Planetarium

As mentioned in the previous post, I like free places that are also educational. So 2 weeks ago, on a day that we didn't have anything else planned, I took the girls to the Planetarium at the Gateway. You have to pay for parking and movies at the Planetarium cost $6-$8, but the exhibits are free. And the Gateway does have the water play area as well.

Ella had gotten a coupon for a free lunch at Costa Vida from her kindergarten teacher, so I took the girls out to lunch. It was quite good. I got a chicken raspberry chipotle salad (the small size) and it was delicious...and the perfect size for me. And unlike most times when we've taken our kids out to eat, they just about cleaned their plates...only a few bites of food went uneaten. :)

Then we headed to the planetarium. They loved the Newton's laws ball area that shows that an object in motion will remain in motion and in the same direction unless a force is exerted on it to cause it to change direction or stop. They also enjoyed watching the Foucalt pendulum. Ella thought it was fun to see how much she would weigh on other planets. They have displays that tell about the planets in our solar system and then you can take a little quiz on a computer0 to see what you learned.

There is an area that tells about comets, asteroids and meteors and you can lift an iron meteorite to see how heavy it is. Ella and Michelle both had a hard time lifting it.


There are a couple of telescopes that point to a tiny picture of Saturn on the wall and you can see how much bigger it looks in the telescopes.

There's a place where a light is shining and you can put a prism under it or a concave or convex mirror to see how the shape of the light changes.

It's worth the couple of dollars parking fee...especially because Michelle and Ella also got to run through the water area afterward. (Gabby absolutely hates sprinklers or any kind of water that sprays on you. She likes baths and pools but doesn't like water spraying or splashing at all.)


For some reason, I only took a few photos (usually I err on the side of overtaking photos...but not this time. :))

Hill Air Force Base Museum

Have you ever checked out the museum at Hill Air Force Base? Did you know it is free? And that they have all kinds of helicopters, planes, and other equipment as well as uniforms on display? And it is FREE. (If you haven't noticed, I like free fun things...especially if they are educational too.)

Alfredo and I have been planning to take the girls to the museum for awhile. He actually took Michelle and Ella when Michelle was about 2 1/2 and Ella was a baby...but we both figured it was time to go again since Gabby and I have never been and we're sure the other girls don't remember it.

It was a bit hot outside, but it was fun to see the cool equipment. I liked the displays inside even better and enjoyed reading a little about the history. (Only a little because with 3 kids, they are anxious to see the next thing pretty quickly.)




Look how big some of these planes are!!







Ella got tired (it had been a busy, fun, but tiring weekend and I think she was ready to be done) and had a tad bit of a meltdown so we only stayed about an hour or maybe an hour and a half. But it was worth the trip.

The Cabin and The Lake

We went with some friends to their cabin. We headed up Friday afternoon. The cabin was beautiful and had a pool, tvs, a playstation, a tennis court and a swingset. The kids had a ball playing on the playground and Alfredo had fun playing tennis with Justin. We got pizza for dinner and relaxed.






Saturday morning we got up, ate breakfast and then got ready to head out on the lake. It was a beautiful day...perfect weather. What a fun time! It has been about 11 years since I was on a boat, and I'd forgotten how nice it is. I tried wake boarding...but was no good...never even got up.






The best part was they had a huge tube called a molecule that we could ride on. Alfredo and I loved it. Michelle and Ella liked it a lot too.

We had a barbecue Saturday evening and then the kids went swimming in their indoor pool.



The only bad part was I didn't apply sunscreen often enough and got a bad sunburn...ouch!

Gabby became buddies with Oaklie, while Ella and especially Michelle had fun playing with Asher. Gabby was a little unsure about the boat at first and she didn't like the molecule at all. But I think even she had a good time, because she's talked about the lake ever since.

Ella, reminiscing, "When I was swimming, I jumped into the pool without a life jacket and I almost drowneded (her word), but my dad grabbed me and I didn't. When we were on the boat,I was scared to go on the tube but I tried it and it was fun! Oh, and, I liked going on their swing set. And I liked my bedroom."

