## Coordinate Pairs

###### Third Grade Lessons

**How Many Points?**- Students work with: (a) a context — distance as a function of time; (b) generating coordinates.**Human Graph I**- Students plot themselves on a Cartesian plane. Each student will get a large card with a place for an ordered pair: (x, y), where x refers to hours worked, and y refers to amount earned. The students must name the coordinate pair for the point they themselves are standing on.**Human Graph II**- Students graph the functions k x 2 $/h and k x 3 $/h. The idea is to show that for each linear function the points fall onto a straight line.**Rates vs Totals**- Students compare points on an hours/pay Cartesian space. The main challenge lies in recognizing that, although one student earned more, the other student was paid better, that is, at a higher rate of pay. They must indicate the difference in pay and the differences in amount worked.

###### Fourth Grade Lessons

**Cartesian Candy Bars I**- We compare ratios of various ordered pairs in a Cartesian grid. The initial discussion concerns the space as a whole; the task will focus on selected points and on the ratio of the dependent variable to the independent variable.**Cartesian Candy Bars II**- Children work on sharing different amounts of candy bars among different numbers of people. They compare ratios (candy bars per person) and plot points in a Cartesian grid.**Fourth Grade Assessment III**- This is a written assessment where children will be asked to interpret graphs and to interpret and determine the truth or falsehood of equations and statements that describe comparisons between quantities.**Graphing Halves and Doubles**- Children work on a problem about distance and time and compare two rates: half a meter per second and two meters per second.**Graphing Thirds and Triples**- Children work on a problem about distance and time and compare two rates: one third of a meter per second and three meters per second.**Varying Speed**- Children are asked to tell a story about a trip depicted through a graph that has varying slopes/speeds.**Varying Velocity**- Children are asked to tell a story about a trip depicted through a graph that has varying slopes/velocities.

###### Fifth Grade Lessons

**Equations and Graphs**- Students will further compare two linear functions in the context of evaluating two plans for shoveling snow. One plan has two parts: a basic charge plus a charge based on the number of square meters cleared. The other plan has no basic charge; it only charges according to the number of square meters cleared. However the per-meter charge is higher than in the other plan. Students are asked to determine the circumstances in which the bill from each plan would be the same. They then examine the graph of the two functions and discuss how equations and inequalities relate to the graph.**Phone Plans**- Students will compare two linear functions in the context of evaluating phone plans. One plan has two parts: a basic charge plus a charge based upon the number of minutes used. The other plan has no basic charge; it only charges according to the minutes used. However the per-minute charge is higher than in the other plan. Students are asked to determine the circumstances in which the monthly bill from each plan would be the same. They then examine the graph of the two functions and discuss how equations and inequalities relate to the graph.**Train Crash**- Students will compare two linear functions represented in a graph. They reason about the problem using (a) the word problem and two diagrams; (b) a graph of position vs. time; (c) a table of values (d) making expressions for each position function; and (e) solving the equation algebraically.