The Mathematics Common Core Toolbox – PRACTICE TEST ITEMS HIGH SCHOOL
The CCSSM requires that students write geometric sequences both recursively and with an explicit formula and use the two representations to model situations. In this task, students consider the use of one or more representations to solve a real-world problem and choose the type of sequence to represent a situation.
Students are expected to make sense of the contextual situation, extract and use mathematics to model the situation and answer mathematical questions, and then return to solve the problem within the context.
Golf Balls in Water
This three-part task requires students to use mathematical modeling. They make sense of the contextual situation, extract and use mathematics to model the situation and answer mathematical questions, and then return to solve the problem within the context.
Isabella’s Credit Card
The CCSSM calls for students to interpret key features of a quantitative relationship from tables with respect to a context as well as to determine a recursive process or describe steps for calculation from a context.
The page that students see resembles a spreadsheet, but it does not function as a spreadsheet.
In this task, students analyze the situation (rabbit population growth) and create a mathematical model that represents it. Students are then presented with a second rabbit population that is slightly different and asked to compare the models for the two populations. This requires students to identify which function parameters and key features of the graph will change based on the adjustment in context. Students then use the two models together to answer mathematical questions.
This task asks students to challenge their traditional way of thinking about exponential models, including starting with the end result and going backward to consider a model that could generate this result.
Transforming Graphs of Quadratic Functions
The high school CCSSM calls for students to experiment with building new functions from existing functions and explain the effects on the graphs of the functions using technology. The understanding of functions through transformations is a relatively new approach in many Algebra classrooms. The notion that parameters have a consistent effect on graphs across function types gives structure and regularity to students’ study of functions throughout their mathematical careers.
While the technology is not essential to solving the problem, it provides a support for students to interact with function transformations and has significant implications for future item development—a next iteration of this task could ask students to manipulate the graph using the sliders and submit their answers through the interactive tool instead of filling in the blanks.