Moving from kindergarten to first grade is a major transition
time for children. After their year in kindergarten where group
learning, play and naptime are the norm; they now must adjust
to being in school for a full day, spending much more time sitting
quietly at a desk and following a more structured schedule. Within
this structure, the first grader takes what was learned in kindergarten
and expands upon it. The goals are the same: there are the curriculum
focal points set forth by the National Mathematics curriculum
that are taught in ways that help the student with reasoning,
making connections, following through to logical conclusions,
designing and analyzing representations and developing the skills
to communicate these points to others. But in first grade there
is much more emphasis on individual work and there is testing.
Number sense and numbers and operations are two phrases describing basically
the same principles of math. Children begin to understand and
use numbers and can read and write numerals up to at least 100
and can count objects up to 100. The students start the year using
math manipulatives such as blocks, figurines and cards, then begin
to move away from the physical objects to doing more of the work
in their heads. By the end of the school year, first graders should
be able to do the counting by 2's, 5's and 10's and should be
able to start from any number to reach 100. The child should understand
the number words and should be able to write them up to the number
12. Comparisons, ordering, equivalent forms and regrouping numbers
are all elements of number sense. Students also are expected to
know the names and values of coins and how to group them to make
equal amounts. First graders are taught about place values and
zero as a place holder. They begin to recognize numbers as groups
of tens and ones.
With comprehension of numbers and number sense comes an ability
to understand addition and subtraction. Simple equations in addition
and subtraction and word problems using phrases like "take away"
or "give to" are introduced. Children also learn that adding and
subtracting are inverse operations and can use them to solve problems.
The symbols for addition, subtraction, equal to, less than and
more than are introduced. They learn about the properties of addition
and can show equivalent forms of the same number using charts,
diagrams and other materials.
A child begins to understand math concepts as well and can demonstrate
how math and measurement are used every day in cooking, shopping
and estimating how long it will be until they have lunch, recess
or dinner. Measuring cups, rulers, clocks and calendars are used
for comparison and practical lessons. Using common objects to
measure other objects is an example of using nonstandard units.
Temperature and the use of thermometers is another topic covered
in the study of measurements.
By the end of first grade, students should have an understanding
of how geometric shapes can be combined to create a unique sum
of its parts. This new whole figure can be described by its own
properties or by its parts and can be recognized from various
angles and perspectives. Geometry and measurement lessons combined
create the ability to give and follow directions to a physical
location and allow the students to describe positions using words
like "above," "below," "under" and "closest."
The most important lessons learned in first grade math are the
skills developed in reasoning, logic and the relationship of the
physical world with the world in the child's mind. First graders
begin to understand the concept of cause and effect and begin
to understand differing points of view. These processes of maturation
enrich the child's ability to appreciate the existence of math
in daily circumstances.