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The students in a sixth grade math class have been steadily
building on the curriculum focal points introduced in the first
grade. These basics are the skill sets suggested by the National
Mathematics curriculum and adopted by many school districts. As
sixth graders, students can use whole numbers, fractions and decimals
in addition, subtraction, multiplication and division fluently.
They are competent with using words to describe these numbers
as well as numerical representation. They can verbally describe
positive rational numbers and can express quantities in a variety
of ways.
Sixth graders have realized that math problems are not confined to a textbook
or a classroom. They have used decimals, fractions and ratios
to solve real world problems presented to them in numerical form,
as word problems and as abstract ideas. When confronted with an
abstract situation, they can choose the proper steps in the correct
order and can solve the problem. When asked, sixth graders can
back up the work they've done with confidence, explaining the
inverse relationship of positive and negative numbers, divisibility
rules, commutative, associative and distributive properties in
addition and multiplication. They understand prime numbers, factoring
and can explain why they chose what they did in calculating their
answers.
These students have learned the history of math and know Roman
numerals and Egyptian number systems. They understand the use
of base 10, base 5 and base 8; they understand place values and
zero as a place holder. When a problem contains parentheses, they
know the order of operations and do the work inside the parentheses
first. In the sixth grade, students can convert feet to meters,
kilometers to centimeters and miles to inches. They can determine
rate and can also use it in conjunction with average speed, distance
and time to solve problems.
In geometry, sixth graders have gone from simple shapes, lines
and curves to polygons, isosceles triangles and pyramids. They
can calculate the circumference and area of a circle as they know
and can use pi as both a number and a symbol. They can calculate
the volume of three-dimensional objects and the perimeter and
area of two-dimensional shapes. These students know triangles
and their angles and can calculate an unknown angle by using their
knowledge of complementary and supplementary angles and their
properties. They can shrink or grow a two-dimensional figure and
understand the relationship between the old figure and the newly
created one.
Sixth graders can calculate percentages for real world use such
as shopping for a bargain or tipping their servers. They understand
the concept of scale and can use it to judge distance in map reading.
They can also graph points on a grid to aid in their use of a
map or to understand and explain how the GPS in the family car
works.
These students should be able to judge whether an exact answer
is needed or if an estimate will be sufficient and they should
be able to say why. They should also know how to use an estimate
to back up their calculations and express confidence in their
solutions.
Students can order a set of data by mean, mode and median and
they can compute the range. They can explain the meaning and importance
of each term and describe how this data was obtained and screened
for relevancy. They can take a small group and make valid comparisons
to a larger population, use data tables to back up statements.
They can also use data they have organized to predict probabilities
and can represent those probabilities as percentages, ratios and
negatives.
The mathematics curriculum in sixth grade prepares students for
the future. They are able to make decisions based on mathematical
reasoning and can analyze situations in a rational manner. They
are able to take their accumulated skills and work from simple
problems to the more complex and they are able to clearly and
logically explain their solutions or results to others.
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