The kids worked in partners—most kids paired with their sibling. (It was 6 sets of siblings in the class of 12 kids—11 boys and 1 girl!) They got a kit with the pieces they’d need, and a booklet outlining step-by-step how to put the piece together. The kids were thus able to help one another if one of the pair got stuck. There was also an instructor to assist, and a big bucket of cool Lego pieces for free building once the project of the week was complete.

The first week they built the Eiffel Tower:

The second week was a windmill, including hooking it up to a motor to make it spin. Daegan got so excited when he finally got the connections the right way so it spun—so did he in the pic.

The third week they made a see-saw (teeter-totter), and the fourth a turnstile with lots of gears. Again, both projects hooked up to motors to move:

Thanks again to Lisa for setting up this class and hosting.

The boys watched the DVD while they ate lunch, and were up and dancing around to the songs when I returned from doing some work in my office. You can watch some clips from the DVD here. They’ve got links to other fun math videos, from Schoolhouse Rocks to Tom Lehrer, on their site on well (see here). Here’s the boys groovin’ to math songs:

And checking out details written on the DVD case (notice Gareth is now reading the case himself, rather than passing it along to Daegan to read to him):

The other product from Googol Power that we’ve been enjoying lately is their Crazy 4 Math CD, which we borrowed from the library. We listen to it in the car a LOT, and I have to admit that even I enjoy the songs and goofy humour. This CD takes a math journey through time, meeting all kinds of famous people and their contributions to our world. Gareth’s favourite song is Track 12 (guess how I know the exact number? ), about electromagnetism. My kids have learned who Nikola Tesla was from this song, as well as Charles Jenkins and John Baird—men instrumental in the invention of television. All kinds of other names appear in this song, from Thomas Edison and Alexander Graham Bell to Tchaikovsky! It’s just awesome! You can read more about this Crazy 4 Math CD here; I’ve excepted a chunk below:

…meet Cleopatra, Archimedes, Galileo, Benjamin Franklin, Amadeus Mozart, and Leonardo da Vinci. Discover how math has greatly influenced our world and that math, the science of patterns, is everywhere — in music, science, nature, art, and architecture. …

Includes 11 songs and dialogue, Pi, Phi, The Golden Mean, Fibonacci Numbers, sound frequencies, amplitude, electromagnetism, gravity, rhythm, skip counting, powers, math patterns, fact families, math questions, historical facts and cool ideas for practicing math.

I will say that Cleopatra with a Texan drawl and Mozart sounding like Schwartzeneggar only add to this crazy humour of this CD, at least for our family. YMMV.

Looking on their website I see they also have a Skip Counting Zone CD, which we’ve not listened to as our library does not carry it, as well as the addition one: Addition Celebration. My kids thought that one was ‘just ok’, so worth a listen if you can get it free/cheap somewhere, but I’d recommend Crazy 4 Math or Multiplication Vacation instead. I believe the CDs are available on itunes as well. Have fun learning your math—and a whole lot more (science, geography, history, etc.) besides! 

Now, a few caveats. If you’ve been reading this blog a while, you’ve no doubt learned that I do not think quickness at basic facts is all that important at the end of the day, though I do think knowing the facts solidly and with a certain proficiency helps. And if knowledge of the basic facts lags too far behind the child’s other math skills, it causes problems. I am starting to run into this more and more with Daegan, who has very strong problem-solving skills, but who gets tripped up on the basic math facts in solving them. So today, for example, our Math U See lesson was about averages—a logical topic in Delta, the book focussed on division. I gave him some enrichment problems from the Math Olympiad book, which I’ve been enjoying vicariously via videos (also found on youtube) from Mike’s Math Page, like:

You are play 5 levels of your favourite video game, and defeat an average of 10 zombies per level. On the first 4 levels you defeated 7, 8, 11, and 20 zombies respectively. How many zombies do you defeat on the 5th level?

Daegan’s basic reasoning is strong, and he tells me that with 5 levels and an average of 10 zombies per level, that’s 50 total zombies defeated. So what we need to do is add up how many zombies you defeated on the first 4 levels, and then figure out how many short you are—which would be the total for the 5th level. So he writes:

7+8+11+20=

and then goes, “7 plus 8….uh, uh….I don’t know!?! Is it 13?” Sigh.

