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Graphing points on a coordinate plane4/22/2024 Then, after students have grown comfortable with the coordinate plane as a way to represent two-dimensional space, they represent real-world and mathematical situations, as well as two numerical patterns, by graphing their coordinates. After a lot of practice identifying the coordinates of points as well as plotting points given their coordinates with coordinate grids of various intervals and scales, students begin to draw lines and figures on a coordinate grid, noticing simple patterns in their coordinates. Thus, students start the unit thinking about the number line as a way to represent distance in one dimension and then see the usefulness of a perpendicular line segment to define distance in a second dimension, allowing any point in two-dimensional space to be located easily and precisely (MP.6). Students’ preparation for this unit is also connected to their extensive pattern work, beginning in Kindergarten with patterns in counting sequences (K.CC.4c) and extending through 4th grade work with generating and analyzing a number or shape pattern given its rule (4.OA.3). Then, in 4th Grade Math, students learned to add, subtract, and multiply fractions in simple cases using the number line as a representation, and they extended it to all cases, including in simple cases involving fraction division, throughout 5th grade (5.NF.1-7). For example, two fractions that were at the same point on a number line were equivalent, while a fraction that was further from 0 than another was greater. Then in 3rd Grade Math, students made number lines with fractional intervals, using them to understand the idea of equivalence and comparison of fractions, again connecting this to the idea of distance (3.NF.2). Students were introduced to number lines with whole-number intervals in 2nd grade and used them to solve addition and subtraction problems, helping to make the connection between quantity and distance (2.MD.5-6). Students have coordinated numbers and distance before, namely with number lines. The following video will show how this works on a picture of a Cartesian plane.In Unit 7, the final unit of the 5th grade course, students are introduced to the coordinate plane and use it to represent the location of objects in space, as well as to represent patterns and real-world situations. The key is to remember that the x-value is the number that corresponds with the horizontal axis and the y-value is the number that corresponds with the vertical axis. Just as x comes before y in the alphabet, x always comes before y in a coordinate point. The pair of numbers (x, y) that represent a point is called a coordinate and x and y are a coordinate pair. When we describe a place on the plane, we describe it in terms of x and y similar to how we label cells in Excel or points on a map. The horizontal axis is labeled as the x-axis and the vertical is the y-axis. On the Cartesian coordinate plane, everything is based on two number lines, one that is horizontal (it lies flat like the horizon) and one that is vertical (it goes up and down). The standard way to represent coordinate systems is on the Cartesian coordinate system. There are many examples of coordinate systems, as shown above. This lesson introduces us to a coordinate system. Introduction to Graphs: Plot Points on a Coordinate System
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