Math is my thing! I love teaching math. Below I describe at each stage what worked best for us. Remember that your child is an individual and may respond differently. Most of what I suggest has helped my children be very enthusiastic math learners. In the right-hand column and at the bottom of the page are some books that I have used often. You can find them in your library. If you click on the link for them you'll be directed to Amazon.com. If you purchase the books I am compensated 5% of the purchase price.

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Preschool | Elementary Ages | Middle Grades | High School | Integrating Math


PRESCHOOL
For your preschooler, math is very simple. Recognizing patterns, learning the names and types of shapes, and learning how to count are good concepts to work on using play at this age. Counting wooden beads and other sets of objects (we call them "manipulatives") can be made into a game. At that age if I have a handful of raisins I usually ask, how many do you want? Then we count out the raisins. Fairly soon, counting becomes easy this way and fairly early what numbers are larger becomes evident! Use pattern blocks to learn the names of shapes and to make patterns. Play games and sing counting to music and rhythms. Give them some play money and a play cash register (even if made up of a cardboard box) and play store with them. They will learn math while playing and having fun.

VISUALIZING MATH IN EARLY ELEMENTARY AGES
       Play is still most important for gaining math skills in 1st and 2nd grade but children are usually ready for a little bit of seatwork as well. Beginning at around age 6, I have used Miquon Math with all of my children (grades 1-3). Miquon teaches HOW math works.  As a child works through the problems she will see how equations are balanced, why division and multiplication are related, how equivalent fractions work, and many other abstract math concepts. Students handle algebra better when they have a good grounding in these concepts. Manipulatives are used to help the learner visualize abstract ideas and to reinforce the concepts, making it easier to remember how addition, subtraction, division and multiplication works.


  At first the Miquon pages might seem confusing and I'm told that the extra teacher materials help very little.  I didn't buy the extra books and haven't really had a good look at them.  But I think if you work through more than just the first few pages you'll get the idea.


Of course we supplement Miquon with other manipulatives and hands on activities such as simply setting the kids up with measuring cups and water to see how fractions work. You might want to consider in investing in several different sets of blocks at this age. We use pattern blocks in elementary grades to teach geometry and area and then later we use them to teach high school geometry (such as the volume of an hexagonal prism). We use base ten blocks in the elementary grades and later when teaching factoring polynomials in algebra. Wooden blocks for the younger children can be used to teach volume of cylinders, triangular prisms and spheres.


 After Miquon I do something really fun with them. We use a book called "Everything's Coming up Fractions" along with Cuisenaire rods.  My oldest two loved using that book as did ALL of my students when I taught school.  You can't say that often!  ECUF is a completely painless and fun way to learn all the ins and outs of fractions.


      In addition to Miquon and ECUF, I supplement with several other resources. I've used many Spectrum Math pages with good success and of course we learn money by using it, fractions by measuring, multiplication using Square Foot Gardening, etc.  We also use manipulatives like base ten blocks, pattern blocks, beads, beans, paper clips, hand made geometric solids, etc...


    After a hurricane many years ago, my husband told my middle son he would be paid $.05 for each pinecone he picked up in the backyard. My second oldest son was reluctant to do it and complained to his elder brother about the job. My oldest son hurriedly replied, "I'll pay you a penny each just for counting!" and made $30 bucks that day. His dad had no idea how many pinecones he was about to have to pay for but my oldest estimated a gold mine quickly!


 Another time my oldest son (age 8 at the time) wanted to grow and sell produce (to me). After a week of constantly asking me questions like "how many lettuce plants can I plant in a square foot" and "how much does broccoli weigh", "how much does corn cost per ear", he worked out that he would make the most money by planting lettuce.  Sure enough, I checked out a book on market gardening and it said lettuce was the prime money maker per acre.


THE MIDDLE YEARS FOR MATH
   After we make sure the fractions are under the belt, I like using the Key To ____ (Algebra, Fractions, Decimals, Percents, Geometry, Measurement) books.  The boys were able to work independently in these easily and still gain a good mastery of the subject while they were fairly young.  Some pages are a little repetitive. I don't mind telling the learner, "Do four problems on the page. If you really understand it, we'll skip it." By the time they finished the series, they had fractions, decimals, percents,and basic algebra down pat. My 10 year old is the third son to use the Key To ___ series and he's just started with measurement.    


MATH WITH HIGH SCHOOLERS
Once the kids reach high school age, we use textbooks.  Houghton Mifflin's older edition algebra books (I and II) worked out well.  The examples are easy to follow and complete and the layout isn't too busy like most newer editions. We skipped many pages in the Algebra I book because the Keys to Algebra book allowed the boys to master most algebra concepts easily. But the Keys to Algebra books lacked good word problems and I'm a huge (HUGE) believer in algebra word problems. Houghton Mifflin's Structure and Method books (early 90's editions) offered a nice amount and well done word problems. 


   For Geometry my oldest used and I very much liked Addison Wesley's Geometry.  My second oldest used Math U See Geometry first and then went back and did all the proofs in the Addison Wesley Geometry book.  I'm a proofs fan.  I think the boys have benefited from having to think out proofs. It exercises a part of their brain that other school work doesn't exercise.  My oldest found that in college one does many trig proofs so having the background was helpful. To illustrate geometry we made good use of geoboards, geometric solids (or stacked pattern blocks), and other visual aids.


    We did the same with Algebra II.  My second eldest did Math U See Algebra II and then we picked up the Houghton Mifflin Algebra II book (I love that book!) and went over anything he didn't get through Math U See.  That made Algebra II very painless. 


Next we used Math U See Precalculus. That program covered the topic very well with little need for extra practice from an outside source. Now we're going a college precalculus text to see what the Math U See Precalculus program didn't cover and so far we haven't found much.


   This is not all the math the boys do or have done in high school. Every day math crops up.  We stress budgeting and banking at this age as these are crucial life skills. My oldest wanted to design an addition to our home with plans for tearing down a wall in his bedroom and extending the room out where we now have attic space.  We used "Blueprints for Geometry" with great success for this project.  He realized that there is a GOOD deal involved in designing an addition and did design one for us.  His grandpa, a retired contractor, helped long distance and we also used his grandma's blue prints (she was a home designer and we have a collection of her designs). 


At some point the kids are ready for calculus. A friend of mine, a retired math professor at a local university, told me to not rush into calculus and to make sure they have a good solid basic understanding first. His opinion is that calculus, a very conceptual math, needs a good grounding before starting so that students don't just learn to move around numbers but do learn to visualize calculus.  My second oldest, now a junior, is just about at the point where I'm going to have to break down and find something in calculus.  Sorry! I can't advise anyone on that one yet but suggestions would be most appreciated.


INTEGRATING MATH WITH OTHER SUBJECTS
I believe the best learning is that which can applied to not just a workbook but to all areas of life. We find teachable moments where we integrate math into other areas. For example, as we read history I pull out the Mathematicians Are People Too books. These books illustrate how math though developed through the ages.

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Good luck to you on finding something just right for your kids :)