I asked Michelle, "What was the best part of going to the cabin?" Her response: "Swimming pool. Going on the lake with the boat. The tube was so awesome because you got to go so fast."

It was fun to get to know Justin's family better. I'd only met his wife once, and I worried that maybe we wouldn't have much to talk about. She is very into fitness and eating right and I was afraid we wouldn't have much in common. But she was great! On the way home, Alfredo and I were talking about it and I commented that we got alog really well but she was probably more adventurous than me...he laughed and said she'd said that she thought I was more adventurous than her since I loved the molecule so much. :)
Alfredo said that is his style of camping...which isn't camping at all. :)

Math Games

Here are a few math games you can try..using only dice or a deck of playing cards or number cards (1-10). (At our local dollar store you can get a 2 pack of playing cards for $1.) For most games, remove the face cards. (OR you can keep them in and decide their value in advance...such as Ace = 1, Jack =10, Q = 11 and K = 12).

War: Remove the face cards (or keep them in and make A =1, J, Q, and K = 10 or 10, 11, and 12) Divide the cards into 2 piles. Each person flips over top card and the person with the highest card wins and takes both cards. If there is a tie, then flip over next card and winner of that round takes all 4 cards. I make the child say, "8 is greater than 4" to practice math language. Player with most cards at the end, wins.

Variations on war:
Peace: The same as war, but the lowest card wins. "6 is less than 9."

Addition War: Each person flips over 2 cards and adds them together...the highest total wins (or the lowest total...your choice...just set the rules at the beginning.)

Subtraction War: Each person flips over 2 cards and subtracts them...the highest difference wins. (Or lowest difference.)

Multiplication War: Flip over 2 cards and multiply. Highest product wins.

Fraction War: Flip over two cards and make a fraction... 2 and 5 can be 2/5 or 5/2... Highest fraction wins. (You can set the rules that the fraction has to be smaller than one so that only 2/5 will work for younger players.) This is challenging...not only are they making a fraction but comparing fractions with different denominators...for most kids this might not be appropriate until around fourth grade.

Concentration: Put part (or all) of the deck of cards spread apart on a table or floor face down. Then flip two cards over and if they are a match, you keep them. If not flip back over and the other person takes a turn. YOu can also do Make Ten Concentration where the two cards have to add up to 10 in order for you to keep them.

Salute: This is a game for 3 players. Two players are dealt the deck of cards, and they sit facing each other. The third player sits where they can see both of the other players. Third player says, "Salute". Then the two players with cards pick up the top card of their deck, without looking and put it on their forehead (so they can't see it but the other person can). Then the third person tells what the sum (for addition) or product (for multiplication) is. Each person tries to figure out what his/her number is...the first person to do so, gets both cards. Player with most cards at end wins.

Lamborghini Game: (or Highest Number Possible)... Play this by writing blank lines on a paper...3 lines if you want to go the hundreds place, 5 lines if you want to go to the ten thousands place, etc. ____ ____ _____. The child is trying to beat the adult and win the "lamborghini" (a hot wheels car). Flip over a card. Each of you must decide on which line to put that number. For example, if you get a 6, you might decide that you will get a higher number later and put it on the tens place. But maybe your child puts it in the hundreds place. then flip over another card... and place it on a line. Keep playing until all lines are filled...then compare your number...if they are lower than you or tied with you, they don't get the lamborghini...you keep it. But if they beat you, they keep it. Play several rounds. The first time or two that you play this, you might reason out loud why you are doing what you are doing. "Oh, I got a 2. That's a small number so I'm going to put it in the ones place." "Now I got a seven. That's a pretty big number...I could still get an 8 or 9, but I don't think I will, so I'll put it on the hundreds place." This game requires both luck and skill so your child has a good chance of beating you once they understand place value.

Top Dog: Divide deck of cards into 2 piles. Each person flips over 3 cards and uses two of them to make the biggest number possible, discarding one card. (With 2, 6, and 9...you'd make 96 and discard the 2 at the bottom of their pile). The person with the highest number is the top dog and takes all the cards. Keep playing until all cards have been used. Person with the most cards at the end is the TOP DOG. You can also draw 4 cards and make the biggest 3 digit number or take 5 cards and make the biggest 4 digit number.

