Building a Solid Math Foundation
A solid math foundation is vital for children to succeed. Without
solid math skills, children will probably have a lot of trouble in school and
Students with weak basic math skills find the subject increasingly confusing
and difficult (and get poor grades). You might notice that your child starts to
develop math anxiety. When a child develops a solid math foundation,
you'll be amazed at how the stress caused by poor math skills disappears.
You might even hear your child say that math is fun!
Building a solid foundation in math requires a systematic approach. Too
many children do not get the broad introduction and ongoing practice that builds
confidence and deep understanding. The primary mistakes that parents
make in teaching/coaching math are:
- having too narrow a focus. Parents tend to overemphasize arithmetic and
overlook the other math areas.
- reviewing math concepts out of sequence.
This article will discuss what is an adequately broad approach to teaching
math and present how Time4Learning, an online learning system, provides such a
foundation for each grade.
A strong math elementary
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
* Number Sense and
Operations - Arithmetic and place value.
* Algebra - From the youngest age, learning to recognize
patterns and sets ("pick the small red fish") creates the groundwork
for working with unknowns and algebraic variables.
* Geometry and Spatial Sense - When children build on their
knowledge of basic shapes, they increase their ability to reason spatially, read
maps, visualize objects in space, and eventually use geometry to solve problems.
* Measurement - Learning how to measure and compare is an important
life skill that encompasses the concepts of length, weight, temperature,
capacity, time, and money.
* Data Analysis and Probability - Using charts, tables, and graphs
will help children learn to share and organize information about the world
What is Time4Learning?
Time4Learning.com is an online subscription site popular for homeschooling,
use. As an example, lets
survey how this curriculum builds a a broad math foundation through the shifting
its focus among these diverse math strands.
Foundation Building - PreSchool and Kindergarten Math
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.
The Basics of Arithmetic First to Third Grade Math
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.
Not Just Arithmetic Fourth and Fifth Grade Math
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.
Sixth to Eight Grade Math More sophisticated geometry, problems, and
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.
curriculum provides a
good example of how to broadly develop skills through the elementary and middle
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