Hence, the xtramath site for extra math fact practice. Daegan liked the ‘addition placement tests’ he did today, and said he was happy to practice on this site “twice per week…maybe more, but let’s start there so I don’t get sick of it.” Okay by me, son. Some things Daegan particularly liked:

-you get a checkmark if you get the answer right within (a generous) 10 seconds. So his first goal is simply getting a checkmark on all his facts (displayed on a grid at the end of each session). You get a smiley face if you can do it in under 3 seconds.

- If you get a question wrong, or run out of time (10 seconds), the answer is given to you to type in. This is a HUGE deal to Daegan who cannot stand programs that do not allow him to correct his mistakes quite quickly.

- It can be done entirely independently, and is short. Today’s intro videos and 3 addition placement tests took him less than 10 minutes, with no help from me other than showing him how to log in.

Things I like:

- It tracks progress and creates reports. We can see quickly which facts are mastered (under 3 seconds), known (under 10 seconds), and need work.

- The program automatically adjusts to give him more practice with the questions he needs it on, and less on those mastered.

- I too love the difference between the smiley faces and the checkmarks. (There is also an ‘x’ for those got wrong, and an hour glass symbol for those where the child did not answer and ran out of time). So many games and programs I have found are “all or nothing”—you either know the math fact, and quickly, or you don’t succeed. Xtramath, in contrast, breaks success into two distinct phases: accurate answers and speed. I like that simply getting accurate answers—even slowly—is rewarded.

Gareth also wanted to try the program, so I set up an account for him too, and he did the same three placement tests (though the questions began to differ). He too said he likes it—though right now he likes anything his big brother gets to do—and wants to do it ‘”once per week or so”. As Gareth is still learning his basic facts; any practice he does is a bonus in my eye. And if he decides he doesn’t want to right now, fine as well. He’s six!

Anyways, if you are looking for a no frills option for basic math fact practice, that tracks your child’s progress and adjusts to their strengths and weaknesses, give this one a try. You’ve got nothing to lose: It’s free! Again, the link to xtramath can be found here.

Daegan got a lot out of this video, and was inspired that night to practice drawing different numerals: Egyptian, Roman, and modern ‘Hindu-Arabic’:

And tonight the boys and I replicated the activity done during the documentary, in which mathematician Marcus du Sautoy explained binary numbers to Terry Jones using egg cups. (We used washed fruit cup containers). I started off by setting up our usual base 10 system (in blocks) beside binary, or base 2, cups:

Let’s begin where it is easiest, in the ‘tens’ place (second from the right in the blocks). Notice that as you move to the left (get larger), each place value increases by a multiple of 10. The hundreds are 10×10 (or 10-squared, or 10 to the power of 2); the thousands are 10x10x10 (or 10 to the power of 3), and so on. It is similarly with with binary, or base 2 system: each place value (‘cup’) to the left increases by a power of 2. 4 is 2×2, 8 is 2x2x2, 16 is 2x2x2x2, etc. Note too that we can express 10 as ‘10 to the power of 1’ and 2 as ‘2 to the power of 1’. The limiting case in both systems—the ‘ones’ or units as they are now more often called—is the base to the power of zero. Anything to the power of 0 is 1. (It’s one of those weird quirks of math; if this bit is fuzzy don’t sweat it).

Now, we’re all quite sure that every whole number we can think of can be expressed in our base 10 system, using the digits 1 through 9, with a 0 as a place value holder. But would you believe every number can also be expressed in binary, using nothing but ones (for a full cup) and zeroes (for an empty cup)? I know the boys didn’t believe it, and it is far from obvious: these cups are labelled 1, 2, 4, 8, and 16. How the heck do I make 22? Or 14? Or 3, for that matter?

So we made a chart, with the ‘normal’ base 10 numbers on the left, and the way we can express those numbers in binary notation—using nothing but ‘1’ and ‘0’—on the right. Here’s the completed chart (again, don’t worry if this doesn’t make sense yet—it will! Even my 6 year old was able to understand this!):

We then started building numbers by putting eggs in the appropriate cups. 1 was simple—an egg in the 1 cup—and looks the same written in binary as base ten: ‘1’. The picture below shows 2, which we’d write in binary as 1-0 (say ‘one-zero’, not ‘ten’); again, 1s show the ‘cup’ or place value filled, zeroes mean that place value is empty:

And 3, or 11 (‘one-one’) in binary; both the 2-cup and 1-cup are filled because 2+1=3.

