Math 6

Key Advances from Math 5 to Math 6

Students’ prior understanding of and skill with multiplication, division, and fractions contribute to their study of ratios, proportional relationships and unit rates (6.RP).
Students begin using properties of operations systematically to work with variables, variable expressions, and equations (6.EE).
Students extend their work with the system of rational numbers to include using positive and negative numbers to describe quantities (6.NS.5), extending the number line and coordinate plane to represent rational numbers and ordered pairs (6.NS.6), and understanding ordering and absolute value of rational numbers (6.NS.7).
Having worked with measurement data in previous grades, students begin to develop notions of statistical variability, summarizing and describing distributions (6.SP).

The Critical Areas for Grade 6 Math are:

The Grade 6 Standards represent a great deal of focused and rich interactions in the classroom. This is necessary in order to enable all students to understand all of the numbers and concepts involved. The Critical Areas are designed to bring focus to the standards at each grade by describing the big ideas that educators can use to build their curriculum and to guide instruction. The Critical Areas for Grade 6 are:

Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems. 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.

Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers. 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.

Writing, interpreting, and using expressions and equations. 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.

Developing understanding of statistical thinking. 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.

Fluency Expectations

Students interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions. This completes the extension of operations to fractions (6.NS.1).
Students fluently divide multidigit numbers using the standard algorithm. This is the culminating standard for several years’ worth of work with division of whole numbers (6.NS.2).
Students fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. This is the culminating standard for several years’ worth of work relating to the domains of Number and Operations in Base Ten, Operations and Algebraic Thinking, and Number and Operations — Fractions (6.NS.3).

What Course(s) follow Math 6?

Sixth grade is the final year in which all students follow the same core math pathway, building a strong foundation in mathematical reasoning and problem-solving.
As students transition into 7th grade, they will have the opportunity to choose a math pathway that aligns with their long-term goals. This decision will impact future coursework, including opportunities for earning college credits in high school. It's important to note that successful completion of a Math 7 Accelerated course is a required prerequisite of enrolling in Algebra 1R/A as an 8th grader. Students may not enroll in Algebra 1R/A from Math 7 since our middle school math acceleration curriculum follows a two-year sequence that condenses three years of math into two. Midway through 6th grade, families should begin considering which pathway is the best fit for their child. Factors such as their child’s confidence in math, problem-solving skills, and future academic aspirations should guide this decision. We encourage families to review the available options carefully and have conversations with their child’s teacher and school counselor to discuss which pathway will provide the right level of challenge and support.
For more information about acceleration options, please click HERE.

University at Buffalo's Gifted Math Program (GMP) provides an enriched and accelerated curriculum for students starting in 7th grade and continuing through 12th grade. By the end of the program, students will complete three semesters of calculus and linear algebra, earning up to 22 semester hours of university credit for their coursework.Classes are held twice weekly, with each session lasting 70 minutes, outside of the regular school day on UB’s campus. Taught by local and university faculty, these courses replace the student’s middle school and high school math classes. GMP courses fulfill New York State’s unit of credit requirements and are included on the student’s high school transcript. Additionally, students receive a college transcript from the University at Buffalo, reflecting their university-level achievements.For more information, visit the GMP website: https://giftedmath.buffalo.edu/.

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