Mathematics

The standards for middle school continue the work started in elementary grades in these four strands: Data, Probability, and Statistical Reasoning (DPSR); Measurement, Geometry, Spatial Reasoning (MGSR); Numerical Reasoning (NR); and Patterns, Algebra, and Functional Reasoning (PAFR). Woven throughout all four strands are concepts building on students’ understanding of problem solving to provide context to the problems they are solving, which will foster critical thinking and collaboration skills.

In DPSR, sixth graders will analyze data sets to identify their statistical elements. They will create graphs and plots to represent data sets, along with interpreting measures of center and spread for those data sets. They will be introduced to probability with simple and complementary events and learn that probabilities can be written as a fraction, decimal, or percent.

In MGSR, sixth graders will use the characteristics of two-dimensional and three-dimensional shapes learned in earlier grades to help them calculate area, surface area, and volume using models, nets, and formulas. Students will use angle measures to find and identify complementarymor supplementary angles, along with exploring angles using a protractor. They will be introducedmto all four quadrants of the coordinate plane and begin plotting and graphing ordered pairs in all four quadrants, to include graphing lines and polygons.

In NR, sixth graders will utilize multiple representations of real numbers to translate, simplify,and solve problems using mathematical and real-world applications. Students will use their priorknowledge of whole numbers to expand into operations with integers and positive rational numbers. They will deepen their understanding of fractions, decimals, and percentages through ordering, sorting, and finding absolute value. The emphasis will be on understanding negative numbers.

In PAFR, sixth graders will expand their understanding of algebraic concepts, being introduced to functions. They will learn the correct terminology related to algebraic expressions, equations, and inequalities, along with distinguishing between expressions and equations, and equations and inequalities. One-step simple equations and inequalities will be used to solve a variety of problems using positive rational numbers. Students will also be introduced to ratios and rates, and how to use them in real-world situations.

The standards for middle school continue the work started in elementary grades in these four
strands: Data, Probability, and Statistical Reasoning (DPSR); Measurement, Geometry, and
Spatial Reasoning (MGSR); Numerical Reasoning (NR); and Patterns, Algebra, and Functional
Reasoning (PAFR). Woven throughout all four strands are concepts building on students’
understanding with problem solving to provide context to the problems they are solving, which
will foster critical thinking and collaboration skills.

In the DPSR strand, seventh graders will continue their analysis of data sets by creating and
analyzing displays, including stem-and-leaf plots and histograms. Students will calculate and
interpret problems using both experimental and theoretical probability. Students will make
connections and understand probabilities written as fractions, decimals, and percentages.
In the MGSR strand, seventh graders will be working with two- and three-dimensional figures to
solve problems involving area, surface area, and volume. Through exploration and discovery,
students will develop an understanding of how to find the circumference and area of circles. This
will be the first time these concepts have been introduced. Students will identify congruent
angles and solve equations relating to angles formed when lines intersect. Distance between
points on the coordinate plane will be found and connected back to the area and perimeter of
polygons.

In the NR strand, seventh graders will extend their understanding of operations to include all rational numbers, promoting student understanding of how rational numbers are used in real-
world situations.

In PAFR, seventh graders will expand on what was learned in sixth grade to develop an
understanding of proportional relationships. Students will represent algebraic concepts using
tables, graphs, verbal descriptions, and equations. Students will distinguish proportional
relationships from non-proportional relationships while making the connection between unit rate
and constant of proportionality. The extension of this knowledge will lead to the ability to solve
single- and multi-step problems while working with expressions and linear equations. Students
will be provided with multiple opportunities to solve a variety of percentage problems.

The standards for middle school continue the work started in elementary grades in these four
strands: Data, Probability, and Statistical Reasoning (DPSR); Measurement, Geometry, and
Spatial Reasoning (MGSR); Numerical Reasoning (NR); and Patterns, Algebra, and Functional
Reasoning (PAFR). Woven throughout all four strands are concepts building on students’
understanding with problem solving to provide context to the problems they are solving, which
will foster critical thinking and collaboration skills.

In DPSR, eighth graders will compare bivariate (two-variable) data. This is the first time that
students will work with two variables simultaneously. They will use scatterplots to organize
bivariate data from real-world situations. Students will describe associations among the data
points in a scatterplot based on direction, form, and strength. Eighth graders will identify sample
spaces and calculate and interpret the probability of compound events, using fractions, decimals,
or percentages to report the probability of events.

In the MGSR strand, eighth graders will use technology to explore volume and other formulas to
include the Pythagorean Theorem. The focus on right triangles will also include Pythagorean
Triples and the relationship among the measures of triangles’ interior and exterior angles and
sums of angle measures of polygons decomposed into triangles. Eighth graders will study
transformations and dilations of polygons graphed on or off the coordinate plane. Students will
also study angle relationships of parallel lines. Students will also use proportional reasoning to
determine congruence or similarity among polygons, finding the missing side lengths and
identifying corresponding angles.

In the NR strand, eighth graders will convert any form of rational numbers to other forms,
which—for the first time—includes translating repeating decimals to their fraction form. This
strand also has students identify the subsets of real numbers and contrast rational and irrational
numbers, which will include working with perfect squares and cubes and their roots. They will
write equations and inequalities to compare real numbers given in real-world settings. Students
will apply the Laws of Exponents learned in seventh grade to include algebraic expressions.

In the PAFR strand, eighth graders will concentrate on functions, learning the slope-intercept
form of a linear function. Students connect proportionality and linear functions together so that
the constant rate of change (slope) and y-intercept can be identified and interpreted. Students will analyze multiple representations of functions to determine if they represent a linear or nonlinear function or represent a non-function. For the first time, students compare two equations to determine if they represent functions with one solution, no solution, or infinite solutions. Also,for the first time, they solve one-variable multi-step equations and inequalities with the same variable on both sides.