And 4, or one-zero-zero (100), along with a hammy Gareth:

Can you figure out how to make 7? Yup—it is 4+2+1, so fill those cups for 111 (one-one-one):

So what number does 1010 represent in binary? If you said 10, congrats—you’ve got it!:

We continued on this way, and soon the boys felt confident enough to record the binary numbers in our chart, as well as create them:

I made a video of the boys building numbers 12 through 17 in binary (I’ll add it when I figure out how!) And yes, that’s the 6-year old rattling off (out of shot) the binary representation of 13. I am utterly amazed at Story of 1s ability to make binary numbers accessible to a child this age!

We ended the session by me asking the boys what the biggest binary number they could currently make (with 5 cups, or place values) was, and they quickly sorted it out. Gareth said it would be written “one-one-one-one-one” (11111) and Daegan added it up: 31. (16+8+4+2+1).

Who knew egg cups could be such a useful math manipulative, eh?

All the numbers (products) have a unique answer (factors), except for the shaded middle row which have 2 answers apiece. So the student ‘sweeping’ the grid would start on the top row: “2 times 2” “2 times 3”…until the shaded row “2 times 6 and 3 times 4” “2 times 8 and 4 times 4”….to the end “9 times 9”. The idea is to have students practice until they can ‘sweep’ the whole honeycomb in 60 seconds or less (though I will de-emphasize speed here.). You can find a video about this game here. And I got the basic honeycomb grid in the picture above here.

Now, I quite like this idea in general, for a few reasons. First, laying it out in terms of answers (products)—there are only 31 of them—simply looks less overwhelming than a traditional times table grid. The commutative property of multiplication is implied—or, to put it in simpler English, a child need only say one of ‘2 times 3’ or ‘3 times 2’ when sweeping over the 6 honeycomb; not both as in a traditional multiplication table/grid. Second, it goes about multiplication from a different perspective, giving the products only. A child with a decent visual memory should quickly learn which numbers are products, and which aren’t: one simply doesn’t need to worry about 47, for example, when it comes to memorizing times tables, a fact that is not so obvious to some when memorizing conventionally (7 times 7 is…49? Or is it 47?). Third, I think this grid is quite adaptable: once your child has mastered a fact, you can colour than product in, cover it with a token, etc. I am also going to try writing these numbers in sidewalk chalk on our driveway and see how Daegan does jumping between the products, both doing the sweeping himself and answering questions I fire at him. 

If you try this out with your kids, let me know how it goes. I’ll update this post once Daegan and I have played around with this multiplication honeycomb a bit more and let you know his thoughts. 

Easy Make and Learn Projects: Human Body (we’re doing Human Body this year)
25 wacky and Wonderful Stories that Boost Vocabulary (Daegan wants to learn about prefixes, suffixes and roots, and this humourous book looks perfect!)
Paragraph Power (D is learning to write paragraphs)
Grammar Cop (notice this humour theme so far?)
25 Mini Plays World History (reader’s theatre as an intro to history works awesome for us)
Great Map Games (elementary map skills are another theme this year)
Read Around the World with 20 Great Picture Books (we’re bibliophiles!)
Mega Funny Division Stories (nice complement to MUS Delta)
Math Practice Puzzles (puzzles over dull drill anyday!)
Origami Math (how fun!)
Funny Fairy Tale Math

and the list goes on and on. I used some of the new material as our math ‘warm-up’ today: Gareth did a few pages from an Algebra Readiness book, while Daegan did some math facts practice in this fun ‘riddle’ format. They both loved the new materials.

I was able to make this an even better deal by using the code 10THANKS in the coupon code slot, saving $10 from my order. Not sure if the code is still working—a friend of mine had some difficulties tonight—but worth a shot. Oh, and you’ll have to hurry—the sale ends tomorrow. Happy shopping and I hope you find some fun additions for your homeschooling / afterschooling!

Ten Times Better turned out to be a far better book and better fit for our family that was apparent from the cover. I’d gotten it out of the library ages ago, and it had laid around, unread—until I got notice this week that it was due back. When I finally got around to reading it aloud to the boys as part of our math lessons that day, we all loved it! It is a series of playful poems (and playful artwork!) featuring different animals, with the first animal saying what he/she thinks the best number is, and why. And the second animal saying, in effect, “Oh, yeah? This ten-times-bigger number is better!” So the book starts with an elephant singing the praises of ONE (as it has one trunk), and a giant squid saying TEN (as in tentacles) is clearly better than one! And on it goes with very logical choices for the animals: a 3-toed sloth, a 9-banded armadillo, a giraffe with 70 spots on its neck. And my children’s favourite animal and line of poetry: “I have 60 teeth” says crocodile, “I’m a great  masticator. (That means I chew first, and ask questions later.).” A delightful book for kids learning multiplication and into animals.

