Nuts and Bolts Living Math
Okay! Now for the nuts and bolts, how do you teach math without worksheets? There are a number of websites, books and sources out there that provide suggestions for teaching math beyond a strict . I’ve noted just a few of the many ideas that can be used to teach concepts.
Dr. Wright's Kitchen Table Math: Book 1 has many practical ideas to teaching math naturally through about age 8. Marilyn Burns has written a number of books as well for teaching math, including About Teaching Mathematics: A K8 Resource, 3rd Edition
Patricia Kenschaft’s “Math Power” is a great book to read to understand from a more mainstream author why each of these ideas are important. Frank Smith’s The Glass Wall: Why Mathematics Can Seem Difficult is another source of understanding the “leaps” children make in understanding what we consider to be very basic mathematical ideas.
A number of children's math readers include extension activities in the text of the reader, or in the back. Series such as MathSmart Readers by Stuart Murphy and Hello Math Readers by Marilyn Burns are good for teaching ideas, and each reader includes suggestions for games and activities that relate to a given concept. Amy Axelrod's PigMath Readers and Loreen Leedy's math books are also wellloved here. Many readers by concept are listed here at the site.
Number Sense and Counting
Count, count, count objects. Young children love to count. Counting seems simple, but when you do it with your child, you begin to see just how rich counting activities can be. Count pieces of fruit or household objects when opportunities arise. Practice arraying objects in ways that makes counting easier, thereby setting up a child to skip count. For example, you can “see” six if it is arrayed in two sets of three, whereas six bunched together is difficult to count other than by ones.
Greg Tang books such as Math For All Seasons are magnificent for demonstrating the rich mathematics that can learned through very simple counting activities. Following the rhymes and pictures in the books shows children and parents unique ways to go about counting that facilitates grouping, skip counting and multiplication later.
You can provide counters out of anything such as paper clips or dried beans and ask your child to count out amounts. Very young children can make groups of tens and ones to match place value names. For example, 2 sets of ten items and 4 single items are called "2 tens, 4 ones" and represent 24.
A Chinese or Japanese abacus/soroban is a fun way to count and begin learning the rudiments of counting and eventually place value. If you don't know how to use one of these ancient calculators that are still in large use, learn how! Instructions are plentiful on the internet and books.
An early game all my children have played for hours to gain sense of the pattern of counting all the way up to 100 and beyond is to bouncecount. I would have the child start with 1, I’d count 2, she’d count 3, etc. If the child starts the count, then you can teach them the pattern of 20, 30, 40 etc. which is difficult for many children. As they become comfortable, you can switch to starting so they practice recalling the pattern of the tens.
To gain number sense as to what numbers are larger or smaller than others, play "Guess My Number".You write or think of a number that your child must guess. For young children start with numbers up to 10 or 20. For older children, go as high as you both agree to. Your child guesses a number and you say "higher" or "lower." Your child adjusts the guess and tries again. Continue saying higher or lower until the number is guessed. Then switch roles with your child. For older children, you can add a limit to the number of guesses, such as 5 or 10 guesses. You only switch roles if your child guesses the number.
Encourage
your child to guess and play with guessing amounts. Guessing games such
as putting a handful of popcorn into a cup guessing the number of
pieces. Then count to see how close the guess is. Laugh about wild
guesses.
As
children’s mathematical abilities grow, begin talking about ways to
make better guesses by comparing unknown quantities to quantities you
do know. Practice estimating large amounts by taking out a portion such
as one quarter and counting it, and then multiplying the amount by four
to approximate the amount.
One
of the earliest exposures all of my children get to rounding and
estimating is shopping. They learn very quickly that $1.99 is "almost
$2.00". This is a rounding and estimating concept. I often think out
loud as we are adding up what we are buying on birthday shopping trips
or other shopping trips.
Skip Counting and Early Multiplication
Count
with your child by twos, fives, and tens as soon as they can begin
comprehending grouping and counting. Again, math readers are excellent
for introducing these ideas. Increase the difficulty as appropriate by
including the remaining numbers through nine. Learn to count by 3s and
then 6s, relating 6s to ‘skips’ of counting by 3s. Learn to count by 4s
as ‘skips’ of counting by 2s. 8’s are ‘skips’ of 4s. A number line is a
great way of seeing these relationships. You can take colored pencils
and draw “humps” to represent each numbers skip counting facts. You can
then see that all the 4 facts will touch the 2 facts, and the 8 facts
will touch all the 2 AND 4 facts, etc.
