When we got back to the hotel, we went for a swim. This was our first time staying at this hotel in Edmonton (the Hampton); it’s quite new and there was a good deal on rooms. And the pool area was fantastic! There was a little kid splash pool that Gareth enjoyed, a larger pool for swimming and playing volleyball, and a large hot tub. No waterslide, but IMO, if you’re gonna do waterslides in Edmonton, you’re heading to the waterpark at West Edmonton Mall anyways.

We had lots of fun. Gareth created a game he dubbed “Dino Ball”, that if you are familiar with “Calvin Ball” from the Calvin and Hobbes comic strip, seemed to have the same rules (or lack of them–you just make ‘em up as you go along). There was throwing and catching:

‘alligator wiggling’:

running and kicking (with the occasional ‘hand ball’)

and general chasing around:

Daegan and I spent quite a bit of time in the larger pool too, as he is now able to swim and LOVES to race me:

Gareth still needs to be in parental arms in the deep pool, and loves goofing around (Daegan practicing his back floats behind us):

He also likes practicing his swimming kicks:

Jim preferred the hot tub:

and Daegan joined him from time to time too, clearly enjoying his birthday trip:

After our swim we headed off to Padmanadi, our fave veggie restaurant in Edmonton. The boys drew in their travel journals to pass the time as we were waiting for our food; it was clear the bug class left an impression:

We stuff ourselves silly with delish food, like this kung pao chick’n (wheat gluten based):

And on our way out, who should we bump into but Katie, the instructor from our Insect class, who was having dinner with friends! How odd in a city of a million people, don’t ya think?

Online Games (mainly found by Daegan):

BBC’s Skeleton Jigsaw, in which you put together the skeletons of 4 different prehistoric creatures (Basilosaurus, Gastornis, Australopithecus, and Woolly Mammoth). There are different levels of complexity, with the smallest bones pieces for the more advanced levels (like what is found on real world dig sites), and large complete bones for beginner levels.

BBC’s Making Fossils, in which you set various conditions in the attempt to make fossils. And just like the real world, “sometimes it works, sometimes it doesn’t.” – Daegan.

TVO’s Dino Dig, a cartoonish game aimed at the youngest paleo enthusiasts, in which you dig for fossils and use what you’ve found to construct a specimen for a museum. The fossils are found in different areas of the world, and you need to use the correct tools at different points during the dig. The Smithsonian has a more complex and realistic version of a similar game.

On CD:

Zoo Tycoon 2 (Canada) (US), in which the boys set up and run a prehistoric zoo. The game requires the boys to think about which animals they want to keep and how many to have, how to keep the animals happy (type of food? type and size of enclosure? other needs?), and how to balance the various roles of their zoo to keep it running (needs of animals vs. needs of visitors, various sources of revenue to offset various expenses, entertainment vs. educational vs. research institute roles, etc.). If things go poorly, you may end up with a “dino rampage”, which requires prompt action by the staff: a robot is used to distract the dino while a tranquilizing team steps in. The boys find this a very fun, if complex game, and it is the one they play the most. 

“I Can Be a Dinosaur Finder”, which is an older game a friend passed along to us. The boys are playing it in these pics:

What are your kids favourite computer games? (I’d love some suggestions that are not dinosaur-related as well!)

We then read the book Less Than Zero (Canada) (US) by Stuart J Murphy, one of the MathStart series. Gareth chose to join us.

We then moved to the hallway, where earlier Gareth and I had created a number line:

I made up a story about the temperature in Calgary one day—zero when we woke, then a bit warmer, then the sun really warmed it up, then clouds cooled it down, then there was a chill wind, then snow. At each part of the story I said how much warmer or colder it had gotten, and the boys moved up and down the number line accordingly. They walked forward when it got warmer, and walked backwards as it got colder. Soon, we had a problem: it had gotten colder than zero. What to do?–Add negative numbers to our number line:

I then made up other stories about riding an elevator (get on at ground level, dentist office on third floor, car is parked in the sub-sub basement, etc.), and spending money (getting and spending their allowance, wanting to borrow extra money to buy a toy dinosaur, etc.). Gareth then asked a really interesting question: What about even numbers? Are any of them negative? (This is an AWESOME question from a 5-year-old!)