The History of Counting was a book that caught Daegan’s attention; Gareth half-listened as he played on the floor nearby. It does exactly as its title suggests, outlining some of the major steps in humankind’s “invention of counting”, from using pebbles / physical markers (counting without numbers), to body counting (“1 is left little finger…11 is left neck…16 is right ear” up to a very limited number: 28), to using different words to represent the same number of different things (like we use “twins” to mean two babies who share a womb, but “duo” to mean two people in other contexts, like music), and so on. We visit the Sumerians (whose ‘base 60’ lives on today in our number system: 60 seconds in a minutes, 60 minutes in an hour, 360 degrees in a circle),  Egyptians, Phoenicians, Greeks, Romans, Arabs, Hindus, etc. up to modern day arabic numerals and the importance of zero and place value. Daegan was particularly engaged with the section on Roman Numerals, and the way the book showed their severe limitations when it came to computation. This is a very abstract concept for a 9-year-old, that’s for sure—understanding why place value was such a big leap over Roman Numerals—but attempting the addition problems in the book:

1084+1797

vs. the same numbers written in Roman Numerals:

MLXXXIV + MDCCXCVII

drove the point home. And even more so when I suggested he try multiplying those numbers instead of adding them! Happy reading!

Ant is on her best behavior when she attends Lion’s dinner party, but she is shocked by how the others act. Elephant talks only about himself; hippo never wipes her mouth and gorilla throws his food! Their behavior is even more outrageous when dessert arrives. Each animal takes exactly half of the lion’s cake, demonstrating very bad manners – as well as the basic concept of division! When the cake gets to ant, there are only a few crumbs left – and the lion hasn’t even had his share! To make amends for such bad manners and lack of cake, ant promises to bake a special one for lion. Not to be outdone by such generosity, the others promise cake as well, each one doubling the number until elephant must bake 256! As ant and lion enjoy a delicious strawberry sponge cake, readers may decide that halving and doubling have never been so much fun. Includes A Conversation With the Author!

My boys both enjoyed this DVD, though perhaps for different reasons. The story is cute and simple and contains some interesting questions about fairness (‘Each animal did the same thing—take half the cake left—yet the results don’t seem fair. How can it not be fair when they all did the same thing?’), interesting math (‘My, don’t the number of cakes quickly get out of control when each animal wants to bake double the number of the previous animal!’), and questions of character (‘What did you think of the way different animals behaved?’). On the story and math level, the DVD fully engaged Gareth (age 6). Daegan (age 9) found the story a bit simple, but was very engaged by the end of the DVD with the conversation with the author, who also did the illustrations. Learning where the author got the idea for the story (from a party he was at where no one took the last piece of food, each just kept cutting off a small bit), how he adapted it for a kids’ picture book, how some of his ideas didn’t quite work out (originally he wanted each animal down the line to be half the size of the previous animal, just like the cake), and how he created the illustrations were fascinating to my older son, who is doing some significant work on writing skills this year.

All in all, a really cute video with lots more going on than a simple story / simple math. I found a copy at our library. Happy viewing!

Digitz Lite

In this app, designed for adults, gems/tiles with numbers on them fall from above and pile up. You are given a target number—it’s 10 on the easiest level—and need to clear the gems that add to 10 by pressing them (e.g. clicking on 4 and 6). If you can do so for long enough, and the gems never pile up enough to reach the top, you win that level. Gareth (age 6.5) finds this game challenging and only focuses on the one-digit plus one-digit ways to make 10 (1+9, 2+8, etc.) whereas Daegan sees more complex combinations (2+3+5, 1+3+6, etc.) to clear more gems at once. The same company makes a Kidgitz app specifically for kids, where you can set the target number from 4-12. In contrast, my random attempt at the ‘hard’ level of Digitz Lite gave me 28 as a target number. I think we’ll be spending the 99 cents on Kidgitz.

