Grade 8 Math C1 TC Claim 1: Concepts and Procedures Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Content Domain: Expressions and Equations Target C [m]: Understand the connections between proportional relationships, lines, and linear equations. (DOK 2) Tasks for this target will ask students to graph one or more proportional relationships and connect the unit rate(s) to the context of the problem. Other tasks will ask students to apply understanding of the relationship between similar triangles and slope. ** ** For example, a task might say that starting from a point on a line, a move 3 4 to the right and one unit up puts you back on the line. If you start at a different point on the line and move to the right 8 units, how many units up do you have to move to be back on the line? Standards: 8.EE.5, 8.EE.6 DOK Target(s): 1, 2 Evidence Required: 1. The student graphs proportional relationships. 2. The student interprets the unit rate as the slope of the graph of a proportional relationship. 3. The student compares two different proportional relationships represented in different ways. 4. The student solves problems by applying the fact that similar triangles can be used to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane. 5. The student derives the equation y = mx for a line through the origin. 6. The student derives the equation y = mx + b for a line intercepting the vertical axis at b. Allowable Item Types*: SR, CR, TE Task Models: 1. SR (DOK 1, 2) Prompt Features: The student is prompted to identify the graph of a given proportional relationship. Or the student is prompted to identify the proportional relationship represented by a given graph. 1. CR (DOK 2) Prompt Features: The student is prompted to describe the
proportional relationship represented by a given graph. relationship that is represented graphically. 1. TE (DOK 2) of a given proportional relationship. 2. SR (DOK 1) Prompt Features: The student is prompted to identify the unit rate from a graph of a proportional relationship. Or the student is prompted to identify the graph that shows a given unit rate. Stimulus 1: The student is presented with a graph of a proportional relationship. Stimulus 2: The student is presented with a unit rate. 2. CR (DOK 1) Prompt Features: The student is prompted to determine the unit rate from a graph of a proportional relationship. Stimulus: The student is presented with a graph of a proportional relationship. 2. TE (DOK 2) Prompt Features: The student is prompted to create a graph that shows a given unit rate. Stimulus: The student is presented with a unit rate. 3. SR (DOK 2) Prompt Features: The student is prompted to identify one or more correct comparisons between two different proportional relationships represented in different ways. Or the student is prompted to identify a proportional relationship that compares to a given proportional relationship in a certain way. Stimulus 1: The student is presented with two proportional relationships that may be represented in a variety of ways, The proportional relationships must be different (not different representations of the same relationship) and involve different representations. Stimulus 2: The student is presented with a comparison of proportional relationships in addition to one proportional
3. CR (DOK 2) Prompt Features: The student is prompted to state how two different proportional relationships represented in different ways compare to each other. Or the student is prompted to create a proportional relationship that compares to a given proportional relationship in a certain way. Stimulus 1: The student is presented with two proportional relationships that may be represented in a variety of ways, The proportional relationships must be different (not different representations of the same relationship) and involve different representations. Stimulus 2: The student is presented with a comparison of proportional relationships in addition to one proportional 3. TE (DOK 2) Prompt Features: The student is prompted to create the graphical representation of a proportional relationship that compares to a given proportional relationship in a certain way. Stimulus: The student is presented with a comparison and a proportional relationship that may be represented in a variety of ways, The proportional relationships must be different (not different representations of the same relationship). 4. SR (DOK 2) Prompt Features: Given points on a line, the student is prompted to identify two similar triangles where the segment between a pair of the points corresponds to the hypotenuse of one of the triangles. Or the student is prompted to identify correct statements given two triangles with corresponding sides on a given line. Stimulus 1: The student is presented with points on a line in the coordinate plane. Stimulus 2: The student is presented with two triangles with corresponding sides on a given line. 5. SR (DOK 1, 2) Prompt Features: The student is prompted to identify the slope and the y-intercept of a line through the origin. Or the student is prompted to identify the equation of a line through the origin. Or the student is prompted to identify the graph of a proportional relationship that may be represented in a variety of ways. Stimulus 1: The student is presented with the graph of a proportional relationship. Stimulus 2: The student is presented with a proportional
5. CR (DOK 2) Prompt Features: The student is prompted to determine the slope and the y-intercept of a line through the origin. Or the student is prompted to write the equation of a line through the origin. Stimulus: The student is presented with the graph of a line through the origin. 5. TE (DOK 2) of a proportional relationship that may be represented in a variety of ways. Interaction: The student uses a tool that plots points and draws line segments between the points to create a figure. 6. SR (DOK 1) Prompt Features: The student is prompted to identify the slope and the y-intercept of a line with a nonzero y-intercept. Or the student is prompted to identify the equation of a line through a nonzero y-intercept. Or the student is prompted to identify the graph of a nonproportional relationship that may be represented in a variety of ways. Stimulus 1: The student is presented with the graph of a nonproportional relationship. Stimulus 2: The student is presented with a nonproportional 6. CR (DOK 2) Prompt Features: The student is prompted to determine the slope and the y-intercept of a line with a nonzero y-intercept. Or the student is prompted to determine the equation of a line through a nonzero y-intercept. Stimulus: The student is presented with the graph of a nonproportional relationship. 6. TE (DOK 2) of an equation given the equation or the slope and nonzero y- intercept of the equation. Stimulus: The student is presented with an equation with a nonzero y-intercept that may be represented in a variety of ways, Interaction: The student uses a tool that plots points and draws line segments between the points to create a figure. Allowable Stimulus Graphs, tables, equations, verbal descriptions
Materials: Allowable Disciplinary Vocabulary: Proportional relationship, slope, y-intercept, similar triangles, origin, coordinate plane Allowable Tools: Calculator Target-Specific Proportional relationships may be expressed graphically, Attributes algebraically, numerically in a table, or in a verbal description. Key Nontargeted Constructs: Accessibility Concerns: Sample Items: MAT.08.TE.1.000EE.C.200 *SR = selected-response item; CR = constructed-response item; TE = technology-enhanced item; ER = extended-response item; PT = performance task