There are 4 cards with a child’s body outline, and 4 reusable sticker sheets, but we decided to play cooperatively and build one body together. So I flipped over a card and read questions (which ranged in difficulty), like:

Which body makes the chemical substance called insulin? Insulin controls how much sugar enters your blood. (pancreas, PAN kree us)
Which body part is about 5 feet long and finished digesting your food?
What body part attaches to your bones and moves your other body parts?

and the question Gareth actually got in the following picture:

Which body part cleans itself with tears?

Since Gareth was able to answer this correctly, he got to add the “eye sticker” to our body:

Both boys really enjoyed this game; it was simple enough not to be frustrating or go on too long, but some questions were challenging enough to keep it interesting. We even learned a few things! Here’s Gareth with our finished body. That kid is such a ham!

You should see the silly grin on his face on the pics of him pointing at the bladder—which I told him I would not post!  Oh, well—at least he’s learning, right?

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. 

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!

I thought I’d start with some language arts apps that Gareth is enjoying. Gareth is now past the very beginning stages of reading and writing, but if your child is at that stage you can search the app store for terms like “learning to read” “phonics” “ABCs” and so on and you’ll find a ton of things, many of them free. But once you get past that very beginning—match the letters and sounds / here’s how you print the letters / let’s make simple CVC (consonant-vowel-consonant) words, like ‘c-a-t’—the pickings slim down considerably. Two of the best I’ve found so far are:

Sight Words by Little Speller

and

Sight Words by Photo Touch

both from the same company, GrasshopperApps.com. The first is a spelling game; the second a reading game. Both games use the same 220 Dolch sight word list, broken up into 5 levels/grades: preschool / K / 1 / 2 / 3. Preschool (Level 1) words include ‘away’ and ‘said’; grade 1 (Level 3) includes ‘could’ and ‘know’ and grade 3 (Level 5) includes ‘eight’ and ‘laugh’. The words do not overlap between lists, meaning you’re getting a unique group of 40-50 words per level. Both games are highly customizable (just go to the settings button), right down to recording your own voice reading the word—something that came in handy as the Sight Words by Photo Touch reading game had an incorrect pronunciation (the voice said “ask” for the word “as”), so I simply recorded my own voice over it. It also means that depending where you live in the English-speaking world, you can customize pronunciations to reflect regional differences, something as a Canadian I appreciate with the grade 3 word ‘about’! The customization options are very detailed and well thought out; let’s looks at the Sight Words by Photo Touch game in more detail.

You play this game by selecting the word being said aloud from a group of cards showing various words on them (like a flashcard). As you progress and do well, the game gets harder by adding more cards to choose from for any given word. You can customize whether or not to give hints, the minimum and maximum number of cards to display, whether or not have error and success sounds, whether you are picking words from only one level/grade, or a few, or all.

The spelling game works similarly, with kids having to put jumbled letter tiles in order to spell the word given. For younger kids you can leave the hints on the screen (the word spelled underneath the jumbled tiles in the centre of the card, as well as shaded in lightly in the tiles area, so kids are matching letters more than spelling. Gareth plays the game with the hints off, so he only has jumbled letter tiles and a blank tiled word space below:

Simple game concepts, but very easy for kids to navigate, and parents to customize. Gareth has played both and likes them, as they are perfect for his literacy level right now.

Another game Gareth enjoys, and which feels more “like a fun game like Mom and Dad play” and less like edutainment, is:

Whirly Word.

This is your basic “make words out of this collection of letters’ game, like Scrabble or Boggle, and there are tons of variants of this game available in the app store, many (like Fishtropolis, Textropolis, and Chicktionary) with free versions.  But Whirly Word is Gareth’s favourite by a long shot, and for several good reasons. First, the letters are displayed in a circle, around a central ‘enter’ button, a layout I think helps new readers / spellers see more easily how various letters can go together to make words; there is no long chain where the first and final letter are far from one another. Second, the game limits itself to 6 letters. Third, it allows 3-letter words. Lastly, you go from one level to another in the game in one of two ways: either by making the longest (6-letter) word, or by making enough words for your progress bar to get past a certain line. This game is VERY generous in that progress bar, allowing my beginning 6-year-old to find enough words (often simple 3-letter CVC words) to make the ‘green light’ come on and allow him to choose to go to the next level. You don’t NEED to go to the next level, however, and for older kids (or adults) you could play to find more or all words before going on. But Gareth LOVES this game, and I can see why. He can play it without help, spell words, and go from one level to the next based on his efforts—just like Mom and Dad do on the far more complicated games like Fishtropolis, which starts at 4 letter words (not 3), and has far more letters (than 6) to combine.

