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Friday, April 5, 2019

Math the Play Way

If you've already done Laundry Preschooland are ready to move on to something just a little more formal, here are some ideas for you.

I believe children need plenty of time working with real things before moving to symbols like written numbers.  We want them to feel comfortable with numbers in real life before they get to workbooks. I think this takes a lot of working with real things, manipulatives, and games, and it's important to get this down before we ever start worksheet drills.

The ideas below are suitable to begin with a child from about three to six, although individual children will differ. They are not in any particular order, so ideas at the end of the post may well be a better place to start than the ideas at the beginning of this post.

Patterns- Learn to look for patterns everywhere, in nature, in the fruits and vegetables in the refrigerator (cut an apple in half sideways and observe the star), on your jewelry, clothing, and in picture books. Tiles on the floor make a pattern, as do designs on wallpaper. Have fun putting together your own patterns using blocks, beads, buttons from Grandma's Button Jar, and coloring supplies.

Dominoes- We get out the dominoes and match the ends. We don't worry about score keeping or anything else- just match a number in your pile to a number at the end of the domino row on the table. This helps them learn number patterns. Later, we play a kind of slap jack game. When I think they recognize the patterns well, I will lay the dominoes face down, turn one over, and the first one to call out the total number of dots and slap his/her hand down over it will get to keep the domino.  You could also do this for younger children using regular playing cards (remove the face cards) from any old incomplete deck.

Cup of Twenty- I do not know why, but my two littlest thought this was a really fun game. I give them each a cup with twenty small counters in it. It can be beads, dried beans, dry macaroni, poker chips, those glass things for planters (they look like flattened marbles) whatever. I would give them a regular set of dice from a game, one with the number dots for 1-6. They each got their own. They took turns rolling, telling me what they rolled (this, again, helps with the recognition of dot patterns from 1-6), and then they removed that many counters from their cup. The first one to zero won. As they play, you can sometimes ask questions about who has the most, who has the least, how many counters they have left, how many counters they have removed all together, etc. Once all the counters are out of the cup, they roll to return counters to the cup- same thing- an occasional question about who has more, who can win with just one roll, how many all together from the last roll and this one. Again,
they just adored this 'game.'

our son and godsons playing with rods
What's in my hand? We used cuisenaire rods. You could do this with any set of manipulatives that have some sort of graduated numeric value.  To begin with, I had them make the stair steps (one through ten in a row), close their eyes, and then I removed a rod, closed the stairs, and they had to guess what I was holding. If you don't have any rod manipulatives, you might try it with a deck of cards, one through ten, or the dominoes.
Next I took our Cuisenaire box which has slots for each separate color, and I wrote the numbers above the right color. My kids could refer to that for help. Then I took a fist full of rods and put them in a bag. I would pull out one rod, keeping it out of their sight, and give them a clue, and they would have to guess what I had in my hand. If I had a six, I might use one of the following clues:
The rod in my hand is bigger than five, smaller than seven.
The rod in my hand is in between five and seven.
The rod in my hand is more than five, less than seven.
The rod in my hand is longer than five, shorter than seven.
I used these different sentences throughout the game because I discovered that one of the children had not ever picked up what 'in between' meant in relation to numbers. And, after all, being comfortable with a variety of ways to state the same number is important for later math concepts.
Once the kids got comfortable (and quick) at answering these questions, I started to give clues like:
The rod in my hand is half of an eight.
The rod in my hand is one more than seven.
The rod in my hand is one less than four.
The rod in my hand plus a one makes a nine.
After we worked our way through the ones facts so that the kids knew them easily (although they did not realize what they'd done), we moved on to more complicated clues. The next step up in clues worked like this:
The rod in my hand is two more than six.
The rod in my hand plus a three equals a seven.
If I had two of these rods, it would make a four.
The rod in my hand is two less than seven.
The rod in my hand is as big as a seven and three put together.
For all of these questions, they are allowed to refer to the box, to get out the rods and work out the answers. When they don't need time to work out the answers to the clues, we move to the next step.

I asked them to show me all the ways they can add two rods to get to a ten, all the ways they can add two rods to get to a seven, and so forth.

How Many Ways- this is another 'game' we play to vary our math times. We used a Lauri number puzzle 1-10 (Number Play, LR-2414, but it seems Kaplan makes it now). There are actually ten small puzzle boards, one for each number. One of the puzzle pieces in each board is the number, and then for the number one, there is one apple, for the number two, there are two pears, for the number 7, we have seven small trees (or whatever, you get the idea).

