was simply to count off the fives and color in each five in their hundred grid. The next day's schoolwork (and the next!) was to memorize the fives, until they could recite it easily.

When a girl had her fives down cold, I gave her a new hundred grid, asked her to put a nickel down on each five, and then use the chart as a reference to solve a page of math problems:

The problems are all just iterations of how much a certain number of nickels equals. To solve the problem, the kid can either skip count over that many nickels, or just count over that many nickels, and then move aside that nickel. The number underneath is the correct answer!

Once the kiddos have all the skip counting and coin denominations memorized, I'm going to send them through the math drills in our Kumon money math workbook as well as some fun projects from my Money Math pinboard. And then when Lemonade Day comes around, providing I can convince the children not to price their lemonade at 63 cents or $1.07 or something else that will require a child to do twenty minutes of abacus work for every transaction, I think we may just have it made!

P.S. It's just occurred to me that I should also teach them to count by tens when beginning at 5. AND I should be mixing more subtraction drills into the prep work, especially two-digit subtraction.

Or I could just encourage the girls to price everything they make at one dollar?

Sydney Masters the Hundred Grid

We're big fans of the hundred grid around here--it's such a versatile math tool! You can use it to help you add and subtract, with skip counting, with coin calculations. Because Sydney likes puzzles, she also occasionally enjoys using our big laminated hundred grid with some overhead transparency number tiles that, even though I bought them at different times and places, happen to be exactly the same size--score!

I especially like the transparency of the overhead tiles, because if a child is still working on number recognition (and, as I learned while assisting Sydney through the most tedious three games of BINGO ever played at their 4-H club holiday party this week, we ARE still working on number recognition!), then that transparency allows instant self-correction.

During our most recent play with this board, I witnessed Sydney unlock one of the patterns implicit in the number grid. No more random seek-and-find for her--watch this girl go!

I was pretty thrilled that I was there to see it happen.

Syd has a lot of focus, and although she wearied a bit of the task near the end, she kept working, because she wanted to see it through:

Success!

Pretty proud kid, right?

We have an old garage sale BINGO set of our own, and I think that we'll be playing a lot of fun at-home BINGO games this week, because not only is Syd clearly ready for number recognition up to 100, but I'm not taking her near another BINGO party game until she has it down--geez Louise, what a nightmare!

Manipulatives That Stand the Test of Time

I've had the idea for this post in my head for quite a while, as my kids get older (upper elementary and middle school--yikes!) and I see that although we've used some manipulatives just a time or two, or a month or two, or even a year or two, other manipulatives have been part of our regular rotation since the children were in preschool.

There are even a couple of manipulatives that I never purchased or spent the time making, thinking they'd be used only sporadically, and have simply wished that I owned several times a year since the kids were young. Silly me!

Cuisenaire Rods

You probably know by now that these and Base Ten blocks are my FAVORITE math manipulatives. We have used them endlessly. The kids have less patience for them now that they know that whenever I whip them out, there's generally a much quicker algorithm waiting for them as soon as I'm done, but nevertheless, they're vastly useful when a kid is having trouble understanding a concept. Two days ago I used them to help Syd understand decimal multiplication--let the ten bar equal one, and you've got several decimal options available to model. And seven years ago, I used them to help Syd understand addition within 5!

Here are some other ways that we've used them over the years:

• commutative property of addition
• introducing multiplication
• long division
• modeling multiplication and division as arrays
• repeated addition (and beginning multiplication)

As with most of the other manipulatives that I'll show you, I've occasionally expanded our collection over the years, as we've needed them for more and more advanced work. In a perfect world, I'd have enough to build an entire decanomial square from them, but we're at the point now where we have enough to do most of what we want to do.

