This activity is similar to the idea of a function machine. There are two levels of the manipulative (called a nomograph). The first is comprised of two vertical number lines, input on the left and output on the right. The second has three number lines to accommodate displaying the composition of two functions. At the first level, students try to find the rule of a hidden function by entering domain values and observing how they are transformed to new (range) values. The transformation is illustrated dynamically by an arrow that connects a domain entry to its range value. At the second level, students investigate composite functions. Inverse functions are treated as special cases of composition.
Students perform a simulation to measure the sound intensity at different distances from the source of a noise, and then use the data to develop an inverse variation model.
Students relate the graph of a rational function to the graphs of the polynomial functions of its numerator and denominator. Students graph these polynomials one at a time and identify their y-intercepts and zeros.
Students will graph one linear inequality and then graph a system of linear inequalities as they apply to an area of land. Students will practice graphing systems of inequalities and determining if a points lies in the solution. In the extension, students are challenged to write a system of inequalities that describe the area of Mississippi.
Texas Instruments activity where Students graph a quadratic function that models the shape of a bridge trestle and then solve the related quadratic equation by completing the square.
In this activity, students will find discounts and sale prices for items selling at 20% off and 40% off by using tables. They will then find the general rules, using a variable, for finding those discounts and prices.
In this activity, students will compare ratios with different denominators, and then with common denominators. They will also find unit rates.
In this activity, students discover the relationship between a change in the dimensions of a rectangle and the change in the corresponding area.