Close to 20:
Remove the kings and jacks from a deck of cards. In this game Aces are one and Queens are zero. The object of the game is to make an addition problem with three addends as close to 20 as possible (see the sample game board below). Each game has five rounds. To play deal out five cards and place them so all players can see them. Each player uses the numbers on any three of the cards to make a total that is as close to 20 as possible; you may use each card only once. The player writes the numbers they chose and total on their score sheets. The points for each round is the difference between the sum and 20 (for example a sum of 24 scores 4 points and so does a sum of 16). Put all five cards in a discard pile and deal out five more for the next round. After five rounds, players total their points and the player with the
lowest score wins.
Score sheet:
Round 1: _________ + _________ + __________ = __________ __________pts
Round 2: _________ + _________ + __________ = __________ __________pts
Round 3: _________ + _________ + __________ = __________ __________pts
Round 4: _________ + _________ + __________ = __________ __________pts
Round 5: _________ + _________ + __________ = __________ __________pts

Variations: Play close to 25 by dealing 6 cards and choosing 4 to add. Play close to 10 by dealing only 3 cards and choosing 2 to add. Or make it harder and play close to 100. Divide the deck in half and each round, each player draws four cards. THey use four of the cards to make 2 two digit numbers that are as close to 100 as possible. Then the points are the difference between their number and 100. (For example, if you draw 2, 7, 3, 9, and 6... you might do 72 + 36 = 108 which gives you 8 points. Or you might do 67 + 32 = 99 which gives you 1 point.) The person with the lowest score at the end wins.

Guess My Number: The child or parent draws 2 cards and uses them to make a two digit number. The other person then must ask questions to try to guess the number. The questions must use math vocabulary, such as: Is it even? Is it greater than 50? If you add the two digits together, is the sum 5? Is it divisible by 3? *Note: This game can be played with multiple players. It can be made harder or easier depending on the age of the child by using smaller or bigger numbers. And you can play without a deck of cards...just think of a number and have the other player(s) try to guess the number.

Go Fish: Each player is given 7 cards, then the rest are put in a pile to draw from. First player asks if the other player has a certain number. If they do, they give it to the first player and the player lays the match down. If not, they say, "Go fish" and the player draws a card from the pile. Variation: Make this more difficult by doing Go Fish +1... The child must ask for a number that is one more than a card in their hand. For example, if they have a 5, then they ask for a 6. If they get it, then they say 5 + 1 =6 and put it down. Play continues until all cards are used. Player with the most matches wins. (You could also do Go Fish +2 or Go Fish +3 to practice those math facts...play same way as Go Fish +1, but add two or add three instead.)

Games Using Dice:

Pig: The goal of Pig is to be the first player to get to 100. The game is played with a pair of dice, and requires a paper and pencil for scoring.
1. The first player rolls the dice, calculates the sum (mentally), then rolls again if he or she wants to. The next sum is added to the first. The player can roll as often as s/he wants to before play goes to the next turn. However...
2. If a 1 comes up on one of the dice before the player decides to stop rolling, the player scores 0 for that round. The play goes to the next player.
3. Worse still, if a 1 comes up on both of the dice, the turn ends and the player's entire total falls to 0.

Use dice to practice probability. You can also use spinners and coins and drawing different colored objects out of a bag. Write down the numbers from 2 -12. Have the child roll two dice and record the total. Repeat about 20 times. Then talk about why some sums were more common (it's hard to get 2...the only way is to roll 1 +1...but it's easy to get 7... 1 + 6, 2 + 5, 3 + 4.) With spinners, record what is landed on and talk about whether the spinner is fair or unfair. Flip and coin and talk about what probability says should happen...and whether that is what happens. Put different objects in a bag... maybe 5 blue blocks, 3 red and 1 yellow. Reach in and pull 1 out...record what color it is and put it back in the bag. Shake the bag to mix objects and then repeat...about 20 times. Record results.