Base Ten Blocks

This is the other math manipulative that I do not know what I would do without. I consider them indispensable, and again, I have expanded our collection several times, especially with more thousand cubes. These blocks, which consist of a 1cm cube, a 10 cm bar, a 100 cm flat, and a 1,000 cm cube, are brilliant for leading a kid into an intrinsic, whole-body understanding of the Base Ten system. You have to have them to understand what you're truly doing when you add or subtract multi-digit numbers. You have to have them simply to model numbers. We use Base Ten blocks and Cuisenaire rods as a single tool, with the Base Ten blocks representing all the powers of ten and the Cuisenaire rods often (although not always--for borrowing and carrying, you should only use Base Ten blocks) to represent all the numbers in between.

Here's some of what we do with them:

• building big numbers
• building decimal numbers and again with the younger kid!
• hands-on rounding
• modeling long division (also with Cuisenaire rods)
• multi-digit multiplication using area models
• subtraction with borrowing across zeroes

Decanomial Square

We came to the game a little late on this one, as it took me literally years to decide that I wasn't going to find exactly the decanomial square that I wanted. Instead, I had Matt make one for me. 

Anyway, you can start using this one as soon as your kid starts learning the multiplication table (or before, of course, as a puzzle or to model repeat addition as area), because it works quite well as a visual multiplication table of area models. However, it's also great for all kinds of area and perimeter studies, as well as how to form equations, and is an easy demonstration of the Pythagorean theorem.

Here's just a little of what we've done with it so far.

You can use the decanomial square with Base Ten blocks and Cuisenaire rods, and I am constantly in search of a cheap Montessori-style pink tower so that I can also use it to demonstrate cubes.

Zometools

These are the priciest of our manipulatives, a cost that I absorbed by making this the kids' big combined Christmas present one year when I'd had a good winter in my pumpkin+bear etsy shop. Although we started using these just for free play to build for fun--which we still do!--these building materials should see the kids through high school, and they're used in universities, and even grad programs, to model some amazingly sophisticated concepts.

Here's some of what we've done with them:

• bubbles and three-dimensional figures (there's a whole mathematical thing revolving around the figures that bubbles form inside prisms)
• crystallizations (ie. three-dimensional pattern building)
• modeling molecular structure (you need the molecule kit for this, just so that you have the cards)
• stellations (or two-dimensional pattern building)

Hundred Grid and Number Tiles

This, on the other hand, is easily handmade (here's how to make the grid, and here's how to make the tiles), although we do have a set of number tiles made for an overhead projector that we use on our light table. You can use the hundred grid and number tiles from the time a kid is wee, simply for naming numbers, ordering them, and counting on. You can use them for skip counting. You can use them for multiplying. If you make a second set of number tiles to match a multiplication table, you can use them for memorizing the table and for playing various multiplication games. 

Here's some of what we've done with them:

• counting with pennies
• hands-on rounding
• Multiplication Touch game
• number matching
• Roll to a Hundred game (number recognition, sequencing, counting, and addition concepts)
• skip counting with coins (money math)

We haven't used the hundred grid lately, although I won't rule out finding another use for it in a later unit. Even if we don't, though, using it from the age of three through the fifth grade is a good amount of use!

Pattern Blocks

We used pattern blocks a ton in preschool and lower elementary, but it's actually only recently that it's occurred to me how useful they can be in upper elementary and the middle grades. We recently used them in Will's lesson on congruent and similar figures, and considering the fact that they've been using these same simple shapes since they were wee, that's a pretty darn good run!

Here's some of what we've done with them:

• building on templates (following directions, shape matching, logical thinking)
• symmetry and similar figures
• free play and creative play (sometimes on the light table!)

Here are some outside links to activities that we've done but that I haven't blogged about, myself:

• mandalas (or snowflakes, if it's winter)
• fractions
• holiday-themed templates for little ones
• measurement
• guided art game (similar to these DIY art dice that we also enjoy)

If you, too, are really into hands-on work for older kids, I'd love to know what manipulatives you use and how you use them.

And if you see a Montessori-style pink tower going for cheap, let me know immediately!

Celebrate the 100th Day of the Year with Me

Every year, the teenagers and I volunteer with the Children's Museum of Indianapolis' 100 Days of School celebration. Area schools bring their kindergartners and first graders to the museum, and in between visiting the exhibits, the volunteers help the kids do fun activities relating to the number 100.

