This visual representation allows for a rich interpretation of these contexts (MP.2, MP.4). 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 rectangular coordinate system is also called the plane, the coordinate plane, or the Cartesian coordinate system (since it was developed by a mathematician named René Descartes.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 resulting grid is the rectangular coordinate system. Horizontal grid lines pass through the integers marked on the -axis]. Vertical grid lines pass through the integers marked on the -axis. ![]() Put the positive numbers above and the negative numbers below. Now, make a vertical number line passing through the -axis at. ![]() ![]() This horizontal number line is called the -axis. Show both positive and negative numbers as you did before, using a convenient scale unit. To create a rectangular coordinate system, start with a horizontal number line. Just as maps use a grid system to identify locations, a grid system is used in algebra to show a relationship between two variables in a rectangular coordinate system.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |