It's In The Cards: Math Games with Playing Cards

There are so many ways to practice math functions with just a pack of playing cards!

 

Addition, Subtraction and Multiplication

Split a deck of cards and simultaneously flip over their top two cards. Each player adds his two cards together to get the final number. (face cards worth ten, ace worth 11) The highest sum wins all four cards

If the cards sums have the same value, the cards are placed in a center pile. The next hand is played normally and the winner of the next addition number battle takes the center pile as well.

For practice adding more than two numbers, flip over three cards instead of just two.

For subtraction, play in the same way, but subtract the smaller number from the larger number.

Multiplication can also be practiced with this game, just multipliying the two cards instead of adding.

Place Value

Players split a deck of cards (face cards and 10s removed, ace worth one)

 and simultaneously flip over either their top three cards to create a 3-digit number. Players may move the cards and place in any position of the number they wish. The player with the larger number, gets to keep all the cards.

Practicing multiplication with cards.

More math games with cards can be found here.

First Day of School 2011-2012, Our 16th Year of Homeschooling

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This year I have a second grader, a fourth grader and two ninth graders.

 We took first day photos this year...

and gave out our traditional school cones.

 And with their new packs of 24 Crayola colors, the boys played Word Roll game from Relentlessly Fun, Deceptively Educational. In addition to reading a graph, they had to read the color words printed on the graph and match it with the colors printed on the crayons.

Instead of using flashcards to practice our addition facts, we played War with dominoes. Quentin had to count the two dominoes and determine which one was the larger, or winner. In addition, James had to determined the amount by which the player had won. We played for about two hours straight and had a lot of fun and a lot of math practice.

Fun with Pascal's Triangle

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We had a lot of fun today playing with Pascal's Triangle, invented by Blaise Pascal, a French Mathematician in 1653. First I started out giving them the following math problem to solve.

Imagine you're buying an ice cream cone. If there are 5 flavors, how many possible combinations are there? How many ways of having no flavors? How many ways of having 1 flavor? How many ways of having 2 flavors? How many ways of having 3 flavors? How many ways of having 4 flavors? And, how many ways of having 5 flavors?

This was a good word problem for my 10-year old to solve. While he was working it out, I cut out squares of colored paper and glued them on another sheet of paper to form a pyramid or triangle. Once he finished solving the problem, I read to him some about Pascal and then I had him fill in all the outside squares on our triangle with the numeral 1. I then asked him to fill in the rest of the squares by adding together the numerals in the two squares that joined above each square. We only had seven rows, including the top 1, before we ran out of room. If I do this again, I might get a larger piece of paper to work from.

Now I told him to count down five rows, not counting the top 1, and look at the numbers that ran across this row. Did he see any similarities to the answers he had for the problem he had worked on earlier?

They, of course, matched.

We counted down five rows because the possible flavors we had to work with in the problem was five. Pascal's triangle can be used to find the answers to any of such type problems with ease.

I then asked him to add up the numbers in each row.

What pattern do you see?

He began saying the numbers out loud, "2, 4, 8...they double each time!"

I then read to him about something called a Galton board. The board is made with nails arranged like Pascal's triangle. Marbles are then poured through it. The probability of an marble ended up in a particular column is easy to work out by looking at the numbers in Pascal's triangle. The final pattern, too, is in the shape of a bell curve.

Galton board, photo from Wikipedia

There are so many fascinating patterns to be found in Pascal's Triangle. What patterns do you see?

Why not build one yourself and see?

Nine Men's Morris

The Elizabethans played Nine Men's Morris as a board game, but during pagents, they also used children as counters while playing it on a field.

To play the game, you will need a board that looks somewhat like this. I could have gotten the boys to measure it out for added math experience, but we chose to do it freehand so we could get to the game.

If you want to measure it out the outermost square should be about 9 1/2 inches, the middle square, 6 1/2 inches and the innermost square about 3 1/2 inches. Leave about 1 1/4 inches between each square. Draw four lines connecting the midpoints of the squares.  Draw circles at each of the corners and midpoints of the squares, for a total 24 points.

To play the game, two players each choose nine counters. The players take turns placing one counter at a time on an empty point on the game board. When all 18 counters have been placed, the players take turns moving one counter at a time along a line to the net empty point. Jumping over a counter is not allowed. Each player tries to make a row of three along any straight line with his counters. A row of three is called a "mill."  On your next turn, you can move one of the counters from your pecious mill to get into position to form another mill. A player who makes a mill removes any one of the other player's counters from the board. You may, however, only remove a counter from the other player's existing mill if no other type of his counters are on the board. Once a counter has been removed, it is out of the game. The losing player is the o ne who has only two counters left on the board or who is blocked from moving.

