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High School students are expected to know the content of the Massachusetts Mathematics Curriculum Framework, through grade 8. These are skills from the framework that students will need:
Construct and use tables and graphs to interpret data sets.
Solve simple algebraic expressions.
Perform basic statistical procedures to analyze the center and spread of data.
Measure with accuracy and precision (e.g., length, volume, mass, temperature, time)
Metric system: Convert within a unit (e.g., centimeters to meters).
Metric system: Use common prefixes such as milli-, centi-, and kilo-.
Use scientific notation, where appropriate.
Use ratio and proportion to solve problems.
Conversion from Metric-to-Imperial (English) and Imperial-to-Metric
Determine percent error from experimental and accepted values.
Use appropriate Metric units, e.g. mass (kg); length (m); time (s); force (N); speed (m/s), etc.
Use the Celsius and Kelvin temperature scales
8th grade math skills that students should have
8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi2).
8.EE Work with radicals and integer exponents.
8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
- Understanding exponents (8-F.1)
- Evaluate exponents (8-F.2)
- Solve equations with variable exponents (8-F.3)
- Exponents with negative bases (8-F.4)
- Exponents with decimal and fractional bases (8-F.5)
- Understanding negative exponents (8-F.6)
- Evaluate negative exponents (8-F.7)
- Multiplication with exponents (8-F.8)
- Division with exponents (8-F.9)
- Multiplication and division with exponents (8-F.10)
- Power rule (8-F.11)
- Evaluate expressions using properties of exponents (8-F.12)
- Identify equivalent expressions involving exponents (8-F.13)
- Multiply monomials (8-BB.6)
- Divide monomials (8-BB.7)
- Multiply and divide monomials (8-BB.8)
- Powers of monomials (8-BB.9)
8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
8.EE Understand the connections between proportional relationships, lines, and linear equations.
8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.EE Analyze and solve linear equations and pairs of simultaneous linear equations.
8.EE.7 Solve linear equations in one variable.
8.EE.7.a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
8.F Use functions to model relationships between quantities.
8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
- Write equations for proportional relationships from tables (8-I.2)
- Find the constant of proportionality from a graph (8-I.4)
- Interpret graphs of proportional relationships (8-I.8)
- Write and solve equations for proportional relationships (8-I.9)
- Find the slope of a graph (8-Y.1)
- Find the slope from two points (8-Y.2)
- Find a missing coordinate using slope (8-Y.3)
- Write a linear equation from a graph (8-Y.8)
- Write a linear equation from two points (8-Y.10)
- Rate of change (8-Z.4)
- Constant rate of change (8-Z.5)
- Write a linear function from a table (8-Z.10)
- Write linear functions: word problems (8-Z.12)
8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
8.G Understand and apply the Pythagorean Theorem.
8.G Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
Selected new skills students will learn in 9th grade physics.
Determine the correct number of significant figures.
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
Apply ratios, rates, percentages, and unit conversions in the context of complicated measurement problems involving quantities with derived or compound units (such as mg/mL, kg/m 3, acre-feet, etc.).
National Council of Teachers of Mathematics
Students need to develop an understanding of metric units and their relationships, as well as fluency in applying the metric system to real-world situations. Because some non-metric units of measure are common in particular contexts, students need to develop familiarity with multiple systems of measure, including metric and customary systems and their relationships.
National Science Teachers Association
The efficiency and effectiveness of the metric system has long been evident to scientists, engineers, and educators. Because the metric system is used in all industrial nations except the United States, it is the position of the National Science Teachers Association that the International System of Units (SI) and its language be incorporated as an integral part of the education of children at all levels of their schooling.
Math is different from physics
Mathematics does not need to bother itself with real-world observations. It exists independently of any and all real-world measurements. It exists in a mental space of axioms, operators and rules.
Physics depends on real-world observations. Any physics theory could be overturned by a real-world measurement.
None of maths can be overturned by a real-world measurement. None of geometry can be.
Physics starts from what could be described as a romantic or optimistic notion: that the universe can be usefully described in mathematical terms; and that humans have the mental ability to assemble, and even interpret, that mathematical description.
Maths need not concern itself with how the universe actually works. Perhaps there are no real numbers, one might think it is likely that there is only a countable number of possible measurements in this universe, and nothing can form a perfect triangle or point.
Maths, including geometry, is a perfect abstraction that need bear no relation to the universe as it is.
Physics, to have any meaning, must bear some sort of correspondence to the universe as it is.
Why-is-geometry-mathematics-and-not-physics? Physics StackExchange, by EnergyNumbers