This year, my teenager and I had hoped to be assigned to the 100-bean maraca station again, but I actually loved the station we ended up at even more!

When kids came to our station, we helped them measure their height and their arm span, and helped them record the information in inches and centimeters:

If the kids had a little extra time because they were waiting on a few kids to finish up, I'd sometimes also have them stand on their tiptoes and then measure their height so we could compare how much taller they were on tiptoes (usually something like three inches!), or we'd see how long they could step or how high they could reach, etc. There's a lot you can do with a horizontal ruler and a vertical ruler!

It's always fun to me to see the range of kids we encounter, and the differences and similarities--we run through something like 250 kids in two hours, so those differences and similarities are really noticeable! Most of the kids, for instance, were around 143-147 centimeters tall, and their arm spans were always a little shorter. BUT they were all wearing shoes, so I told them that if they hadn't been, their arm span would be the same as their height! It was especially fun for kids to measure themselves against the horizontal ruler and then step back to visualize their arm span, so now I'm on a whole kick about how early ed classrooms ought to have those rulers set out the same way that most of them probably have height charts, so kids can visualize lengths in two planes. 

Many of the kids could not write numbers bigger than 100, but many could, and nearly all could write the numbers below 100. Several kids did a cute thing in which if I said, for instance, that they were 145 centimeters tall, they would write "100 45" on the line. I'd then show them what it looked like to combine it into 145, but I thought their solution was so clever, especially coming from different kids from different schools!

The 100th Day of School wasn't a thing when Matt or I were in school, so it wasn't on my radar when the kids were little enough to have fun with it, and I'm actually really sad about that, because we LOVED random little holidays and celebrations like that, and it would have been as super cute as our yearly celebration of Pi Day and everyone's half birthdays and May the Fourth. The celebration is a fun excuse for kids not just to practice the one-to-one correspondence of counting and the fine-motor skills of writing the numbers, but also to build context and meaning for the concept of 100, and explore the way that larger numbers work.

It turns out that this year, the 100th day of the year is Monday, April 10, which is quite a respectable homeschool day to celebrate a holiday! Here are some activities that I think would be fun--and educational!--to do with younger kids to celebrate the 100th day of the year:

paper chain. We made SO MANY paper chains when the kids were younger! Syd, especially was all in on paper chains, and we used them a lot to count down to various big events. Here's the paper chain birthday countdown that we made in anticipation of her fourth birthday, including the discovery that tearing a link off of a paper chain? OMG, such horror. Such despair.

That's why I actually think a paper chain counting UP to the 100th day of the year would be so great. Every day you don't tear a link off--you ADD one!!! Much less distressing to those tender, tiny hearts. 

For bonus points, make these laminated index cards with the numbers and number words on them for kids to match, trace, and add to their collection each day.

hundred grid fraction art. This reminds me a little of the mathematical map coloring that the kids loved just a few years ago! Kids color a pixel design onto a hundred grid, then can play with rearranging the colors and recording the fractional or decimal representation of each color.

roll to a hundred (or roll to zero). This is a fast-paced game that both of my kids loved long after they'd mastered their numbers, addition, and subtraction to 100. And it incorporates coloring, which is ALSO super fun (and utilizes those fine-motor skills, ahem):

This would make a fun "party game" for the hundredth day of the year, and you could even possibly convince a kid to fill out a blank 100 grid in preparation.

build with 100 things. This works well if you've got sets of more than 100 of various building toys, like LEGOs or blocks, but it would also probably be even more fun and creative if you chose seemingly random things. Can you build something or create a design using 100 pennies? Can you build a structure using 100 books? Who can build the biggest pyramid out of 100 rocks? Tiny little things in bulk also make fabulous math manipulatives, so it wouldn't be a terrible idea to splash out and buy your kid a 100-set of something small and cute as a 100th Day of the Year gift.

write a googol. That time that we read a book about googols, and then I asked each of my small children to write one, turned into a bit of a wacky adventure.