Durer's Melencolia I (1514) and The Magic Square

As we were studying Dürer's Saint Jerome in His Study last week, I discovered that it was one of a set of three large prints he made in 1513–14 known as his Meisterstiche or "master engravings."  Another of the three is called Melencolia I. (The third one is Knight, Death, and the Devil). The prints seem to correspond to the three kinds of virtue in medieval scholasticism—moral, theological, and intellectual. Melencolia, being the depiction of intellectual scholasticism, has many interesting elements -tools of geometry and architecture, the polyhedron truncated rhombohedron (which, by the way, is now known as "Durer's solid"), an hourglass, a scale or balance, and compass.

The most interesting part of the engraving, however, is the "Magic Square" in the upper right hand corner of the engraving.  A magic square is a grid of numbers in which you may find the same sum when adding the numbers within it in many different patterns and combinations. Durer's square is a  4 × 4 magic square with its rows horizontally, vertically, angles down, the four quadrants, (the four squares in each of the corners), corners and as well as the sum of the middle four numbers equal the same number, 34, which happens to belong to the Fibonacci sequence. You can even connect the numbers to form a parallelogram by connecting the numbers 3, 5, 14 and 12 to form 34. Another charming touch is that the numbers 15 and 14 appear in the middle of the bottom row, indicating the date of the engraving, 1514.

Then we made our own Magic Square. 

First start by making a 4 × 4 grid and filling it in with the numbers 1-16 in order. Take the numbers in the diagonal from the top number 1 to the bottom number 16 and erase them and then fill them back in, in the opposite order.

Now do the same with the other diagonal -from 4-13.

Now start adding. See how many sums of 34 we get?

Then we compared it to Durer's square, to see how is it the same and how it is different?

Why don't you try it and see what you think?

Can you make more magic squares using the same method with different outcomes?

Tapatan; a game from the Philippines

Tapatan is a simple game that people in the Philippines play. Although beautiful wooden boards can be found there, other families have the board marked on the doorsteps of their homes. Usually the game pieces are round wooden counters made of dark and light wood. We drew our board on some cardstock and used some of our Othello pieces for the game. We found the rules for how to play in Math Games & Activities from Around the World.

To Play the Game:
Players take turns placing their pieces on the game board. Once they are placed, they move the pieces along a line to the next empty point. Jumping over a piece is not allowed. Players continue taking turns. The winner is the first player to make a row of three counters in their color. A row can be made horizontally, vertically or diagonally.

Quentin has some trouble seeing things diagonally. We first noticed it when we played Othello and again in this game, so we decided that we might practice that skill with some Tic-Tac-Toe. I kept playing, trying to force him to make three-in-a-row diagonally. After several games he became a little better at seeing them.

Then this book tied in nicely and is a reader at his level. It has interesting game variations in the back.



Learning Those Tough Teens

I saw this cute game at Montessori Tidbits, which Leann had gotten from the makinglearningfun yahoo group. When I asked her about the game, was kind enough to go back to the game's inventor (Debi Goodman) to get permission to share it with me

You can now fnd it at the blog, Mrs Goodman's Frog Blog, where it is available to print out.

(By the way, when I got it, I could easily change the name of it, so I added Quentin's name so it would be personalized for him.)

Quentin has a great grasp of simple addition, subtraction, multiplication and division, but still has difficulty with those tough teens. Sometimes he says their name correctly, sometimes he understands what they represent, but at other times he gets them confused and mixed up. Statistics say that only 50% of 5th graders in the U.S. understand place value but that over 90% of Japanese and Chinese children understand place value in first grade. In looking at why, it was discovered that in the Asian number system, numbers 11-19, for example, are called 1-ten, one through 1-ten, nine, instead of having unique names as we do in English. This is continued throughout all their numbers, going on with the twenties and so on, calling them 2-tens instead of our shortened version. This constant reinforcement of what the numbers actually stand for give the Asians an concept of place value at a very early age.

I needed to figure out a way for Quentin to get the practice he needed with this without making it a miserable process, and a game always seems to make learning facts more enjoyable.

