Your friend asked you to enter a texting/typing competition but have months to practice. We know practicing something makes you better at it.  You will be given your current speed and how well you improve over each month.  It is your job to find your texting/typing speed given a number of months that you have practiced.  You are also to look over other student’s work to see if they made an error and if so, where. 

This problem involves solving a system of algebraic equations from a context: depending how the problem is interpreted, there may be one equation or two.

This learning video deals with a question of geometrical probability. A key idea presented is the fact that a linear equation in three dimensions produces a plane. The video focuses on random triangles that are defined by their three respective angles. These angles are chosen randomly subject to a constraint that they must sum to 180 degrees. An example of the types of in-class activities for between segments of the video is: Ask six students for numbers and make those numbers the coordinates x,y of three points. Then have the class try to figure out how to decide if the triangle with those corners is acute or obtuse.

This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations.

Students are exptected to identify the slope of the line with the unit rate in this real world problem.

This task provides the opportunity for students to reason about graphs, slopes, and rates without having a scale on the axes or an equation to represent the graphs. Students who prefer to work with specific numbers can write in scales on the axes to help them get started.

This task involves solving equations with rational coefficients, and requires students to use the distributive law ("combine like terms"). The equation also provides opportunities for students to observe structure in the equation to find a quicker solution, as in the second solution presented.

This 10-minute video lesson provides an introduction to 2nd order, linear, homogeneous differential equations with constant coefficients. [Differential Equations playlist: Lesson 13 of 45]

This 8-minute video lesson continues the discussion from the previous video and shows how to find the general solution. [Differential Equations playlist: Lesson 14 of 45]

This 6-minute video lesson continues the discussion from the previous videos and introduces some initial conditions to solve for the particular solution. [Differential Equations playlist: Lesson 15 of 45]

This 9-minute video lesson continues the discussion from the previous videos and provides another example using initial conditions. [Differential Equations playlist: Lesson 16 of 45]

This 12-minute video lesson looks at useful properties of the Laplace Transform. [Differential Equations playlist: Lesson 30 of 45]

This 10-minute video lesson looks at using the method of undetermined coefficients to solve nonhomogeneous linear differential equations. [Differential Equations playlist: Lesson 22 of 45]

This 11-minute video lesson gives another example using undetermined coefficients. [Differential Equations playlist: Lesson 23 of 45]

This 8-minute video lesson gives another example where the nonhomogeneous part is a polynomial. [Differential Equations playlist: Lesson 24 of 45]

This 6-minute video lesson concludes the series on undetermined coefficients by putting it all together. [Differential Equations playlist: Lesson 25 of 45]

This task requires students to use the fact that on the graph of the linear equation y=ax+c, the y-coordinate increases by a when x increases by one. Specific values for c and d were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.

This task helps students solidify their understanding of linear functions and push them to be more fluent in their reasoning about slope and y-intercepts. This task has also produced a reasonable starting place for discussing point-slope form of a linear equation.

This task can be used to both assess student understanding of systems of linear equations or to promote discussion and student thinking that would allow for a stronger solidification of these concepts.