Math 2 Syllabus
Ms. Tomasiewicz
Unit1: Shadows
The central question of this unit is, “How can you predict the length of a shadow?” The unit moves quickly from this concrete problem to the geometric concept of similarity. Students work with variety of approaches to come to an understanding of similar polygons, especially similar triangles. Then they return to the problem of the shadow, applying their knowledge of similar triangles and using informal methods for solving proportions, to develop general formula. In the last part of the unit, students learn about the three primary trigonometric functions -sine, cosine, tangent- as they apply to acute angles, and they apply these functions to problems of finding heights and distances.
Unit 2: Do Bees Build It Best
In this unit students work on a following problem: Bees store their honey in honeycombs that consist of cells they make out of wax. What is the best design for a honeycomb? To analyze this problem, students begin by learning about area and the Pythagorean theorem. Then, using the Pythagorean theorem and trigonometry, students find a formula for the area of a regular polygon with fixed perimeter and find that the larger the number of sides, the larger the area of the polygon. Students then turn their attention to volume and surface area, focusing on prisms that have a regular polygon as the base. They find that for such prism - if they also want the honeycomb cells to fit together – the mathematical winner, in terms of maximizing volume for a given surface area, is a regular hexagonal prism, which is essentially the choice of the bees.
Unit 3: All About Alice
This unit start with a model based on Lewis Carrol’s Alice in Wonderland, a story in which Alice’s height is doubled or halved by eating or drinking certain foods she finds. Out of the discussion of this situation come the basic principles for working with exponents- positive, negative, zero and fractional – and introduction to logarithms. Building on the work with exponents, the units discusses scientific notation and the manipulation of numbers written in scientific notation.
Unit 4: Orchard Hideout
The central problem of this unit concerns a couple who have planted an orchard on a circular lot. They want to know how long it will take before the trees grow large enough to hide the center of the orchard from the outside world. Answering this question requires students to study circles and coordinate geometry. They develop the formulas for the circumference and the area of a circle, as well as the distance and midpoint formulas, and learn to find the distance formula from a point to a line. Another theme of the unit is geometric proof. Throughout this unit, students apply their knowledge they learned in earlier units about similar triangles, trigonometry, and the Pythagorean theorem.
Unit 5: Is There a Difference?
In this unit, students collect data and compare different population groups to one another. In particular, they concentrate on this question: If a sample from a population differs in some respect from a sample from a different population, how reliably can you infer that the overall populations differ in that respect? They begin by making double graphs of some classroom data and explore the process of making and testing hypotheses. Students realize that there is variation even among different samples from the same population, and they see the usefulness of the concept of a null hypothesis as they examine this variation. They build on their understanding of standard deviation from the Year 1 unit The Pit and the Pendulum and learn that the chi-square statistic can give them probability of seeing differences of a certain size in samples when the populations are really the same.