I like using the pieces to this puzzle because they are small, they do not roll around, and because more than one child can work with it at a time. While one child is using one part of the puzzle, another child can be working with a different part of the puzzle. However, anything you have could be used in a similar way- felt pieces, beans again, grapes, raisins, or buttons. Just make sure these small counters are not available to a younger child who is going to put something in his mouth and choke on it.

We take a whiteboard and I draw a blank form for a math equation. I use a circle, a plus sign, another circle, and then an equals sign. It looks kind of like this:
( ) + ( ) =

I put the number we are working with in the place where the sum belongs, then gave my kids that amount of small manipulatives. Their job was to move them around in the circles to show different ways of making six.   They would write down each of the math problems they figured out. So a child might put two manipulatives in one circle, the remaining four in the second, and then write down 2 + 4 = 6. I started playing like this with my eldest, lo these many years ago (1988), only we sat at the table and used paper plates for our circles and poker chips for manipulatives.  Use what you have, don't get wrapped up around finding the perfect thing first.

Math games to play with a regular deck of cards
Take out a set for numbers one through ten. Have the kids put them
in order smallest to largest, and then largest to smallest.
Give them a set of beans and have them put one bean, plastic disc, penny, button, acorn, seashell, pebble, or whatever you have  over each spot (this is helpful for learning one to one correspondence).
Play War- a great way to learn less than/more than (Divide the deck between two players. Holding their cards face down, the players turn their top cards over simultaneously. The player with the highest card wins, taking both cards)
Play Go Fish- At first this helps with identification, later only ask for pairs of cards that add up to ten, or six, or whatever. Give her a set of small counters to work out the combinations she needs in concrete objects first.
Board games 
Sorry- the older Sorry which involved rolling the dice. Games like this help them learn counting carefully (one to one correspondence), number patterns (on the dice), adding two dice together, and strategy.
RAcko is another great math game, and they don't even know they are doing 'math.'
Money- count the coins in your purse, sort them by size and color, learn their denominations, count nickels by fives, dimes by tens.
Counting real things- eggs in the egg carton get counted by twos, so do matched socks, eyes in the room, shoes. At the store, count onions into a bag, asking how many more and how many less you will have if you add three, take three out, and so forth. Count out cans of soup. Ask your child to put ten apples in a bag, or five cans of pineapple in the shopping cart. Let your child guess how much a bag of fruit or vegetables will weigh, and then let the child weigh the bag.
Books- Occasionally when you are reading aloud together and a number is mentioned (Ma gave Laura two pancakes, for instance), ask questions like, "How many would Laura have if Ma gave her two more? How many will Laura have left when she eats one? Watch for opportunities to think about numbers in all your read alouds- ask questions like "is that a lot or just a few? Can you show me that many fingers?
Once activities like this have become natural and your child's replies easy and fairly quickly, then add some number sentences- as you are playing 'What's in my hand,' take a moment to show her on a whiteboard that you could write out the answers in two ways. You could write, "The green rod and a red rod make a train as long as a six rod." Or you could simply write
it with numbers: 4+2=6

First get the concrete stuff down, the hands on things with real objects, then take the abstract ideas, written numbers and number sentences and apply them to the concrete stuff she already knows and feels comfortable with. Once they've gotten good at games like 'what's in my hand,' most kids can quickly see that the sense in having the symbols for 'and this many more' (+); is the same as (=).

The Computer- There are also some fun math games on the computer, although we don't use these much. If we were using these, I would also leave out counters for her to use. I would also permit manipulatives to be used with worksheets when those are first introduced.
A wise hsing mom once told me that if you start with manipulatives, they tend to resort to those external manipulatives more than their fingers. This is good, because it takes more time to count things out with external manipulatives, so that it is naturally a self- reducing activity. Kids will only use the manipulatives as long as they have to have them, and because it is tedious to count out five beans, and then four beans, and then count them all together, eventually they will remember their math facts and stop needing the extra assistance.

