• 9-12: 2B/H3. Mathematics provides a precise language to describe objects and events and the relationships among them. In addition, mathematics provides tools for solving problems, analyzing data, and making logical arguments.

• 6-8: 2C/M2b. Using mathematics to solve a problem requires choosing what mathematics to use; probably making some simplifying assumptions, estimates, or approximations; doing computations; and then checking to see whether the answer makes sense.
• 9-12: 2C/H3. To be able to use and interpret mathematics well, it is necessary to be concerned with more than the mathematical validity of abstract operations and to take into account how well they correspond to the properties of the things represented.

• 6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.
• 9-12: 4F/H2. All motion is relative to whatever frame of reference is chosen, for there is no motionless frame from which to judge all motion.
• 9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.

• 9-12: 9B/H4. Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.

• 9-12: 12B/H2. Find answers to real-world problems by substituting numerical values in simple algebraic formulas and check the answer by reviewing the steps of the calculation and by judging whether the answer is reasonable.

• 6-8: 12C/M2. Use computer databases to store and retrieve information.

• 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

• 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

• N-VM.1 (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
• N-VM.2 (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
• N-VM.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors.
• N-VM.4.b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

• F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

• G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.^?

• RST.9-10.10 By the end of grade 10, read and comprehend science/technical texts in the grades 9—10 text complexity band independently and proficiently.

A unique and highly engaging two-week unit on vectors.  Beginning physics students build understanding of vector properties by doing real pilot navigation training.  This problem-based learning module comes with complete guides for teacher and learner.  The final assessment is a virtual pilot test flight.  Cost-free with teacher registration

• Physics First Vectors Unit
• Conceptual Physics Vectors Unit
• Algebra-Based Physics Vectors Unit
• AP/Calculus-Based Physics Vectors Unit