Charles T. Koontz Intermediate

• 1. Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates.
• 2. Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems. Students extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane.
• 3. Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.
• 4. Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability.
  
  Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected. Students in Grade 6 also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.

Focus: World Geography, History & Culture: Patterns of Continuity and Change

Time Period: Beginnings of Human Society to the Emergence of the First Global Age (1450) – Represents the first five Eras of the Students in sixth grade will continue to expand the knowledge, skills and understandings acquired in the fourth and fifth grade studies of North Carolina and the United States by connecting those studies to their first formal look at a study of the world. Sixth graders will focus heavily on the discipline of geography by using the themes of location, place, movement, human-environment interaction and region to understand the emergence, expansion and decline of civilizations and societies from the beginning of human existence to the Age of Exploration. Students will take a systematic look at the history and culture of various world regions including the development of economic, political and social systems through the lens of change and continuity. As students examine the various factors that shaped the development of civilizations, societies and regions in the ancient world, they will examine both similarities and differences among these areas. A conscious effort should be made to integrate various civilizations, societies and regions from every continent (Africa, Asia, Europe and the Americas). During this study, students will learn to recognize and interpret the "lessons of history;" those transferable understandings that are supported throughout time by recurring themes and issues.

The standards are organized around five strands: history, geography and environmental literacy, economics and financial literacy, civics and government and culture. The strands should not be taught in isolation, but woven together in an integrated study that helps understand the ancient world. Additionally, the course includes two types of essential standards – one that identifies the skills that students should master during the course of the year and another that identify the knowledge and understandings. The skills should be taught within the context of applying knowledge and understandings to a study of the ancient world.