One easy game to play to figure out ways to make ten: You need four pictures of a train or a truck for each player. Trace the ten rod on the bed of the train or truck. Draw a pie chart with five sections. Color each of those sections to match your rods, 1-5. Make a spinner- you can do this with a brad and a paperclip. Take turns spinning, put the corresponding color rod on one of your trains. You can't move any rods after you've put them down, can't go over ten, and must have exact numbers to complete trains. Winner loads all four trucks or trains first. Later add numbers 6-10 to this.  (more ideas here)

Learning place value is the next step, I think, and a program such as Math U See is terrific, although there are others, too. It's also helpful to learn to count to 20 in a language such as Japanese, where the numbers passed ten are literally "Ten and 1; Ten and two; Ten and three; Ten and four..." Counting pennies, dimes, and dollars is also helpful for learning place value.

Throughout the day look for opportunities to estimate numbers and test your answers. The more you do this, the better the child will get at picturing numbers in his head- although that's not encouragement to fill a kindergarten aged child's days with constant oral math quizzes.  Do something like this when it is unforced, not interrupting a child who is busy at productive play, once a day over a long period of time.

Include your children in the real life math problems you are doing. I need to put up a fence, how much fencing do I need? What kind of math problem is that? I need to paint the wall, how much paint do I need? I need to buy carpeting, how much carpeting do I need? We need to set the table and we're having five guests for dinner. How many places shall we set? I'm doubling this recipe and since it calls for 2 cups of flour, how many will I need?  Or just explain that you are using math and what you are using it for- figuring out the gas mileage, the grocery budget, a tithe, fabric for a project, look for all the ways you use math in real life and point them out as you go through life together.

Keep your math lessons and games shorter than your child's attention span, and always quit while they are still having fun and well before frustration kicks in.

You can find more fun math games in the books Family MathFamily Math for Young Children, and one of the many books that have been written to go along with a set of cuisenaire rods (we liked Super Source, and Super Source for K-2)
You can incorporate math discussions into almost any book you read, but here are some of our favorites.
The Hello, Math series- this series is by no stretch of the imagination great literature, but they are fun math lessons. Some of our favorites have been:
MOnster Math Picnic
One Hungry Cat
More or Less a Mess

Here are two of our favorite 'math' picture books:
Over in the Meadow
Counting Creatures

Counting songs:
I have a short playlist of our favourite counting songs

My children are grown now and four of them have children of their own.  The above resources are things I used with them when they were small.  I am sure there are shinier, newer things out that are just as good.  You don't need to spend a lot of money or make sure everything is perfect.  Use what you have or can easily get.  I had my grandmother's real button box  and used it all the time (Kondo notwithstanding).  You may prefer the beads from a necklace that broke, dried beans, acorns picked up in the woods, or something else.   Adjust these ideas to your children and your family.  Think about the goal first and be flexible in how to reach it.  Make it a natural part of your daily lives- and be sure the littles still have plenty of free play time, and especially out-of-doors play.

Tools to help you implement Charlotte Mason methods:  

$5.00- Education for All, vol 2- the Imagination (and more) issue!- transcript of the imagination talk from the AO Camp meeting, with additional material I had to cut to save time.  
 $5.00- Education for All, a new CM journal,   Feed Your Mind!  This issue contains several articles on handicrafts, outdoor play, nature study and science. See sidebar for purchasing options if you are in the Philippines.

 $3.00 Five Little Peppers and How They Grew Copywork (grades 2/3, carefully selected with an eye toward finely crafted sentences, lovely bits of writing pleasant to picture in the mind's eye, and practice in copying some of the mechanics of grammar and punctuation typically covered in these years.

  $3.00 Aesop's Fables Copywork for Year One!  Carefully selected with an eye toward well written sentences, memorable scenes, and some practice copying sentences that model the basics of capitalization and punctuation.   Suitable for use with children who have already mastered the strokes and letters for basic penmanship.

Picture Study!  Miguel Cabrera's beautiful, diverse families, painted in 18th century Mexico this package includes 9 downloadable prints along with directions for picture study and background information on the artist and his work. $5.00

Common Kitchen:  What's for lunch?  Isn't that a common problem in homeschooling families?  What to fix, what is quick, what is frugal, what is nourishing?  How can I accomplish all those things at once?  We homeschooled 7 children, and I was a homeschooling mom for 29 years on a single income.  I collected these recipes and snack ideas from all over the world.  These are real foods I used to feed my family, my godsons, and sometimes my grandkids.  Includes some cooking tips and suggestions for sides, and for a variety of substitutions.  I think every family will find something they can use here. $5.00

Webpage with great ideas for exploring early math concepts, especially for visually impaired children, adaptable for many situations:

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