Math manipulatives can be very effective when teaching kids math. They work best when used in combination with the right curriculum. The manipulatives themselves are great, but to make learning successful you need to identify the learning style of the child you're teaching and present the curriculum in that manner. Manipulatives can be used with all accredited homeschooling curriculum such as; Saxon, Horizons, and Singapore math.
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Those studying and using mathematics accepted Euclids work, which was a compilation of all the mathematics known at his time, and which has continued to be used as the basis of geometry taught is schools for over 2000 years.
When you study the theory of geometry, it is pure mathematics. However, when you start using the geometry you have learned in other, more practical areas, then it becomes applied.
Math is short for Mathematics. The definition of which is "the study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols." See http://www.answers.com/topic/mathematics the complete definition and reference on mathematics.
One-half of one-third is one-sixth. Using fraction manipulatives would be one way to visually verify that a one-sixth piece would cover half of a one-third piece.
One-half of one-third is one-sixth. Using fraction manipulatives would be one way to visually verify that a one-sixth piece would cover half of a one-third piece.