I couldn't find any cute plastic penguins to use as game pieces, so we just used counters. (Why is it you can never find the toys you want when you want to use them for school?) He really enjoyed playing and we played four games in a row the first time we sat down to play. When we landed on a square, you had to say the name of the number and what the number represents. For example, for the numeral 14, he had to say "fourteen," and "one ten and four." He had some trouble at first in saying both of those elements but after hearing me say a few of them on my turns, he was able to do them all. A few more times and he will have them down and it was all done in a very fun way -with a little game instead of a number of workbook pages.

We have played for treasure.

We have played it in a candy land.

We have played it for kisses.

Mathwire has more ideas for learning the teens.

PYRAMATH Cards

Someone tipped me off (I can't remember which blog now, sorry) that Freely Educate announced that you could get a free deck of math cards in your mailbox, so I sent for them. They arrived promptly and the boys were excited and anxious to play as soon as we got them. They are brightly colored number cards (0-9) with the words for the numbers in several languages and roman numerals.

The object of the game is to provide a way of practicing addition, subtraction, multiplication and division in a game format. My 10 and 6 year olds picked up the rules quickly and played two games in about a half-hour. Quentin (6) needed some help with figuring out his options, but James (10) could do it without any help, although I am not sure whether he explored all of his options with two digit numbers. They had some confusion over the rule that you only use the ones (or units) place with the cards in answers that have more than one digit.

All-in-all I thought it was an enjoyable game and a good way to review math facts as it was attractive to the boys and they seemed to enjoy the games they played.
I was very impressed with the sincerity and kindness of the correspondance I have had with the company.

"...feel free to email us, ask question - we are not some big aloof company; we are a couple of college teachers trying to make a difference. Also - help us get the word out, anyway that you can or feel comfortable. Tell your friends that might have children struggling in math.
We also want to have something that you can use and tell your friends. If you purchase any products at shop.iseecards.com you can use the promo code mathisfun for 50% off anything up until April 7. You can give this code to as many people that you want.

Finally, if you have friends or folks that are unemployed or cannot afford the cards due to a limited budget - have them contact us. We will make sure that they can get these games for their children. We don't want anyone unable to provide these excellent learning games to their children because of cost. Good games make for good learning and every child deserves a chance at that." 

Disclaimer: I received this product free through the company owner in exchange for my candid review. A positive review was not required, nor did I receive any further compensation. All opinions expressed are mine. I am disclosing this in accordance with the FTC regulations.

Potion Making: A Math Game



at Time to Craft



When I saw this math game at Time to Craft, I was very intrigued. I left a comment there, telling of my interest to know more and Cheryl treated us to full explanations and even print-outs of the game that her daughter, Arabella, made. She even game me permission to share the idea with you. I love the blogisphere because you can meet the nicest people. I showed what she sent me to my boys, and they were very interested and even had some ideas of their own. The point of the game is to be able to match the different ways a fraction can be written whether it be a decimal, percent or non-reduced fraction.

Their game board is similar to snakes and ladders, with about 26 squares, 20 of which have shapes which are divided into fractions (1/2, 1/3, 1/4, 1/5 and 1/6.) One square is a "Miss a Turn" square. You can make it any style you would like, to personalize it as it suits your needs. Cheryl's daughter is interested in Harry Potter, so she chose to make it like a moving staircase, and kept the snake but added a trap door for one square, that leads to the tail of the same snake. We made ours a Magician's castle and had the path going every direction, and ended up having many more squares. It is interesting what happens when a whole group of people work on a project together!

The potion list that Cheryl sent me was very cute and clever but it was based on the Harry Potter books, which we don't read, so we modified it to suit us. Sam made me a list of some interesting potions we could make such as "Sleep", ""Fly" and "Fireball." We started out with a sheet with several circles divided into 8ths, 6ths and 5ths. These would be the parts or components list for the potions.  Players need to pick up components of the potions according to what fractions they land on, picking up various parts of the ingredient until he made a whole. This added an element of adding/subtracting fractions.
Next you need to make a deck of cards which have each fraction written out as a decimal, percentage and another fraction (eg. 1/2, 0.5, 50%, 2/4). Arabella used an old pack of playing cards. We used cut out pieces of cardstock.

Cheryl and her daughter adapted a regular 6-sided die so that there were two sides with one, two sides with two and two side with three as the game is too quick with a regular 6-sided die. We decided to use a ten-sided die since we had many more squares to travel.

Now that all the materials are ready, you are ready to play.

The Rules of the Game:

I have adapted this just a bit, but most of it was created by Cheryl's daughter.