I had the boys “double jump” in the positive numbers from one even number to the next. They then “double jumped” backwards, and saw both than zero is an even number, as is –2 (and –4, etc.):

Daegan then asked how many negative numbers you could have. I asked him about the positive number line.

Mom: Does it stop at 9 like in our hallway?
Daegan: (laughing): No!
Mom: How far does it go?
Daegan: To infinity!
Mom: So how far does the negative number line go? To negative 10? Negative 100? Negative thousand? Negative million? Negative billion?…
Daegan: Oh! So it goes to negative infinity!

I also positioned the boys at different spots on the number line and asked them who was at the greater / larger number. The boys saw that while 5 is greater than 2, –5 is NOT greater than –2.

We then went back to the problem of the day, which Daegan was able to solve by drawing a vertical number line (like a thermometer). There was some interesting learning there about how to draw on hash marks, label it, etc. As an adult I take for granted how to construct this sort of number line, but this was Daegan’s first time drawing one:

I then talked about how number lines came in (at least) two forms, horizontal and vertical. I showed him Cartesian graphing, and we found and labelled various points. I said that we’d see this in math again later, but notice that this “high school level graphing” is really just about number lines with positive and negative numbers:

I wanted to make this more concrete for him, as I could see he was a bit puzzled. The book Less Than Zero involved keeping a much simpler graph of the main character’s money, as he earns or borrows. But when would you ever use a Cartesian graph? Aha! I’ll talk about flying to various dinosaur sites, and needing to be able to track the location to send palaeontologists back to do digs. So with the help of an airplane eraser, from the Origin Airport (0, 0), our plane flew up (lots of finds, like the Burgess Shale, are in mountain slopes that used to be on sea bottoms) and down (into valleys and badlands—places below in altitude / sea level measurement from Origin Airport):

For the horizontal axis, I talked about the plane flying east and west. This caught Daegan’s imagination and I was THRILLED to see him extend this concept by running to our world map in the hallway:

Of course! Why didn’t I think of that a minute ago? Our world map has latitude and longitude lines on it, and hence a (0, 0) point where the equator and Prime Meridian connect:

But instead of labelling with negative numbers, maps use directions: north (positive y-axis, or vertical number line), south (negative y-axis), east (positive x-axis, or horizontal number line) and west (negative x-axis). But these labels allow us to do the exact same thing as with Cartesian graphing, like find and label precise spots on the globe. And the numbers for the degrees of latitude / longitude work the same was as the Cartesian graph, getting larger in absolute value as you move away from the origin, point (0, 0).

We then played a bit of the card game Zero—a variant of 21—but Daegan found it too challenging. He did like 21 a lot though, which I started with to introduce him to the idea, so we’ll come back to that as a way of practicing addition facts. We tried this game on the computer, which turned out to be pretty easy for him, even on the “hard” levels. We watched this song on youtube (and did the arm motions, making – and + signs with our arms, to the number line dance. My wiggly boys loved this!):

We then wrapped it all up by watching the Cyberchase episode “Less Than Zero”:

A few weeks back I came across a printable for  these very simple exercise cards, which I then cut out and pasted on index cards. They give one simple movement for each letter of the alphabet:

Unfortunately, I have since lost the link (Amendment! You can find the Exercise ABCs printable here), but these cards and the general idea are simple enough to create on your own. We use them to “get the sillies out” when we need a break from our seatwork, or during a transition from one activity to another. They are also helpful during that last hour before dinner when everyone’s nerves are frayed. They’ve led to lots of laughter, especially since Mom (and Dad if he’s around) take part too. I’ll let you create your own mental visual of me “Y y Moving Like a Yo-yo!”

To use, we simply pick a (face down) card (or 2, or 3, or….) at random. But you could easily have your kids verbally suggest a movement for each letter of the alphabet in turn (hint: Q might be “Quickly walk in place”), or have them design their own exercise cards with handmade drawings or clip art to help non-readers—the sillier the better. Have fun bringing more movement and laughter into your homeschool!

