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.