Challenge
your child to count by tens in patterns such as 4, 14, 24, and so on.
We do this for years in fun contexts. Eventually they see the patterns
and use them.
Our
family has enjoyed the Schoolhouse Rock classic, Multiplication Rock
for years. The videos introduce each skip count table in a fun and
interesting way. Skip count music tapes, chants, etc. are ways to help
even young children learn to memorize the sequence of these tables that
will later become known as their multiplication facts.
“Strew”
measuring devices around your home for your children’s play. My
children have all loved tape measures and spent happy hours measuring
things and asking me to help them compare measured objects. Rulers are
made readily available. Scales, measuring cups, spoons, etc. are all
available.
A
first measurement concept is comparison of sizes. Your child can place
objects in order by height, and then by length, then by weight, etc. A
number of the math readers provide an excellent introduction to
understanding relative sizes.
In
the grocery store or when putting away groceries, you can ask which
item weighs the most, and decide together by holding the objects or by
reading the weights on the labels. Famous riddles such as “which
weighs more, a pound of feathers or a pound of lead?” are fun to
explore the idea of weight.
You
can explore volumes by testing various shapes to see which one holds
the most or least water. For example, you can use an empty softdrink
bottle and a saucepan to ask a question such as, "If you fill the
bottle with water and empty it into the saucepan, will it all fit? Will
it overflow? Which holds more?" This can be done with any size
containers.
In
exploring distances, you can use ways to measure other than standard
units. Use the length of your child’s hand and foot to measure
distance, and then your own. "How many heeltotoe footsteps will it
take for you to walk across this room?" After there is a result ask,
"Will it take me more or fewer steps to cross the room?" Try to
estimate and recognize that if your foot is larger, you'll take fewer
steps. There are fun games we’ve played on www.pbskids.org Cyberchase
site that deal with measuring and comparing using different units.
If
you and your child enjoy making projects, you can make a tape measure.
Tape together strips of paper and mark them in inches or centimeters.
Or make your own ruler.
Read
weights of items that are written as decimals. Encourage your older
child to read the price labels on meats or deli items. Can he or she
tell that 1.25 pounds is 1 1/4 pounds? If the price is $2.69 per pound,
can he or she estimate what 2 or 3 pounds would cost?
Grocery Math website: http://www.ed.gov/pubs/parents/Math/grocerymath.html
Find
shapes in every environment you and your child interact  home, the
park, on the road, in the stores, etc. Go on a scavenger hunt with your
child to find objects around the house that have particular shapes,
such as circles, squares, rectangles, and triangles.
Look
for solid shapes. Encourage your child to identify solid shapes by
name: rectangular prisms for cereal or shoe boxes, cylinders for cans,
spheres for oranges, cubes for dice in box games.
Collect
a large variety of objects from around your home and find ways to group
objects by their resemblance to shapes. Help your child distinguish
between 2D flat shapes like triangles from 3D shapes like pyramids.
My
children have played with tools such as Pattern Blocks, K'nex, Legos,
base 10 blocks, and Zome Tools from an early age. Related creations to
common shapes, and challenge your kids to build shapes.
Patterns are the foundation of mathematics. Make patterns with beads, colored threads, dominoes, Pattern Blocks, any regular object that can demonstrate patterns. Have your young child use different beans or colored beads (or paper squares) to create patterns. You can take turns making patterns such as 1 red, 2 blue, 1 red, 2 blue, and having the other person tell what comes next in pattern. As your child becomes comfortable with this, the complexity of the patterns can increase.
Encourage your child to notice and discuss patterns in nature and objects around them. Picture books are again wonderful for helping children see patterns. Two outstanding books that come to mind is an out of print Time Life I Love Math book, Right in Your Backyard, and Nature's Paintbrush.
When you go to the store or the library, notice how things are grouped. All of my kids have seemed to grasp the organization of a store from exposure, but discussing it with your child is one way of making links.

Number Sense and Counting
Estimating and Rounding
Skip Counting & Early Multiplication
Measurement and Time
Shapes and Geometry
Patterns and Sets