We talked briefly about what subjects and predicates were, and then mixed the subjects and predicates up, and put them face down into piles:

Daegan then made “silly sentences”, learning that subjects and predicates can be mixed and matched. This activity was met with lots of smiles and giggles, and even rolling on the floor at one point:

Here’s some of the silly sentences he made:

And I’d like it noted, for the record, that not one of these sentences was about dinosaurs! We’ll build on this activity in future, changing out nouns and verbs a la Mad Libs, adding in adjectives and adverbs, etc.

We talked about the dice activity he had done previously as he was working, and Daegan recalled that the most common sum when you roll two dice was 7. I asked him why 7 and he said “because it is in the middle [of the graph].” I asked him what he thought the most common domino sum would be and he thought 7 again. Hmmm….we’ll see.

As he worked he realized we needed to make a 0 (zero) parking lot. I pointed out that when we worked with the dice, the smallest sum (parking lot) was 2, from the roll 1-1. With dominoes we have both 0 and 1 as possible sums. Daegan thought that was sort of interesting, but didn’t think it would affect the result; we should still get more 7s than anything.

He kept adding and sorting (which also gave me some insight into which sums he had down and which he is still struggling with), and made little car noises as he did so. Vrrrrrooomm! Beep! Beep! Squeeeak! It was all I could do to keep a straight face.

Just one last domino to go, the 4-2 domino with a sum of 6.

Well, this sent Daegan into a tizzy. “I must have made a mistake! The sixes have the most! It should be seven!” After helping him calm down, I reminded him that he had told me that when it came to dice, the 7s had the most as they were in the middle of the graph. What is in the middle of your domino parking lot?

I reminded him again about how dominoes have zeroes, but dice don’t. “Zeroes change everything in math!” I emphasized. “Don’t forget that!” I showed him how the zero made the 0 and 1 parking lots possible, how the zero made a way to sum to six that doesn’t work with seven (there is a 0-6 domino, but not a 0-7), and I briefly reminded him of yesterday when he had misread 201 as “twenty-one.” I wrote 21, 201, 2001 on a piece of paper and talked VERY BRIEFLY about place value and zeroes. “Zeroes are a really big deal in math, despite being nothing,” I joked. 

Still not entirely convinced, I took away the 0 and 1 parking lots, leaving only 2 through 12—just like dice sums—and asked him to find the middle. Sure enough, the middle is now 7:

As a final step we talked about the bar graph we made with the dominoes in our parking lot, and how the shape of the graph was the same as with the dice—steps up and down to a high central point—even though the exact middle number differed:

Daegan told me later he found these domino activities “kind of fun, and kind of confusing.” Excellent son—that’s the wonderment of math!

I gave Gareth his pile of sticks and he gave it a go:

He then drew the sticks on paper, and coloured them in.

It had to stifle a laugh as he was concentrating so hard, he had the little-kid-tongue-sticking-out thing going on:

Meanwhile, Daegan got busy with his group of 10 one-side-blue sticks. He was rather enthusiastic about the dropping part, and more than once they ended up scattered across the dining room floor as well as on the table:

I then extended this activity briefly with Daegan, to demonstrate the associative property of addition. We used 5 red sticks and 5 blue sticks, and dropped. We got 2 blue sticks, 2 red sticks, and 6 uncoloured ones. I drew the following:

Originally I only drew the picture and wrote 2+2+6 = 10. I grouped the coloured (red and blue) sticks together to demonstrate left-hand side addition in the picture above (i.e., (2+2)+6, or 4+6), and grouped the red sticks with the uncoloured sticks to demonstrate the right-hand-side (i.e., 2+(2+6), or 2+8). Daegan understood that with addition, it doesn’t matter how the numbers are grouped—you arrive at the same answer.  

There are in fact many different magic squares; the common elements being only that the vertical, horizontal, and diagonal sums add to the same total, and that each integer in the grid can be used only once. I found some simple magic squares on this site, and used them as templates to make magic squares for Daegan to try. We did the “sum of 12” magic square, which uses the integers 0 through 8, and the classic “sum of 15” magic square, which uses the integers 1 through 9. I filled in four of the answers to make things quite easy to start off with, as we’re still working on basic addition facts, not complex puzzle-solving strategies. Here’s the magic squares sheet I made up. Note that for each column, the answers are simply rotations of one another.

