Appendix: NYS Standards:

The state requires that at the Elementary school level a student should be able to “demonstrate fluency” in basic math concepts and use appropriate methods of solving problems as follows:
* Adds, subtracts, multiplies, and divides whole numbers correctly; that is; (c)
i. knows single digit addition, subtraction, multiplication, and division facts;
ii. adds and subtracts numbers with several digits;
iii. multiplies and divides numbers with one or two digits;
iv. multiplies and divides three digit numbers by one digit number

* Estimates numerically and spatially (f)
* Measures length, area, perimeter, circumference, diameter, height, weight, and volume accurately in both the customary and metric systems (c & p)
* Computes time (in hours and minutes) and money (in dollars and cents) (c)
* Refers to geometric shapes and terms correctly with concrete objects or drawings, including triangle, square, rectangle, side, edge, face, cube, point, line, perimeter, area, and circle; and refers with assistance to rhombus, parallelogram, quadrilateral, polygon, polyhedron, angle, vertex, volume, diameter, circumference, sphere, prism, and pyramid (p & c)
* Uses +, -, x, /,$,%, and decimal point, correctly in number sentences and expressions (c)
* Reads, creates, and represents data on a line plots, charts, tables, diagrams, bar graphs, simple circle graphs, and coordinate graphs (c)
* Uses recall, mental computations, pencil and paper, measuring devices, mathematic texts, manipulatives, calculators, computers, and advice from peers as appropriate, to achieve solutions; that is, uses measuring devices, graded appropriately for given situations, such as rulers (customary to the inch; metric to the centimeter), measuring cups (customary to the ounce; metric to the milliliter), and scales (customary to the pound; metric to the gram) (c & p) (p.168)

The state requires that at the Middle school level a student should be able to “demonstrate fluency” in basic math concepts and use appropriate methods of solving problems as follows:

* Computes accurately with arithmetic operations on rational numbers (c)
* Knows and uses the correct order of operations for arithmetic computations (c)
* Estimates numerically and spatially (f)
* Measures length, area, volume, weight, time, and temperature accurately (c)
* Refers to geometric shapes and terms correctly (p)
* Uses equations, formulas, and simple algebraic notation appropriately (f)
* Reads and organizes data on charts and graphs, including scatter plots, bar line, and circle graphs, and Venn diagrams; calculates mean and median (f)
* Uses recall, mental computations, pencil and paper, measuring devices, mathematic texts, manipulatives, calculators, computers, and advice from peers, as appropriate, to achieve solutions (c) (p.168)

The state also has requirements for High school level students to be able to “demonstrate fluency” in math as follows:

* Carries out numerical calculations and symbol manipulations effectively, using mental computations, pencil and paper, or other technological aids, as appropriate (c)
* Uses a variety of methods to estimate the values, in appropriate units, of quantities met in applications, and rounds numbers used in applications to an appropriate degree of accuracy (c)
* Evaluates and analyzes formulas and functions of many kinds, using both pencil and paper and more advanced technology (f)
* Uses basic geometric terminology accurately, and deduces information about basic geometric figures in solving problems (p)
* Makes and uses rough sketches, schematic diagrams, or precise scale diagrams to enhance a solution (p)
* Uses the number line and Cartesian coordinates in the pane and in space (c & p)
* Creates and interprets graphs of many kinds, such as function graphs, circle graphs, scatter plots, regression lines, and histograms (c)
* Sets up and solves equations symbolically (when possible) and graphically (c)
* Knows how to use algorithms in mathematics, such as the Euclidean Algorithm (f)
* Uses technology to create graphs or spreadsheets that contribute to the understanding of a problem (c)
* Writes a simple computer program to carry out a computation or simulation to be repeated many times (f)
* Uses tools such as rulers, tapes, compasses, and protractors in solving problems (p)
* Knows standard methods to solve basic problems and uses these methods in approaching more complex problems (c) (p.168)

A New York state has separate standards for “Scientific Connections and Applications.” These standards require a student to produce demonstrations in understanding as follows in Elementary school:

* Big ideas and unifying concepts, such as order and organization; models, form and function; change and constancy; and cause and effect (f)
* The designed world, such as development of agricultural techniques; and the variability of technological designs (f)
* Personal health, such as nutrition, substance abuse, and exercise; germs and toxic substances; personal and environmental safety (f)
* Science as a human endeavor, such as communication, cooperation, and diverse input in scientific research; and the importance of reason, intellectual honesty, and skepticism (f) (p.202)

In Middle school the standards for the same category are:

* Big ideas and unifying concepts, such as order and organization; models, form, and function; change and constancy; and cause and effect (f)
* The designed world, such as the reciprocal nature of science and technology; the development of agricultural techniques; and the viability of technological designs (f)
* Health, such as nutrition, exercise, and disease; effects of drugs and toxic substances; personal and environmental safety; and resources and environmental stress (f)
* Impact of technology, such as constraints and trade offs; feedback; benefits and risks; and problems and solutions (f)
* Impact of science, such as historical and contemporary contributions; and interactions between science and society (f) (p.202)

Finally, the High school standards of scientific connections and applications are as follows:

* Big ideas and unifying concepts, such as order and organization; models, form and function; change and constancy; and cause and effect (f)
* The designed world, such as the reciprocal relationship between science and technology; the development of agricultural techniques; and the reasonableness of technological designs (f)
* Health, such as nutrition and exercise; disease and epidemiology; personal and environmental safety; and resources, environmental stress, and population growth (f)
* Impact of technology, such as constraints and trade-offs; feedback; benefits and risks; and problems and solutions (f)
* Impact of science, such as historical and contemporary contributions; and interactions between science and society (f) (p.202)