Going to Boston: This game requires three dice and pencil & paper.
In one turn, the first player rolls all three dice. The highest roll is put aside. The next two dice are rolled and the highest number is put aside again. The last dice is rolled, then all three dice are added together.
The winner is whoever gets to a predetermined amount first, such as 100.
Variations on the game are adding the first two dice and multiplying the sum by the third; using any combination of addition, subtraction, multiplication or division to get the highest number possible, or just using two dice to practice basic math facts (addition, subtraction or multiplication).

Array Arrangement: Multiplication
Using a pair of dice, the students are to draw the product on graph paper as a rectangular array.
For example, if a 4 and a 3 are rolled, that means 4 x 3 = 12. The array is drawn as 4 rows and 3 columns, to make a rectangle. Each time a square number is drawn, let the students color it in red. Label each array with the number sentence it goes with.

Many of the card games could also be played by using dice in place of the cards.

See, I told you...math is fun!!!

Math Power--Part 2-- Elementary School

One point that she brings up several times in the book is that math can be hard. Even for mathematicians, it isn't easy to grapple with a problem (especially one where no known answer exists yet)... and there are moments of frustration. Just because you can solve a problem doesn't necessarily mean it is easy... and just because you have to struggle, doesn't mean you aren't smart or aren't good at math.

Here are some activities that Math Power suggests for elementary school age children...and a few of my own suggestions mixed in:

1. Blocks and puzzles continue to be great toys...including puzzle books, jigsaw puzzles, logic puzzles, and cubes or blocks that link together. Calculators are good tools for children to become familiar with and use.
2. She suggests using maps and creating math problems with them. Maps are great for measurement...and they relate geometry to arithmetic. You can also use time lines to create problems.
3. Children who play music usually do better in math. If you are inclined, you may have your child learn to play an instrument.
4. She mentions games that she feels are especially good at teaching math: rummy, parcheesi, checkers, battleship, and chess. I would add Monopoly Junior. In addition, with a deck of playing cards there are all kinds of games you can play. I will probably add another post with some ideas of games to play with a deck of cards.
5. Have your kids cook with you. This can give them real life practice with fractions as well as doubling (if you double the recipe) or dividing in half.
6. Turn your activity into a quick math problem. For example, if your family is going to the movie and it costs $6/person, have your child figure out what the total cost will be. Or if one bag of popcorn will feed 2 people and you have 4 people, how many bags do you need? If you're going to the store to buy just a few items, have your child estimate how much you are spending. Or group the items so that they are in groups that are about $10 each and have them count the number of groups to see how much you are spending. If you are at the pool, and it is 2:15 and you have to leave at 3, how much longer can you swim? Have them figure out change...if the movies cost $24 total, and I give the clerk $30, how much change will I get back? Or if the candy bar costs $0.54 and I give the clerk $1, how much change will I get back?
7. Give your child a ruler and have them measure things. I can attest (as she talks about in her book) that measurement is an area that most teachers don't spend enough time on and that many children struggle with (partly because it is confusing to switch back and forth from metric to customary with young children...but we are required to do just that.) Give your kids extra practice at home. Have them measure the room and furniture and come up with a plan to rearrange their bedroom or the living room. If you're buying an appliance have them measure the space it needs to fit in and measure the appliance to make sure it will fit (Good advice anyway!!)
8. Do some basic "algebra". Put some items in your hand and have your child count them. Put your hands behind your back and place some items in one hand and keep it hidden, then show the other hand with its items. How many items are behind your back? Simple algebra. (Same thing can be done by hiding some of the objects under a cup.)
9. Perhaps the most important thing you can do is help your child recognize patterns...number patters, shape patterns, etc. Math really is an understanding of patterns. Recognizing patterns of dots on dice, noticing patterns in geometric designs, noticing patterns on paper or clothing. Patterns are everywhere and this is such an important skill for mathematical understanding.
10. She has a whole section on fractions (five pages long.) Fractions need to be understood as a number of things...part of a set, part of a whole, as division, as probability, as a proportion. She gives some good activities... Cut pizzas/sandwiches/apples into different fractions and label them (in words) for your child. Use a spinner and spin it several times and then write your result as a fraction.
11. Create graphs together. When friends come over, ask them what their favorite drink or candy bar or whatever is...and then put it on a graph. As your children read during the summer, create a bar graph or picture graph to record the number of books read (or the number of days read). This summer, there was a little bit of arguing happening between my two oldest...enough that it was annoying me. So I created a "being kind" picture graph and they get to add a sticker when they are kind. It motivates them to be kind and get along, but we can also talk about how mnay stickers we have in all. How many more do we need to have 25? If Ella earns 6 more, how many will she have? etc. The graph itself is important but the discussions around it are even more important.
12. Have your child estimate. How many M&M's are in your bag? How many minutes until dinner will be ready? About how long is the table? About how much money are we spending at the store today? And so on.

