Math 3 Syllabus

Math 3 Syllabus

Ms. Tomasiewicz

Unit1: Fireworks

The central problem of this unit involves sending up rockets to create a fireworks display. The trajectory of the rocket is a parabola, and this unit continues the algebraic investigations of Solve It! (Year 1) with a special focus on quadratic expressions, equations, and functions. Students see they can use algebra to find the vertex of the graph of a quadratic function by writing the quadratic expression in a particular form.

Unit2 : Meadows or Malls

The title problem of this unit concerns a decision a city must make about land use. This problem can be expressed using a system of linear equations and inequalities. The problem thus lends itself to solution by means of linear programming, a topic introduced in theYear 1 unit Cookies. Building on their work in that unit, students see that a key step in solving the problem is to find various points of intersection of the graphs of the appropriate equations. This in turn leads to the need to solve systems of linear equations. Along the way, students learn about graphing equations in three variables is a plane, and study the possible intersections of planes in space.

Because graphing calculators allow students to find inverses of square matrices (when the inverses exist), matrices are good tool for solving systems of linear equations with several variables. So, in addition to strengthening their skills with traditional methods, students learn to express linear systems in terms of matrices and develop the matrix operations required to understand the role of matrices in the solution process.

Unit 3: Small World, Isn’t It?

This unit opens with a table of data of world population over the last several centuries, and asks this rather facetious question: If population growth continues to follow this pattern, how long will it be until people are squashed up against each other? In order to gain insight into this problem, students study a variety of situations involving rates of growth. Based on those examples, they develop the concept of slope, and generalize this to idea of the derivative, the instantaneous rate of growth. In studying derivatives numerically, their they discover that exponential functions have the special property that their derivative is proportional to the value of the function, and see, intuitively, that population growth functions ought to have similar property. This, together with simplified growth models, suggests that an exponential function is a reasonable choice to use to approximate their population data.

Unit 4: High Dive

The central problem of the unit involves a circus act in which a diver is dropped from a turning Ferris wheel into a tub of water carried by a moving cart. The students’ task is to determine when the diver should be released from the Ferris wheel in order to land in the moving tub of water. In analyzing this problem, students extend right-triangle trigonometric functions to the circular functions, study the physics of falling objects

9including separating the diver’s motion into its vertical and horizontal components), and develop algebraic expression for the time of the diver’s fall in terms of his position. Along the way, students are introduced to several additional trigonometric concepts, such as polar coordinates, inverse trigonometric functions, and the Pythagorean theorem.

Unit 5: Pennant Fever

One team has a three-game lead over its closest rival for baseball pennant. Each team has seven games to go in the season (none of which are between these two teams). The central problem of the unit is to find the probability that the team that is leading will win the pennant. Students use the teams’ current record to set up a probability model for the problem. Their analysis of that model requires an understanding of combinatorial coefficients and uses probability tree diagrams as a tool. In the process of their analysis, students work through the general topic of permutations and combinations, and develop the binomial theorem and the properties of Pascal’s triangle. They also apply their general understanding of binomial distribution to several decisions – making problems involving statistical reasoning.