Major Work of the Grade Seventh Grade Stacy Wozny NCCTM Conference 2012

Research Major Work of the Grade NC Educators CCSS Progressions Smarter Balanced Assessment Consortium NC Department of Public Instruction

Proportional Relationships

7.RP.2 Recognize and represent proportional relationships between quantities Decide whether two quantities are in a proportional relationship Identify the constant of proportionality Represent proportional relationships by equations Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation

Proportional Relationships Decide whether two quantities are in a proportional relationship: –If the comparison of y to x for all points in the table represent equivalent ratios –If the graph passes through the origin (0, 0) and shows a straight line –If the equation is in the form of y = kx where k is the unit rate

Proportional Relationships Identify the constant of proportionality: –The constant of proportionality is the unit rate –From the table, look at the ratio of y to x –From the graph, look at the steepness of the graph or look for the y-value where x is one –From the equation, look for the coefficient of x

Proportional Relationships Represent proportional relationships by equations: –Students write equations from context and identify the coefficient as the unit rate which is also the constant of proportionality –The constant of proportionality is the coefficient of x in the equation y = kx.

Proportional Relationships Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation: –(4, 10) could represent 4 items that cost $10.00 where each item cost $2.50 –(0, 0) represents that 0 items purchased means 0 cost

Proportional or Not Sorting Activity There are 4 envelopes containing problems, tables, graphs, and equations. In each envelope determine which relationships are proportional. Match the problems to their corresponding tables, graphs, and equations. For the proportional relationships, determine the constant of proportionality from each representation.

Lessons for Learning Selected tasks from the DPI Week-by- Week and Strategies Document rewritten to align to CCSS

DPI Contact Information Kitty Rutherford Elementary Mathematics Consultant Johannah Maynor Secondary Mathematics Consultant Barbara Bissell K – 12 Mathematics Section Chief Susan Hart K-12 Program Assistant