November 11, 2016

This is a high school instructional unit that features nine lessons relating to vectors. Students build understanding of vector properties as they learn airplane navigation. Problem-based learning activities include reading real-time weather maps, tracking airplanes flying in U.S. skies, calculating vector components, analyzing effects of wind velocity, and completing training segments similar to a private pilot certification program. Participants have access to help from experts at the Polaris Career Center. Comprehensive teacher guides, student guides, reference materials, and assessments are included. This resource was developed by the Center for Innovation in Science and Engineering Education (CIESE). Participation is cost-free; additional options are available for registered users.

- Mathematics > General
- Education > General

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

Make sense of problems and persevere in solving them.

Attend to precision.

Represent and analyze quantitative relationships between dependent and independent variables.

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.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

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.

Represent and model with vector quantities.

(+) 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).

(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

(+) Solve problems involving velocity and other quantities that can be represented by vectors.

Perform operations on vectors.

(+) Add and subtract vectors.

Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

Interpret functions that arise in applications in terms of the context

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.?

Define trigonometric ratios and solve problems involving right triangles

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.?