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or column relative frequencies to look at subgroups within categories. The row and column relative frequency tables are ultimately used to Tnd evidence whether any associations are present in the data.
The unit then transitions to bivariate numerical data which are visualized using scatter plots and lines of best Tt. Students use technology to compute the lines of best Tt and observe how well the linear models match the data. Residuals and correlation coeVcients are used to quantify the goodness of Tt for linear models.
The unit closes with an exploration of the diWerence between correlation and causal relationships as well as an opportunity to apply their learning to anthropology and sports.
F1 Functions
In grade 8, students started to work with functions. They learned that a function is a rule that assigns to each input exactly one output. They represented functions in diWerent ways, with verbal descriptions, algebraic expressions, graphs, and tables. They used functions to model relationships between quantities, in particular linear relationships. In this unit, students build on this previous work to expand their understanding of functions and to model a wider variety of mathematical and real-world situations.
In the Trst four lessons, students recall the deTnition of a function and use graphs to represent a variety of situations. They are then introduced to function notation and use it as an eVcient tool to communicate precisely.
Next, students are introduced to the domain and range of a function. They Tnd both, given the context of a situation or by examining an equation. They study piecewise-deTned functions. This type of function opens up a variety of new situations that can be modeled with mathematics, for example parking charges that increase every half hour or membership fees that Trst grow linearly until a maximum amount is reached and then stays constant. The absolute value function can also be written as a piecewise function and it allows us to describe ideas like absolute error or distance from a point. The distinct V-shape of the absolute value function graph is convenient for beginning to
explore transformations of graphs. Students connect horizontal and vertical translations of the graph with changes to the equation of the represented function.
Building on some preliminary work with graphing earlier in the unit, students then spend four lessons focusing on connecting features of graphs with features of situations. Graphs are a powerful tool to visualize and compare situations. Students create graphs from verbal descriptions and, conversely, they tell a story from a graph. They learn about
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Course Guide Algebra