1. Each player takes a spellbook sheet with circle divided into different fractions and some colored pencils (although you could use just a regular pencil.)

2. Give each player 7 cards.
3. Youngest goes first. Roll the dice and move your counter that number of squares.
4. If the player has a card that matches the square's diagram, then fill in  the amount on the  potion graph for a potion of choice. Discard the card and pick up a new one. Pass the die to the next player.

5. If a player offers a card that does not match, and the other players catch it, they must go back two squares.
6. If there is no match, pass the die to the next player.
7. If a player has two cards that add up to the square, he can use both cards at once. (For example, if you land on a square with a shape that is half-filled in, and you have cards with 0.25 and 1/4 on them, you can use both cards to equal the 1/2).
8. First one to get all the ingredients for two of the spells, has the ability to begin heading back home to the beginning square. Once the first person returns to the home square, everyone tells how many spells they have all the ingredients for, and the one with the most wins!

More here.

Math Games Fit For A King

The Counting House Game at Fairy Dust Teaching

When I saw these lovely math games at Fairy Dust Teaching, I knew that my youngest son would love them. They excite the imagination as well as make an interesting way of practicing math skills. 

To make the boards, we used one 12 x 12 sheet of scrapbook paper per board, a number grid and anything you would like to decorate your board. I used a piece of foam to make the crown. To play the games you will also need a die (we used a 10-sided die for the 100 grid, but Sally at Fairy Dust Teaching, used a 6-sided die for her 20 and 30 grids) and glass counting gems or pennies. Sally also uses peg people.

The Counting House
To play: The child roll a die and counts out this amount of gems and places them on the counting grid. He must count the numbers on the grid as each additional amount of gems are added, until he gets to his final number on the grid. But first, before he plays, tell him a story. Sally has created a lovely story about Mr. Thirty to go with her 30-board. I wanted to use a 100's board, so I created a different story.

Once upon a time there was a King who needed to collect the yearly taxes from his subjects as harvest season had just now ended . So he sent out his men to search the kingdom high and low to find all of the people in the kingdom. They found cottages amid the wood, and houses along the streams. They found dwellings in a little town and those all alone. At each place they collected the taxes and took them to the king's counting house. The people were expecting this because this happened every year this time and the king expected to get 100 coins for that is what he brought in each year. Please check for the King - roll the King's royal dice to see how many coins are collected at each house and fill the Hundred Counting House.

Another variation for older students is for them to keep track of their die rolls and make a very large addition equation.

War of The Kingdoms
You need as many game boards as players, with a minimum of two boards/players. Each game board is a kingdom. The player is the King or Queen of that Kingdom.

To Play: This is a game is just like the The Counting House except  that each player rolls the dice on his turn and then puts that number of markers down on his board. The first player to fill their number board, is the Kingdom that wins!

Joining Kingdoms
This game takes a different board. This board can be a castle or a crown shape, with two circles or squares on it, one large, and one small and a place in which numbers can be put above the boxes. It also requires gems, a 10-sided die (or six, if you wish) and number cards or tiles.

To play:
Roll a die twice to get two different numbers that you will count out markers into the circles on the game board using the "jewels." The number that is less goes into King Less' smaller circle and the number that is more goes into the King More's bigger circle. How many are there when they share and join their jewels together? Next, the child must find that number in the number cards and put it on the joined square. But first before you play, here is my version of the background story (Sally has another version.)

Once upon a time there lived a king who was small in stature (but large in wisdom)  King named King Less and a king who was very tall and broad (but not so bright) named King More. King More kept taking over more and more land and yet he had trouble keeping track of it because he wasn't very bright. King Less kept losing provinces to King More and he kingdom had shrunk to a very small one indeed. His kingdom was a happy one, however, because he was kind and managed his kingdom well.  One day, as King More was taking over more villages to his kingdom, he saw that the people in King Less' kingdom were much happier than in his own so he decided to go to the King Less to find out how he could be have more happy kingdom. King Less told him, "I will teach you the secret to having a happy kingdom if you can help me defend my kingdom from invaders on all sides - then we both will have more!"  That day King Less and King More joined their kingdoms and became co-rulers. King Less, although he was small and brought less land to their union, used his wisdom to run the kingdom within, while King More used his strength and the wealth of all his land to defend the boarders of their kingdom. Together they had a very happy and strong kingdom.

Laminate boards for durability.  These games should be played with adult supervision and are intended for children 5 years old or older as they use small pieces on the game boards.  Please adjust for safety if you are making these for younger children.

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