I scrolled Pinterest to look at other ideas, and while a lot of projects made me cringe or looked super corny, there was also tons of non-cringe, non-corny ideas to build a kid's numeracy and inspire them to love larger numbers and help them feel festive and celebratory. Many of the printables displayed would also work well for us homeschoolers to celebrate the 100th day of the year. I know that *I*, for one, will be coloring and wearing a giant cardboard 100-shaped hat on April 10!

Homeschool Math: Graphing Candy

There's a lot to cover with fractions, decimals, and percents, but fortunately, since they're all ways of representing the parts of a whole, your kiddos can review all of them together.

For our hands-on math enrichment lesson one day, my goal was to show the kids concrete representations of fractions, decimals, and percents, to have them practice the conversions, and to let them explore how they can model these relationships.

If that sounds dry (and it does), then let me explain to you that it was actually super fun, on account of...

CANDY!!!

We went to the grocery store and picked out several small bags of assorted candies, the kind that naturally come in various colors or flavors. I was surprised that it was impossible to find the small bags of M&Ms that I remember from the checkout aisle as a kid, but we ended up happy enough with Mike & Ikes, Reese's Pieces, Sour Patch Kids, and Sweet Tarts.

I bought a package of each for each kid, because I also thought that it would be interesting to compare each kid's results.

After I had made each kid promise not to eat any candy until they'd finished counting, I gave the kids their various little boxes and bags of candy and lots of little dishes. For each candy, each kid had to do the following:

1. Count the total number of pieces of candy in the package.
2. Count the total number of each kind of candy.
3. Calculate, for each kind, the fraction, decimal, and percentage of that kind to the total number of pieces.
4. Create a pie chart to represent the relationships between the candies.

Here is the page of Will's calculations. She doesn't have the neatest handwriting, but at least, after years of nagging, it is at last legible... to her:

And here are their pie charts!

I was interested to see that the ratios between each type of candy didn't remain consistent between the two packages that the kids studied, in any candy that they studied.

If we did this again, I'd make a chart ahead of time for the kids to record their results before graphing, and make it clear that I expected organized results that everyone, not just the kid recording the results, could read.

Extension activities that I'd also consider the next time:

• Use the leftover candy for candy science experiments. There are a ton online, invented in large part by parents desperate to use up Halloween candy, but they're all pretty cool.
• Or use the leftover candy for baking or decorating. Most of the candy that we used would taste good in cookies or brownies.
• Buy several packages of one candy, graph them all, then use the results to calculate an average of each type of candy in the mix. This would make a good STEM Fair project.
• Have the kids write up their results in an essay.

The kids LOVED this activity, and were super invested in the process. Sure, it made for a sugar-filled day and evening, but it was a small price to pay for such intense math practice, conducted fuss-free!

Here are some other fun ways to play with fractions, decimals, and percents:

• Make Rice Krispy Treat fractions. 
• Play edible chess. 
• Make fraction flags. 
• Play Spiraling Decimals. 
• Make pizza box fractions. We got a couple of small pizza boxes from our favorite pizza place to do this project. 
• Play Roll a Whole.
• Make fraction art on a hundred grid. 
• Write your name on a hundred grid. 
• Do color-by-fraction pictures.
• Play First to 50.
• Use dominoes as fraction manipulatives.
• Make play dough fractions.

And here are just a few resources that we've also enjoyed:

The Sieve of Eratosthenes as an Aid to the Memorization of Prime Numbers

Just as memorizing sight words can help a kid read better and more confidently, there are tons of math facts that, if memorized, will make a kid's calculation work quicker and more confident. 

Our culture is well used to having kids memorize the multiplication tables through at least 10 (through 12 is better!), and certain formulas like the quadratic formula or the Pythagorean theorem, but it's so helpful to just know, when you're busy doing your algebra, say, if a number is a perfect square or a Pythagorean triple, etc. It builds confidence when a student is learning advanced math concepts, and it increases their speed and fluency, which they will VERY much appreciate whether they're working through a page-long proof or an SAT problem set!

