Back To CourseScience Standards Information for Teachers
5 chapters | 140 lessons
The West Virginia Next Generation Standards were devised to raise the educational bar for West Virginia's public school students, with updated standards that emphasize material understanding (as opposed to rote memorization), real world skills and critical thinking. The standards are progressive, and cover grades K-12.
At the heart of these standards are eight stated Mathematical Habits of Mind, which are practiced at all levels of schooling. These eight habits form a strong theoretical foundation for the student as they progress further into their mathematical studies.
MHM #1. Make sense of problems and persevere in solving them. A student proficient with this habit can internally explain the meaning of the problem and analyze the given data before devising a solution. They know how to consider similar problems or special cases while forming this solution, and evaluate their own progress as they continue toward its completion.
MHM #2. Reason abstractly and quantitatively. When approaching a math problem, a student proficient with this habit makes use of decontextualization, by distilling the problem into its symbolic or abstract elements, as well as quantitative contextualization (working with actual units, operations and values).
MHM #3. Construct viable arguments and critique the reasoning of others. This means that a student knows how to make use of stated definitions and proven results to construct their own arguments. They employ logic and reasoning and consider the context of the data when determining the efficacy of an argument or a proposed solution.
MHM #4. Model with mathematics. This is a student who knows how to identify a situation in their daily life that may benefit from using mathematics. They then decide the best tools or principles that apply to the situation and use them mindfully.
MHM #5. Use appropriate tools strategically. This student also knows which tools they will need to use when solving math problems. They know how to use these tools correctly, and know when said tools may provide only an estimation (or may otherwise limit the precision of the results).
MHM #6. Attend to precision. A student proficient with this habit strives for clarity and accuracy when communicating, calculating and when solving a problem. This requires a thorough understanding of the operations and units of measurement being used.
MHM #7. Look for and make use of structure. By looking for patterns and familiar structures in math problems, this student gains a greater understanding of mathematics in general. For example, this student remembers certain distributive patterns (such as 8 x 8 = (8 x 5) + (6 x 4)), or they may be able to break down algebraic functions into parts or look at them as a whole unit.
MHM #8. Look for and express regularity in repeated reasoning. This student understands the significance of repeated actions during computation. For example, they know that when they encounter a long division problem that falls into a pattern of identical actions, they are probably dealing with a repeating decimal.
What follows is a quick look at the standardized content and skills that all public school students will master, covered over a few key grades: kindergarten, 3rd grade, 5th grade, 7th grade and high school.
Kindergartners will learn the basics of counting, beginning with the names and order of numbers, then how to count to 100 by ones and tens and how to write the numbers 0-20. Also, they learn how to compare numbers (greater than/less than), and how to figure out How Many? (with objects in different configurations). The concept of place value is also introduced by having students decompose bigger numbers (from 11 to 19). At this level, basic addition and subtraction (within 10) are introduced visually, and by using sounds (such as clapping), fingers, role-playing and word problems. Kindergartners learn how to describe, classify and compare attributes that can be measured (such as length or weight), as well as geometric shapes.
For 3rd graders, the standards cover four major areas. The first is multiplication and division (whole numbers, within 100), which emphasizes the understanding of the relationship between the two operations, as well as how one can use the different properties of operations to solve problems. Next, students will begin to work with fractions and the idea that a fraction simply represents a given portion of a whole. At this stage, students learn how to reason with the sizes of these portions (e.g., knowing that 1/2 is a larger portion than 1/8, while 4/8 is the same as 1/2). The third topic covered is area; how to calculate the area of a two-dimensional region with both addition and multiplication. Finally, students will begin deepening their studies of geometry, classifying and partitioning shapes, and learning how to express these portions as fractions. Other topics may include perimeter, bar or picture graphs, volume, mass and time.
In 5th grade, students continue learning about the addition and subtraction of fractions, including fractions with unlike denominators. They will also begin to multiply and divide fractions by applying the concepts they already know about multiplication and division. Students work with decimals (to the thousandths place) and the place value system, identifying patterns in numbers when multiplying them by powers of ten. Also covered are multi-digit multiplication, measurement conversion, volume (as it relates to multiplication) and graphing with the x/y coordinate system.
During 7th grade, mathematics continues to progress in complexity. Using what they know about rational numbers and linear expressions, students will learn how they can use algebra to create solutions for real world problems that involve unknown variables. They will work with percentages and other ratios, observing how writing an expression in different ways may foster a better understanding of how to solve a problem. Students will also continue working with geometric figures and angles, including drawing, measuring and solving problems with these figures. Finally, 7th graders will gain a working knowledge of population sampling and probability models.
By the time students reach high school, they may find that their peers are now taking math classes at different levels. However, the general mathematics standards in high school cover several topic areas over four years.
Functions: Students will begin by learning about the construction and purpose of mathematical functions, range and domain, function notation and graphing. Quadratic functions are also covered, and eventually, students will encounter polynomials, inverse functions and the trigonometric functions.
Algebra: In high school, students continue learning ways to express a situation with algebraic models. They are later introduced to more advanced expressions, such as quadratics, equation systems and complex numbers. Students may also encounter sigma notation and finite series, as part of an introduction to calculus.
Statistics: Students will continue learning about different ways to predict, model and interpret data. These methods include using and building linear models, data plots and probability distribution graphs.
Geometry to Trigonometry: At this level, students may work with geometry on its own merits, but also as a stepping stone to trigonometry and calculus. Covered concepts include congruence, transformations and using algebra to prove geometric theorems. Some emphasis will be placed upon the right triangle as a basis of instruction in trigonometry (ratios, Pythagorean identity, the unit circle). Conic sections and circles (arc lengths, sectors, etc.) are also featured.
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Back To CourseScience Standards Information for Teachers
5 chapters | 140 lessons