Again, it's very important as the parent that you follow your child's cue. Make it fun..turn it into a game, and stop when they want to stop. Don't worry too much about wrong answers...you can correct them gently or again, ask them to explain their thinking and how they solved the problem. (Of course, if you homeschool, you will have to worry more about right answers and doing math even if they aren't in the mood...but even still try to make math fun as much as possible. Avoid overdrilling them on facts or computation. This is just a small part of math...and most kids will get the facts IF they really understand the concept which is far more important.) Encourage them to solve the problem in their own way. When we were kids, most of us were taught one right way to compute... but for most problems there are a number of correct ways to approach the problem. In fact, some of the algorithms we were taught are actually more difficult and lead to more errors. Encourage creative thinking...and encourage them to keep trying when math seems hard. A great insight might be just around the corner!

I did another post on how I think math teaching has changed since I was in elementary school... if you want to read it, go here to math mumblings.

Math Power: Part 1...Review and Preschool Activities

Just read an interesting book. (Surprise, surprise... I know! :)) It was Math Power: How to Help Your Child Love Math, Even If You Don't by Patricia Clark Kenschaft.

Here's my review from Goodreads:
This isn't a book you can pick up and read in one sitting, and while written for parents, I would guess that many parents wouldn't read it all. But she raises a lot of good points, particularly about testing and the negative consequences of testing (and this was written BEFORE No Child Left Behind!). I appreciated that while she had plenty of criticism for public education, she tried to treat teachers fairly and point out the many difficulties of being a public school teacher. In addition, I really believe that in some areas we have made good progress...some of her complaints no longer seem true... (while others are still right on!) She also gives some good, concrete ways that parents of younger children (preschool-elementary) can really help their children gain math skills and help them see math as fun and engaging...which I think it is or can be!! I also really thought that she raised a good point when talking about math phobia/math incompetence. Almost no one would proudly state that they "never did learn to read" and yet in our society, it seems perfectly okay to say that you "never were any good at math" or "never did understand ______ (algebra/geometry/or whatever)." She also discussed how in nearly every other country in the world, if you ask people what it takes to be good in math, they talk about hard work and effort and determination. Here, a lot of people talk about having parents who were good at math, having good teachers, being "born" with the ability....people think it is based on genes and teaching rather than the child's hard work.

Wish I could photocopy her chapters on testing to give to my administrator/district officials/state legislators/national leaders/etc.

Wish I could copy her chapters on games/math work for preschoolers and children for all the parents of my students as well as all my friends that have young kids. It did give me what I think/hope is a good idea for this coming year at school...and has made me more cognizant of ways I can foster math in my own home. :)

*************************************
As I mentioned in my review on Goodreads, there was a lot to think about in this book. I especially think that it is important for all of us to understand that if you want to be good at something, you have to work hard at it. Yes, good math teachers are critical...but ultimately, the teacher can only do so much if the child is not willing to put in effort.

I do think there have been some positive trends in the teaching of math since this book was published in 1997. I know that at my school we spend a lot of time teaching kids multiple strategies for solving problems, encourage them to invent their own strategies or use the method that works best for them, ask them to talk about how they solved problems and why they did what they did, and use a lot more manipulatives and engaging activities than my teachers did when I was growing up. In many ways we are headed in a better direction. (Unfortunately, I also think that in many ways the testing frenzy our nation is under is doing a lot of harm and little or no good.)