When my kids were pretty little, we dedicated the first ten minutes of the first car trip of the day to memory work, and they memorized a lot of advanced concepts by rote then (most famously, the first 25 digits of Pi, a party trick that they still both often pull out over a decade later, lol!), but it's a better aid to learning and to memorization to have them, whenever possible, create for themselves the anchor chart that contains the information I want them to memorize.

So when I realized recently that my teenager has lost most of the prime numbers to 100, I pulled back out the same activity that she used to create her Prime number chart back when the kids memorized the primes to 100 the first time around back in 2016.

It's the Sieve of Eratosthenes!

Creating the Sieve of Eratosthenes is simple. All you need are a hundred chart and some colored pencils or crayons. This hundred chart has the numbers by rows, and this hundred chart has the numbers by columns. This hundred chart is blank, for some sneaky real-world handwriting practice writing the numbers to 100. 

To create the sieve, you simply start with the first Prime number, 2. Don't color it, but color all of its multiples. Bonus points if you unlock the pattern and color it that way! The next uncolored number is your next Prime number, 3, so leave it blank but color all its multiples. It makes a pretty pattern, too!

Carry on through 7, and by the time you've colored the last multiple of 7, you'll have colored every composite number through 100, and every uncolored number is a Prime. Your grid will look like this:

photo credit: Wikipedia

I think the patterns that it makes are beautiful and fascinating!

While you're working, it's best if you have a Ginger Gentleman supervise you:

While you're working, you also might notice that you have a sudden, inexplicable swarm of Asian lady beetles inside your home. Would the Ginger Gentleman like to meet one?

He very much would!

Please note: no Asian lady beetles were harmed in *that* particular encounter. When Matt got home and found the swarm and went for the vacuum cleaner, though, well...

The Sieve of Eratosthenes is a quick, enjoyable, non-rigorous enrichment activity for an older kid, best used for a review of Prime numbers or to construct a memory aid/anchor chart. However, you can actually also do this activity with quite young kids, since multiplication is the only skill required. It's fun and hands-on, the patterns are pleasing, and it gives kids a really interesting math concept to explore.

Here are some good books to use with younger kids in partnership with this activity:

To extend the fun, younger kids can play Prime Number Slapjack or color in a Prime path maze. If kids are a bit older and are ready to properly learn about Primes, composites, factor trees, and the factorization of Primes, this lesson and this lesson are excellent jumping-off points. 

We have a lot of wall space in our home, and my kids have always enjoyed making large-format posters, maps, and charts to put on our walls. A large-format hundred chart mounted on a wall lets kids have a different experience coloring it in mural-style, and would also allow room for kids to write each composite number's factors into those squares. Alternately, extend the hundred chart to 1,000 and keep sieving, although I wouldn't blame you for eventually pulling out the calculator!

Here are some books that older kids and adults would enjoy; completing a reading assignment (and perhaps even a response essay!) builds context and adds rigor to an otherwise simple activity, and is a good way to facilitate different ages/abilities working on the same project:

Here are some other math facts that a student could aid fluency by memorizing:

• fraction/decimal conversions
• PEMDAS
• Quadratic formula
• squares
• square roots (perfect square factors and simplified square roots to 100)
• Pi to several digits
• Pythagorean theorem
• Pythagorean triples
• triangle identities
• SOH CAH TOA

P.S. Want to follow along with my craft projects, books I'm reading, dog-walking mishaps, encounters with Chainsaw Helicopters, and other various adventures on the daily? Find me on my Craft Knife Facebook page!

Hands-on Rounding, or, I cannot Make This Concept Any Clearer

Rounding is just non-intuitive.

Not only do you have to wrap your head around the fact that you're going to pretend that a number is a different number, but you have to remember that even though it's called rounding DOWN, you don't round down by subtracting 1 the same way that you might think that you round up by adding 1 (that's not *really* how you round up, but if you're nine, that might be how you've explained it to yourself).

Oh, and rounding up if the digit is 5? That doesn't actually make sense; it's just a convention to memorize.

