A strong math elementary math curriculum teaches these five math strands (yes, there are many other ways of grouping these areas into as few as four and as many as eight different areas but we like this approach):
 
* Number Sense and Operations - Arithmetic and place value.

Time4Learning.com is an online subscription site popular for homeschooling, afterschool, and summer use. As an example, let’s survey how this curriculum builds a a broad math foundation through the shifting it’s focus among these diverse math strands.

The preschool program combines language arts and preschool math into one integrated learning sequence. It starts with the basics such as following simple instructions given verbally by cartoon characters such as "Click on the Crayon". Once the children are interacting successfully, they will learn through a fun set of learning games the basic concepts such as similar and different, quantity, sequence, comparisons, and shapes. Notice that the focus is on learning about sets and features which is pre-algebra. The features and patterns get more complicated and basic geometry is introduced. Then at the end of preschool and in the kindergarten math program, the concepts of comparative quantity and greater and less than are introduced. The focus is not on the simple question of having the kids learn to count up to ten although it is taught.

Advancing to first grade children will turn their primary focus to numbers and operations. They will learn to add and subtract numbers to one hundred. First grade math will include learning more about geometrical figures and objects, measurement of length, weight, capacity, time, and temperature, use of money, graphs and charts used for data analysis and prediction, and algebraic patterns. In second grade math children will compare and order whole numbers to one thousand, they will group objects into hundreds, tens and ones, relating the groupings to a written numeral. In numbers up to 1000, the children should know the place value of any designated digit. Second grade math introduces fractions. By the end of second grade and in the third grade math program, reinforcing math skills met in previous years, children will move on to a more rigorous structure. Third grade word problems can combine multiple skills in the same problem. Children will work with numbers through the hundred-thousands or more. They learn about decimals in the context of money and get experience with fractions up to 100. Third grade math opens them up to a greater understanding of measurement techniques, geometry and algebraic thinking. It will be a challenging year as they are presented with many new and complex concepts.

The major math strands for the fourth grade math curriculum are number sense and operations, algebra, geometry and spatial sense, measurement, and data analysis and probability. This year they are expected to know basic multiplication and division. They will recognize that two fractions are equivalent or non-equivalent and learn to add and subtract fractions using drawings, story problems and algorithms. During fourth grade, math students use a wide variety of tools and procedures to measure length, area, volume, and perimeter. They investigate angle measures, learning about the common angles of 45°, 90°, and 180° (straight angle). They'll learn to use these angles as reference for measurement of other angles. During fifth grade math, students master the concepts and mechanics of multiplication and division including the commutative, associative and distributive properties. They are expected to learn to factor and recognize prime numbers to 100 and recognize squares. Fifth grade math students are taught to find factors of numbers including the rules of divisibility and to determine if they are prime or composite. They express whole numbers as products of prime factors and determine the greatest common factor or the least common multiple of two numbers up to 100 or more. In fifth grade they multiply by powers of 10, demonstrating patterns. They identify and apply rules of divisibility for 2, 3, 4, 5, 6, 9, and 10, and use models to identify perfect squares to 144.

In sixth grade math, students build on what they learned in fifth grade math, which led them to the decimal base-10 number system, finding factors of numbers to 100, and multiplication of decimals to hundredths. They compare decimals to fractions, and add, subtract, multiply and divide decimals and fractions. It will be an exciting year full of new, complex math concepts. During seventh grade math children learn about decimals, percents, exponents, scientific notation, ratios, and square roots. Seventh grade math opens them up to a greater understanding of measurement techniques, geometry and algebraic thinking. In eighth grade math, students work with positive and negative numbers, exponents, and the order of operations, as well as scientific and standard notation. They learn more about working with whole numbers, fractions, mixed numbers, decimals, and integers.

There are many successful approaches to curriculum from hands-on applied mathematics to strict standards-based education. However, all the best curriculum take a broad approach to the math curriculum and struggle to provide a coherent sequence with ongoing review and reinforcement of previously-learned skills and concepts. Time4Learning's math curriculum provides a good example of how to broadly develop skills through the elementary and middle school years.