Finally, I’ll mention a game I love, and is a good stretch for Daegan (age 9) or older kids:

Word Jewels

In this game, you have a honeycomb of letters and need to make words, moving from any letter to a connected one (does not have to be in a straight line). But there’s a twist: to go from one level to the next, you need to use all the letters that have a red background. The game starts deceptively easy: in Level 1 there is only 1 of 25 honeycombed letters that is red, and you are given just one turn to eliminate it by spelling a word that includes that letter. (Any letters you use to spell disappear, and the rest of the honeycomb letters slide down with new ones added at the top, like Bejewelled Blitz). In round 2, 2 red letters and 2 turns, and so on, but you soon max out on the number of turns you get to eliminate all the letters (9 turns is the max). I found it fairly challenging by the early teen rounds (eliminating, say 14 red letters in 9 turns), and the highest I have ever gotten is level 26 (yes, one past all 25 letters being red and needing to be used). You have one other helper in the game, and that is the ‘shake’ button, which reshuffles the letters on the screen, allowing you to proceed if you get stuck. (Take my advice—get rid of those Js early, or they have a way of getting stuck in corners!) You get points for the words you make, more points for longer words, as well as points for any unused moves (if you are able to clear the red letters in 3 moves instead of the 4 you were given, for example). ‘Shake’ carries with is a points penalty, but it does not count as a turn.

Have fun, and I’ll share some more apps later!

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!

Here’s some pictures. Daegan split his bowling between the one-armed traditional roll of a bowling ball, and the ‘two-hand between the legs’ roll, whereas Gareth generally stuck to the between the legs method.

Jim and I gave advice and encouragement:

My grandma must be proud. It’s her 92nd birthday tomorrow, and she was a bowler most of her life, well into her 80s if I am remembering correctly. Continuing the legacy! Next, to teach the boys canasta!

because this is the card he turned over, and the die (multiplier) in question:

If the player calls out the correct product (answer), he/she keeps the card in his collection pile. The player with the largest collection pile at the end of the game—the most cards—wins. We added the variant that at least once per game I would call out an incorrect product, and if Daegan caught it and called “Challenge!” and then could supply the correct answer himself, he got to keep my card. Kids LOVE correcting adults when it comes to math facts, in my experience.

There are a number of things I quite like about this game. It’s short and fast—far faster having a child answer in writing on a worksheet the same number of problems—and uses everyday household objects. It is also almost endlessly adaptable to the needs of your student / child. Kids ready for more of a challenge could roll two dice instead of one, and sum them as the multiplier, hence practicing up to the 12 times tables. We, on the other hand,  simplified our deck of cards, removing 7s and 8s as Daegan has not yet got to them in his learning of multiplication in Math U See, book Gamma. You can play with the same multiplier (die roll) through an entire deck to practice on set of facts in depth, or you can roll the die every few cards to get a new multiplier involved—we played and enjoyed both ways. And you can make it more competitive by playing the way Long originally suggested in her book, where both players “shout out” the answer as a card is flipped, and the first to give the correct product gets the card.

Gareth saw that he could make the word SUB, so he flipped up the B. He also could have flipped the B by making BUS, or flipped the G and H by making GUSH, or the F L and H by making FLUSH, etc. The object of the game is to be the first to flip up all your letters, but as Gareth is still early in the ‘learning to spell / learning to read’ game, I was just happy to see him create legitimate words, and kept my own word creations at a similar level to his.

The game is quick and can be played at many different levels. When all four of us played a match, Daegan had three letters remaining and rolled, as follows:

He could only see HIT, but there was a word that would have allowed him to use all his letters and win the game. Can your child figure it out?

The other sign of Gareth’s increased confidence in reading came last night at the dinner table, as we were eating a rather bland stir-fry. “Is that hot sauce?” Gareth asked, pointing at a bottle on the table, a question which surprised us as, like many 6-year-olds, he is quite happy with bland food. But he had a follow-up question: “Does that say ‘red hot’?”

As far as I know, that is the first time Gareth has definitely read words in his environment. He’s ‘read’ other things before, like “Burger King” or “Diego”, but I would think they are him recognizing logos rather than true reading.

I’ll be giving the boys their annual reading level assessment tomorrow; I am curious what sort of improvement we’ll see over last year, for Gareth in particular.

In the picture above, Gareth is showing 1 finger and Daegan 5. Though originally a multiplication game, I adapted it as Gareth is working on his addition facts. So Gareth said, “one plus five equals six” and Daegan said “one times five is five”. Here’s another, where both boys showed 3 fingers:

Here, Gareth called out “six!” (3 + 3) and Daegan called out “nine!” (3 x 3). Once the boys got comfortable with the game, we tried it with two hands per player, and hence more fingers. The first was as you’d predict (kids tend to go to extremes first, eh?), 10 and 10:

The boys were able to rattle off the sum (20) and product (100) without difficulty. But the next Fingers! round, they managed to stump each other: 8 and 6. This picture was taken with them in the midst of laughing with one another: “I don’t know what it is when you add / multiply those numbers!”