But enough of that. I did think it would be nice to share some of the ideas from her book (plus a few of my own) on how parents can foster a love of math in their children. So many of the ideas are easy to implement and can be done by anyone and would have long lasting impacts on your children's feelings toward math...and hopefully would also help them be more successful.

So ideas for preschool aged kids:

1. Say nursery rhymes. Many nursery rhymes have counting and numbers built in. (Such as 1,2 Buckle My Shoe...etc.)
2. Play games. Lots of games include counting and simple adding and subtracting... games like Chutes and Ladders, Candyland, etc.
3. Give your kids blocks and other building toys. This teaches them spatial sense, shapes, etc. which will help with geometry. You can get fancy pattern blocks that have hexagons, trapezoids, triangles, etc. but you can also get wooden or foam or other blocks.
4. Dominoes and face playing cards teach kids to recognize numbers in a pattern and face cards can be used for tons of math games. (You can also just make your own cards with cardstock by writing the number and adding dots on the card like a domino would have.)
5. Count people in line at the store, count how many fingers and toes, count how many french fries on his plate.
6. Have your child be the one to pass out the grapes or the cookies, making sure that everyone gets a fair share. (This is division! :))
7. Read books that include math. There are literally hundreds available. Want some lists or recommendations? Check out these sites: Children's Picture Books or Barb's books or Pragmatic Mom. There are probably loads of other lists as well out there on the web. In my classroom, I have a list organized by math topic that has well over 200 books on it.
8. As you take a walk or play in the house, do a shape hunt. Can you find squares? Rectangles? Triangles? Circles? Hexagons?... or look for solids... can you find cubes? Cylinders? Cones?...etc.
9. After your child can consistently count to 10, you can start adding with your fingers (or simple objects). Hold up 2 fingers on 1 hand and 3 fingers on the other and ask how many fingers. After they say five, say, "Yes, 2 plus 3 equals 5." You're beginning to teach addition and also helping them gain math vocabulary.
10. Buy puzzles. They also develop beginning math skills and spatial awareness. (Plus, some puzzles include shapes, maps of the US and other things they might gain some additional knowledge from.)

**Most important thing though is that as a parent, your job is to make math fun. Particularly at the preschool age, it doesn't really matter if your child masters these skills. If they don't want to play right now, stop the game. If they get the wrong answer, don't stress about it. You might ask them (whether they get the right answer or not) to explain how they did it. They might have a great strategy for solving that you might never have thought of...or they might have some small confusion that you can help them clear up. But make it fun!

Oregon--Day 4

On Monday, it was the 4th of July! We got up and had a yummy (free) breakfast in the hotel's restaurant. Then we headed to the Portland Temple. It was, of course, very beautiful and peaceful.







After the temple, we got in the car and enjoyed the beautiful drive to the Oregon Coast. We waded in the water (it was too cold to swim!), watched a dog having the time of his life as he ran/swam into the water to catch a ball his owner threw out to him, enjoyed walking along the beach, and the kids played in the sand. Gabby, especially, had a great time playing with a couple of pieces of driftwood and digging in the sand.

We had lunch at a little Mexican restaurant about a 1/2 mile from the beach. Then we headed back to Portland, enjoying another gorgeous drive.

The girls were dying to swim in the hotel's pool, so we spent an hour swimming. Then we headed over to Vancouver, Washington to see what is supposedly the biggest fireworks display west of the Mississippi. Not sure if that is true, but it was quite amazing! What a fun day. It was so fun to be somewhere new on the 4th of July, to enjoy the beauty of this beautiful world (beach/ocean, forests, river, waterfall, flowers all in 2 days time!), and to be together as a family. It was just about a perfect vacation. Alfredo said that maybe he'd like to make this a new family tradition...to take a short trip somewhere in the US each year for the 4th of July. I don't know if we really will or not, but maybe. Definitely, we both want to take our kids to see some of the amazing places in this country and perhaps other places in the world as well. Let them learn about geography and history and culture through experience, not just through reading and schooling. :)

More pictures to come soon (the rest are on Alfredo's cell phone...I need to download them still!