Eighth Grade Mathematics
Representing, applying, and analyzing proportional relationships
Students extend their understanding of proportionality to include representations on a coordinate plane and applications, including slopes of lines. They contrast proportional relationships with relationships that are not proportional.
- Generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation
- Use of algebraic representation to show scale factor (more formal language)
- Use of similar right triangles in exploring slope
- Graph proportional relationships interpreting the unit rate with slope
- Use of tables or graphs to determine rate of change and y-intercept
- Represent linear proportional and non-proportional situations with tables graphs and equations in the forms of y=kx and y=mx+b
- Use of the term bivariate sets of data as opposed to scatterplots
- Use a trend line to approximate the linear relationship between bivariate sets of data (aka line of best fit)
- Solve problems using direct variation
- Distinguish between proportional and non-proportional relations using y=kx or y=mx+b
- Identify functions using ordered pairs, tables, mappings, and graphs
- Write an equation in the form of y=mx+b
Making inferences from dataStudents use representations of association, center, and variation to make inferences from data.
- Construct a scatterplot and describe the data to address questions of association such as linear, nonlinear, and no association between bivariate data.
- Determine the mean absolute deviation and the quantity as a measure of the average distance data are from the mean using a data set no more
Using expressions and equations to describe relationships, including the Pythagorean TheoremStudents select and use expressions and equations to represent and solve problems involving rational numbers. Students use geometric properties, including the Pythagorean Theorem, to solve problems.
- Determine the distance between two points on a coordinate plane using the Pythagorean Theorem
- Write, model, and solve one-variable equations or inequalities (from real-world situations) with variables on both sides using rational number coefficients and constants
- Use equations to establish facts about angle sum and exterior angles of triangles as well as angles created when parallel lines are cut by a transversal
- Identify solution (x,y) to two linear equations (system of equations) from the intersection of graphed equations