I wanted Syd to understand the concept of rounding, not just memorize a rule that doesn't make sense to her, so using this post on hands-on rounding as a spine, we went over it again from the beginning.

The post doesn't mention using a hundred board, but we've relied on our hundred board a lot throughout Syd's entire math education, so once again we began a lesson by having Syd build it:

I've got three sets of these 1-100 tiles, two DIY sets and one for the light table/overhead projector, so I could leave the 100 grid intact and give Syd a second set of tens to use in making a number line between two consecutive tens:

This part was all review, as she had no trouble with any of it.

Syd built a number line between two consecutive tens a few times, each time with me handing her the numbers in between at random. We then reviewed rounding to the nearest ten by noting on each number line which consecutive ten a number fell between, and which consecutive ten it was closer to.

Numbers ending in 5, of course, round up merely through convention, as we also discussed.

To end the activity on this day, Syd and I played a game with two 10-sided dice. One of us was "Rounded Up" and the other was "Rounded Down;" we each took turns rolling the two 10-sided dice, making a number from it, then deciding if that number rounded up or down and giving a point to the correct category.

Although the points go to the correct category regardless of whose turn it is, when it's your turn to roll, you can do your best to build a number that gives you the point. It's tricky, though, because you can't always build a number that goes your way!

I let this lesson settle for a few days while Syd worked on different concepts in her Math Mammoth, then we had another lesson on rounding to the nearest hundred and thousand.

Syd didn't seem confident in building a number line between two consecutive thousands, so I had her do so using the hundred flats from our Base Ten blocks as physical markers, with each hundred written on a torn piece of paper--use what you've got! I then used a domino to mark a place on the line--9,600, say--and gave Syd another domino to use as a game piece to hop to each thousand:

The thousand with the fewest number of hops to get to it, obviously, is the thousand that the number is closer to.

After this, we turned to our light table, and I asked Syd to build another number line between two consecutive thousands:

I used the dry-erase marker to modify the 0-100 tiles to make them into numbers in the thousands (30, for instance, became 5,300), then asked Syd to place them on the number line. She found this a LOT harder than working with a number line between two consecutive tens. Her number line got so wonky, in fact, that I abandoned the tiles work, gave her a different number line--9,000 to 10,000--and asked her to simply draw in the hundreds in between.

As she did so, I noticed that she did not have 9,500 in the middle--actually, it was very close to 9,000---so I asked her to check her spacing. She was VERY not happy with this, because she knew then that she'd made an error, and she HATES making errors.

Aside: That's an attitude that we work on a lot, by the way. I see it as a very destructive type of thinking that will keep her from establishing a strong and persistent work ethic, so I speak constantly of the fact that knowledge and skill do not enter one's brain by magic, but instead require a lot of training to achieve. When one has the correct answers immediately, one is not learning, but reviewing. Learning is the space in which we try to spend much of our school days, I tell her, and we know that we are in that space if we are struggling and making mistakes.

Hopefully one day that will sink in!

Because Syd was tipped off that she'd made an error, all of her will became focused not on finding and correcting her error, but instead on defending it to the death. She insisted her spacing was perfect. I noted that there was only a finger's width of space between each integer up to 9,500, but that the others on the way to 10,000 were really far apart. She decided to deliberately misunderstand me, and began screaming that I wanted her to write everything with one finger in between, and that was impossible. I excused myself to my room, and told her that she should choose another activity, and we'd finish the lesson later. I then read quietly for an hour while Syd screamed the house down in the next room.

Of course, eventually one must finish one's schoolwork if one wants an hour of screentime, and one DOES want this hour, so much, much, much later, Syd went back to work with a good attitude renewed:

I was still pretty over it, so Matt finished the review with her, and then they played the same dice game, this time with four 10-sided dice, with the goal, again, to decide if the number rounded up or down to the nearest thousand:

Afterwards, I quizzed Syd by throwing out more numbers, and she was able to round them all correctly! She was also SUPER happy to do so, because she knew that she was getting them all correct.

Have I mentioned that this child exhausts me? Oh, my word, she exhausts me!

But, of course, so does the other one...