Match-Up Math Lite

This is one of Daegan’s favourite games. A random collection of tiles is laid, with some covering / blocking others (they are shaded indicating you cannot play them yet). On the tiles is a number (1, 6, etc.) or a math fact (1+0, 3+3, etc.), and you need to clear matching facts, ideally doing so strategically so as to unblock other tiles. If you get stuck, you can hit the shuffle button, but it’ll cost you some points. This game has 3 different levels, with the difficult level having both more complex questions (8+7, 12+9) and a more complicated tile layout. I like that this game is not as simple as matching a math fact to its sum; sometimes the only way to clear the tiles is to realize 3+6 and 8+1 are a match. The full version, at $2.99, includes the other three operations, as well as fractions, percents, and decimals. Haven’t bought it yet, but given how much Daegan likes this one, I probably will. 

PopMath Lite

This game is best suited to Gareth (age 6) rather than Daegan, and is similar to the previous app, Match-Up Math, except it is far simpler. You have a few balloons that float, and you are to find matches between the balloons with numbers (8) and the balloons with addition facts (4+4). I can’t see this app having as long a life as the others, but it is a great option for younger siblings wanting to play an app game independently like their older brother. The full version is only 99 cents, and includes the other three operations, and from the screen shots in the app store, far more complicated levels.

Kakuro Zone Lite

I love Kakuro puzzles, and we’ve incorporated them before in our math learning—see here for a detailed explanation of how they work, with lots of pics. Kakuro puzzles are like addition crosswords, sometimes called cross sums puzzles. I like this particular app as the interface is clean and intuitive, and the easy level is easy enough for my 9 year old to do.  Might get the upgraded app just for me—I love math puzzles that incorporate a logical reasoning component.

Snake Puzzle

This is a type of math puzzle I’ve not seen before, and both boys like it (though Gareth requires help to complete even the easy level, as there is a strong logical reasoning component.) In the simplest level, you are given a 5-by-5 grid with 25 numbers. Some of these numbers are yellow and represent the target numbers, or sums, you must add to. You solve the puzzle by tracing your finger over the non-yellow numbers, making a ‘snake’ connecting them together, and draw to connect the snake to the correct sum. Some snakes are easy—you might have a 3 in a corner, as in the screenshot, with the only one set of numbers nearby that can ‘snake’ (be connected) to make 3, s2 and 1. Sometimes the snake is hard to figure out, like when you have a yellow 5 in the middle of the board surrounded by 1s, 2s, and 3s—there are make combinations that would work. In the screenshot, the 9 is like this—there are several ways to snake to 9 right now, so I need to start elsewhere and see what tiles are left. And just like a real snake, your sum can twist and turn—it need not be a straight line—it just must be connected (no diagonals, though). Play around with this one if you like math/logic puzzles—it’s quite unique and a lot more challenging than it first appears, especially on the larger grids. The full app is 99 cents, and again this is one we are going to get.

Have fun playing with your math—and don’t worry, LOTS more math apps to come!

Daegan has rolled a 1, 6, and 3, so he could cover a variety of numbers on the board, like 10 (1+6+3), 4 (1+6-3), 18 (1x6x3), 3 (6/3 + 2), and so on. Here’s Gareth’s roll:

And what he chose to cover—the 11.

The game gets more challenging as you go along, as certain numbers are all covered and no longer available. This forces the player to try different mathematical operations until he/she finds one that works. For example, my roll of 3, 4, 5 about halfway through the game could not be used to cover 12, as there were no 12s remaining. So I am forced to use math beyond simple addition.

I’ve played this game with Daegan twice now, and Gareth once (today), and it has gone down quite well with the boys. They like playing cooperatively, and we all help each other find alternate answers when the board starts getting full. The boys get a kick out of creating numbers not on the board too—like negative numbers (2 times 2, minus 5 is….negative 1! Laugh, laugh, laugh—I have mentioned that I’m raising geeks, yes?) Daegan surprised me by doing some simple division among his answers today (we haven’t gotten to division in the Math U See curriculum yet), and he wanted to make some into fractions too. This game is obviously endlessly adaptable, and you could easily create your own board with fractions, mixed numbers, negative numbers, larger numbers (for multiplication) etc. on it if that was what you were working on.

Oh, and the game took us just under 30 minutes in total to play—and I can tell you neither of my kids will sit and do worksheet drill for anything close to that long! (And frankly, neither would I as a kid). Have fun playing with your math!