MIDDLE GRADES 6-8 | ||
| Number and Operations Students in the middle grades represent real numbers using manipulatives, pictures, number lines, and symbols in a variety of contexts. Relationships among rational numbers are explored and equivalence among fractions, decimals, and percents is recognized and explained. Students extend their understanding of place value to decimal and scientific notation and use the properties of real numbers, including zero, one, and inverses. Numerical comparisons are expressed as ratios and rates and problems are solved using ratio, proportion, and percent. Students develop fluency in computation with rational numbers as well as with relationships among numbers, including primes, composites, factors, and multiples. They explain exponents and square and cube roots of numbers, develop facility with estimation and mental computation, and use calculators appropriately. Measurement In the middle grades, the study of perimeter and area is expanded to include surface area and volume of prisms and cylinders and formulas are developed for computing these quantities. Relationships among length, perimeter, area, and volume are studied. Students draw objects to scale and use scale drawings to solve problems. Geometry Students use the properties and relationships among geometric figures to solve problems. Congruence, similarity using ratio and proportion, and the Pythagorean theorem are studied. Students continue to study symmetries and transformations and become proficient at visualizing and recognizing transformed figures in the coordinate plane. Three-dimensional figures are drawn and built using different views. Data Analysis and Probability Students investigate increasingly complex data sets and, with the appropriate statistical measures, solve problems involving multiple data sets. More sophisticated representations, such as histograms, box plots, and scatter plots, highlight an increased understanding of the spread and grouping of data and the relationships between variables. Students identify basic patterns and trends in tables and charts and use them to make predictions. They describe the distribution of data using measures of central tendency. Students explore extremes in data and the misuse of representations to communicate information. With bivariate data, students learn to recognize relationships, estimate, and make predictions. In particular, linear relationships are identified and used to investigate bivariate data. Students conduct experiments and simulations to investigate basic probability, including dependent and independent events. Experimental results are compared with theoretical probabilities and students learn that the level of agreement between the two often depends on the number of times an experiment is repeated. Students learn to make inferences and predictions based on the outcomes of their experiments and simulations. Algebra Students in the middle grades begin to use the language of function, identifying patterns and relationships in context and expressing them algebraically. Variables are used to describe the interdependence of quantities and build an understanding of slope as the rate of change between quantities. In order to solve problems, ordered pairs of data are generated and used to identify a linear relationship between quantities graphically and algebraically. From tables and graphs students recognize nonlinear relationships and functions. Linear equations and inequalities are solved using multiple strategies, including manipulatives, tables, guess-and-test, working backwards, and algebraic methods. Students simplify algebraic expressions involving real numbers and variables and apply algebraic methods to solve a variety of problems. Grade 6 | ||||||||||
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G6WW1-3.pdf