Gareth worked out the sum by counting on his hands (more advanced kids could group to 10—i.e., 8 + 6 = 8 + (2 + 4) = 10 + 4 = 14—or what I call ‘split doubles’, i.e. 8 + 6 is a lot like 7 + 7 where one unit has moved from one 7 to the other, splitting up the double). Daegan and I worked out his product by thinking about what 8 x 6 means—8 groups of 6, or 6 groups of 8. I suggested he think about 6 groups of 8, and split those groups up to 5 groups of 8, and 1 group of 8. Daegan can skip count the answer to 5 groups of 8 (5 x 8, or 40) and when you add one more group of 8, you get 48. There is advantage in being able to think about multiplication (or any math question) this way, breaking it back to what you know already, so don’t be too quick to insist kids simply memorize the times table without understanding what multiplication means, IMHO. 

Other variants we tried were 3 people, one hand each—and as I was the third person I was careful to keep my digit small (1 or 2) so that Daegan would have an easier time multiplying. The one time I decided to go for a 5, the boys the did the same, and Daegan was able to figure out  5 x 5 x 5 by thinking of quarters (5 x 5 is 25, 25 x 5 is like having 5 quarters…125!). We also tried 3 people, two hands, but as the products there go to 1000, be prepared to have a pen and paper nearby. You can also make the game competitive by awarding points for correct answers, or to the player who answers first, or play until one player has made the word “M-A-T-H” or “F-I-N-G-E-R-S” where a letter is given for a wrong answer. 

In conclusion, fun game, no prep or special materials needed, and a good choice for kids who like to move their bodies while learning. Keeping this one in my repertoire  of “how to pass the time while waiting at the….”.  

This morning the boys and I read an intriguing book, The Token Gift  (Canada) (US).  It tells the fictional story of an old man from India, Rajrishi Mohan, discontent with what he has accomplished in life. If only he had been king, then he would have amounted to something! His wife reminds him to think back to his youth, and the game he created that is now played by so many—chaturanga, or, as it is known today, chess. Detailed, lush pictures take us back to his youth, and how the game of chess evolved from other games of chance using dice, to a 4-person game involving “4 divisions” (of the military: chariots, elephants, cavalry, and infantry) and a mix of strategy and chance, to the modern game of chess—pure strategy—as we know it today. The man is interrupted by a messenger sent from the king, who commands Mohan to the palace.

He makes a journey of several days, and meets with the king, who wishes to give Mohan a gift to thank him for inventing the game. “I have enjoyed played it since I was a boy—and the game’s emphasis on careful thinking and strategy has given our generals many advantages on the battlefield. I was surprised—and delighted—to learn that the inventor of this game lived in my kingdom.” Mohan refuses the offer, but the king insists, and Mohan requests what the king takes to be a small, or token, gift: for each of the 64 squares on the chessboard, he will accept some rice, with 1 grain for the first square, 2 grains for the second, 4 for the third, 8 for the fourth, and so on, doubling each time.

The king promises to provide this gift, and sets about meeting it. Servants start piling rice—1 grain, 2 grains, 4, 8, 16, 32, etc. but they soon run into difficulty, and the king sends for the Royal Mathematician. This part of the story is exceptionally well done, I think, as we learn that by square 16 there needs to be 32768 grains of rice—or about as much as in one sack of rice. Now the doubling begins anew, and by square 32 the king needs 32768 sacks of rice—more than the kingdom can grow in one year, but about equal to 1 shipment of rice.  And by square 48 he needs 32768 shipments of rice, or as much as the world can grow in a year, and by square 64 we learn it would take the world 32768 years to grow the amount of rice required! The king resigns in shame, for a man unable to keep his word is not a man of honour, not a man worthy of being king.

So now Mohan has his wish, and is king. But he wanders the halls of the palace feeling empty inside still—he realizes he is still the same person, and being king is not the answer. So his one and only decree is to abdicate his throne and reinstate the old king, pointing out that wisdom without honour—as he demonstrated in himself by tricking the king—is not desirable in a leader. “And,” he adds to the king, “Perhaps this will make you an even better leader, now that you know that things aren’t always as they first appear.” The story ends with a page about the possible origins of the game of chess, much of which was worked into this fictional account.

So there you go—a book with math, chess, history, a look into another culture AND a morality lesson! My two were quite taken with it; I’d recommend it for kids at least 6 or 8 years of age. Despite being a picture book, it is densely packed and with lots of text—not toddler or preschooler friendly, I’d think. Happy reading!