Unit Summary
In Unit 7, the final unit of the year for Grade 5, 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.
Students have coordinated numbers and distance before, namely with number lines. Students were introduced to number lines with whole-number intervals in Grade 2 and used them to solve addition and subtraction problems, helping to make the connection between quantity and distance (2.MD.5—6). Then in Grade 3, 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). 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 Grade 4, 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 Grade 5 (5.NF.1—7). 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 Grade 4 work with generating and analyzing a number or shape pattern given its rule (4.OA.3).
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). 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. 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. This visual representation allows for a rich interpretation of these contexts (MP.2, MP.4).
This work is an important part of “the progression that leads toward middle-school algebra” (6—7.RP, 6—8.EE, 8.F) (K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, p. 7). This then deeply informs students’ work in all high school courses. Thus, Grade 5 ends with additional cluster content, but that designation should not diminish its importance this year and for years to come.
Pacing: 14 instructional days (12 lessons, 1 flex day, 1 assessment day)
For guidance on adjusting the pacing for the 2021-2022 school year, see our 5th Grade Scope and Sequence Recommended Adjustments.