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Virginia SOL 2016 A.6

The student will a) determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line; write the equation of a line when given the graph of the line, two points on the line,

or the slope and a point on the line; and graph linear equations in two variables.

A.7

The student will investigate and analyze linear and quadratic function families and their characteristics both algebraically and graphically, including a) determining whether a relation is a function; domain and range; c) zeros; d) intercepts; e) values of a function for elements in its domain; and f) connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs. The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of linear and quadratic functions.

A.9

These instructional shifts, when coupled with a Math 360 and Smart Pal Curriculum , increasingly keep students on the slope. This is evident by her increasing SOL pass rates; up to 87% in 2019 for her urban high school students, in which strong math students typically enroll in Algebra I courses in middle school. Before her instructional shift, most of her students completed worksheets correct

her students ’ faces, and watched them become more engaged as their mathematical self confidence grows. Some of her students now ask if they can stay and work in her class, rather than go to their next class when the bell rings. We share these shifts with Virginia educators in the hope that all Virginia students deepen their understanding of Algebra. This activity is chosen first because the images of the water tank filling and emptying are great exam ples of positive slope and negative slope respec tively, and provide good reference points for dis cussions. The activity begins with the three acts of the Water Tank task (Meyer, 2011). The first and last act are whole class activities, while the second act is a partner activity. All the resources needed are available in the Links & Show Notes of a Vrain Waves podcast (Kalb, Peters and Meyer, 2018). Act One: The students view a short video clip of water flowing from a hose into a water tank. The class discusses the questions that arise in their minds and what they notice while watching the video. They conclude the discussion by agreeing on the question: how long will it take to fill up the water tank? Each student predicts a possible cor rect answer. Activity 1: Using Three Acts to Introduce Slope

ly, but they had difficulty relating their learning to the real world. They were unable to car ry out linear trans formations and they would demon strate conceptual misunderstandings. For example, be lieving a line with a negative slope is a line with a nega tive y - intercept. Her teaching prac tices continue to improve, so that

Figure 1: Photo by Dan Meyer (2011) used with permission

today most of her students can accurately identify sign, ratio, and units for a slope. These are skills that many Algebra I students find challenging to master. (Teuscher and Reys, 2010). In addition, she has seen the joy of intuitive understanding on

Virginia Mathematics Teacher vol. 46, no. 2

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