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numbers and consider the meaning of pairs that are solutions and pairs that are not solutions.
Next, students move from repeatedly solving equations for one of the variables when all the other variables have been speciTed, to solving them before the variables have been speciTed and obtaining a general purpose formula for the variable of interest in terms of the others. In particular they consider linear equations in two variables that model constraints, such as budgets. This work prepares them for later units, where they start to regard one of the quantities in a constrained situation as a function of the others.
Then, students build on grade 8 work and use graphs of equations in two variables to compare two equations. They compare equations that describe a quantity that depends on another in linear fashion, and they also look at pairs of constraint equations that form a system, where you are interested in a pair of numbers that simulaneously satisTes both equations in the system.
Students then move from graphical methods to algebraic methods of solving equations. They review solving linear equations in one variable with a deeper focus on the reasoning behind the steps than they had in middle school. Then they consider solving systems of two linear equations in two variables, both by substitution and by elimination, again with a focus on the reasons why operations on systems such as adding two equations in the system produce a diWerent system with the same solution as the original.
In the Tnal lessons of the unit, students study inequalities; Trst they look at inequalities in one variable, then inequalities in two variables, and Tnally systems of inequalities in two variables. They solve inequalities and represent the solutions graphically. They consider situations that can be described by inequalities, and interpret points that are solutions and points that are not solutions in terms of the situation.
S2 Two-Variable Statistics
In grade 8, students informally constructed scatter plots and lines of Tt, noticed linear patterns, and observed associations in categorical data using two-way tables. In this unit, students build on this previous knowledge by assessing how well a linear model matches the data using residuals as well as the correlation coeVcient for best-Tt lines (found using technology). The unit also revisits two-way tables to Tnd associations in categorical data using relative frequencies.
The unit begins with categorical data arranged into two-way tables that students manipulate to examine the relative frequencies of combinations of categories. Students Tnd the relative frequencies for combinations relative to the whole data set as well as row
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