We used plastic number tokens (from a dollar-store version of Sudoku, the game board from which has long since disintegrated) to fill in the squares, making the sheets reusable. Here’s Daegan in deep thought with the sum-to-12 grid:

Even though a magic square uses three numbers for each sum (whether across, down, or diagonal), this activity gave Daegan lots of practice on his basic (two number) addition facts, as he had to sum the two to work out the missing number. This is how he solved the above square, adding down the columns first (e.g., 6+5 = 11) and then subtracting that sum from 12 to get the missing number (12-11 = 1).

Here’s the completed square:

He employed the same strategies on the ‘sum of 15’ square. First, he put on the tokens for the numbers already filled in on the grid:

Then, he selected which square to solve for next. Daegan had a bit of difficulty understanding which square(s) to begin solving first. In the above picture, we do not yet have enough information to solve the lower right corner square, for example. But all in all, and despite some moments of frustration, he had fun with these puzzles:

I began giving each boy 1 stick. “What can you make?” I asked. We quickly found out the answer: not much with only 1 stick! You could make 1 (one), I (capital ‘aye’), or l (lower case ‘ell’). That was about it. I then gave the boys a second stick. “What can you make now?” Here’s some of the possibilities, both letters and numbers:

Note that the final two shapes could also be symbols: the equal sign, or the plus (adding) or times (multiplying) sign.

With three sticks there were even more letters and numbers, and our first shape. Here are some of them:

And with four sticks we could make a couple of shapes, and more:

I threw out words like ‘quadrilateral’ and ‘rhombus’, and pointed out that all squares are rectangles, but not all rectangles are squares. Gareth decided he’s played enough and wanted to do some drawing, but Daegan was keen add more sticks. We focussed on shapes from here on in.

With five sticks, a pentagon:

At this point we abandoned the paper underneath, as it was sliding around and making it harder than it needed to be to place the sticks in position. I told Daegan that another shape you could make with 5 sticks was a star, and showed him how to do it, using the interior angles of the pentagon as a guide:

With six sticks, Daegan got very excited about hexagons. “I know where we see those in nature! In a beehive!” And he started flapping his arms and buzzing like a bee:

He then opened the nearby cupboard and got out some Crispex cereal, another hexagon. It got gobbled up nanoseconds after I got this shot:

We then played around making shapes inside the hexagon (as we had done with the star in the pentagon), and found this:

Note that as these are all equilateral triangles, we can use this image to prove that the interior angles of a hexagon add up to 720 degrees. (Each angle in the triangle is 60 degrees, as 60 x 3 = 180 degrees, which is the number of degrees in  a triangle. Since two angles from each triangle are used to make the interior angles of the hexagon, and there are 6 triangles, you get 6 x 120 = 720 degrees). I did NOT do this with my seven year old in case you are wondering!

We quickly made a heptagon (7 sides), talking about how you don’t often see that shape anywhere, and moved on to the octagon. Daegan had an idea right away to complete the image:

Have fun with this activity; it’s quite flexible and can be adapted to different ages and abilities.

He began by putting the numbers in order, like on a number line:

And then he added the correct word below each number. As Gareth is at the ‘sounding out’ stage of reading, I helped him with this part, such as putting the three number words that start with ‘T’ together so that he could more easily figure out which went with 2 (or 3, or 10).

Once all the cards were laid out in order, we read the words together. I did this to make the concentration / memory game easier for Gareth, a sort of quick primer. I then shuffled and laid out the cards, face down:

I ended up adapting the conventional rules after a while, and allowing cards turned over to remain turned over. When either a number or word matching one that was already turned over was flipped, I stopped Gareth and asked him to find the match. The point of this game was the literacy skills, after all, not the memory work.

To finish off, I gathered all the word cards and had Gareth read them to me (with help), leaving the number cards on the floor. I then asked him to pass me the number cards so as I could put them away, but did so via riddles, which he loved. “Pass me the number of people in our family” (4), “Pass me how old you are” (5) “Pass me the number of legs a spider has” (8), etc. Felt a bit like Mary Poppins there in the clean up. “For every job that must be done, there is an element of fun. You find that fun and –snap!—the job’s a game!”

I am going to make similar cards to support his early literacy on colours (word, coloured blob) and animals (dog, pic of dog; cat, pic of cat, etc.) but I’d love other suggestions! Or other ideas to incorporate play / games / riddles into his learning to read.