Math 3

Scope and Sequence for Integrated Math 3

Students begin the course with a study of solid geometry. They examine cross-sections of solids and make connections between cross-sections and dilations. Students also use square root and cube root graphs to illustrate the relationship between scale factors and scaled area and volume. This work is an opportunity to revisit functions and how they can be represented in a variety of ways.

This work leads students to analyze situations that are well modeled by polynomial functions before pivoting to study the structure of polynomial graphs and equations. Students do arithmetic on polynomial and rational functions and use different forms of the functions to identify asymptotes and end behavior. Students solve rational and radical equations and learn to recognize when the steps used to solve these types of equations result in solutions that are not solutions to the original equation. Students also study polynomial identities and use some key identities to establish the formula for the sum of the first terms of a geometric sequence.

Students then return to their study of exponential functions and establish that the property of growth by equal factors over equal intervals holds even when the interval has non-integer length. Students use logarithms to solve for unknown exponents, and are introduced to the number and its use in modeling continuous growth. Logarithm functions and some situations they model well are also briefly addressed.

Students learn to transform functions graphically and algebraically. In previous courses and units, students adjusted the parameters of particular types of models to fit data. In this part of the course, students consolidate and generalize this understanding. This work is useful in the study of periodic functions that comes next. Students work with the unit circle to make sense of trigonometric functions, and then students use trigonometric functions to model periodic relationships.

The last unit, on statistical inference, focuses on analyzing experimental data modeled by normal distributions. Students learn to use sampling and simulations to account for variability in data and estimate population mean, margin of error, and proportions. Students develop skepticism about news stories that summarize data inappropriately.